Watermarking, Compression, and Their Combination for 3-D ...
Transcript of Watermarking, Compression, and Their Combination for 3-D ...
Numéro d’ordre : 2007-ISAL-0099 Année 2007
THÈSE
présentée devant
L’Institut National des Sciences Appliquées de Lyon et
Yeungnam University
pour obtenir
LE GRADE DE DOCTEUR
ÉCOLE DOCTORALE : ÉLECTRONIQUE, ÉLECTROTECHNIQUE, AUTOMATIQUE FORMATION DOCTORALE : IMAGES ET SYSTÈMES
par
Jae-Won CHO
Watermarking, Compression, and Their Combination
for 3-D Triangular Meshes
Soutenue le 7 décembre 2007
Jury :
M. Marc ANTONINI DR CNRS Rapporteur externe M. Ki-Ryong KWON Professeur Rapporteur externe Mme. Françoise PRETEUX Professeur Examinatrice M. Hyun-Soo KANG Professeur Examinateur M. Kook-Yeol YOO Professeur Examinateur Mme. Isabelle MAGNIN DR Inserm Président du jury M. Ho-Youl JUNG Professeur Co-directeur de thèse M. Rémy PROST Professeur Co-directeur de thèse
INSA Direction de la Recherche - Ecoles Doctorales 2007 SIGLE ECOLE DOCTORALE NOM ET COORDONNEES DU RESPONSABLE
CHIMIE
CHIMIE DE LYON http://sakura.cpe.fr/ED206 M. Jean Marc LANCELIN
Insa : R. GOURDON
M. Jean Marc LANCELIN Université Claude Bernard Lyon 1 Bât CPE 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cedex Tél : 04.72.43 13 95 Fax : [email protected]
E.E.A.
ELECTRONIQUE, ELECTROTECHNIQUE, AUTOMATIQUEhttp://www.insa-lyon.fr/eea M. Alain NICOLAS Insa : D. BARBIER [email protected] Secrétariat : M. LABOUNE AM. 64.43 – Fax : 64.54
M. Alain NICOLAS Ecole Centrale de Lyon Bâtiment H9 36 avenue Guy de Collongue 69134 ECULLY Tél : 04.72.18 60 97 Fax : 04 78 43 37 17 [email protected] Secrétariat : M.C. HAVGOUDOUKIAN
E2M2
EVOLUTION, ECOSYSTEME, MICROBIOLOGIE, MODELISATION http://biomserv.univ-lyon1.fr/E2M2 M. Jean-Pierre FLANDROIS Insa : S. GRENIER
M. Jean-Pierre FLANDROIS CNRS UMR 5558 Université Claude Bernard Lyon 1 Bât G. Mendel 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cédex Tél : 04.26 23 59 50 Fax 04 26 23 59 49 06 07 53 89 13 [email protected]
EDIIS
INFORMATIQUE ET INFORMATION POUR LA SOCIETE http://ediis.univ-lyon1.fr M. Alain MILLE Secrétariat : I. BUISSON
M. Alain MILLE Université Claude Bernard Lyon 1 LIRIS - EDIIS Bâtiment Nautibus 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cedex Tél : 04.72. 44 82 94 Fax 04 72 44 80 53 [email protected] - [email protected]
EDISS
INTERDISCIPLINAIRE SCIENCES-SANTE M. Didier REVEL Insa : M. LAGARDE
M. Didier REVEL Hôpital Cardiologique de Lyon Bâtiment Central 28 Avenue Doyen Lépine 69500 BRON Tél : 04.72.35 72 32 Fax : [email protected]
MATERIAUX DE LYON M. Jean Marc PELLETIER Secrétariat : C. BERNAVON 83.85
M. Jean Marc PELLETIER INSA de Lyon MATEIS Bâtiment Blaise Pascal 7 avenue Jean Capelle 69621 VILLEURBANNE Cédex Tél : 04.72.43 83 18 Fax 04 72 43 85 28 [email protected]
Math IF
MATHEMATIQUES ET INFORMATIQUE FONDAMENTALE M. Pascal KOIRAN Insa : G. BAYADA
M.Pascal KOIRAN Ecole Normale Supérieure de Lyon 46 allée d’Italie 69364 LYON Cédex 07 Tél : 04.72.72 84 81 Fax : 04 72 72 89 69 [email protected] Secrétariat : Fatine Latif - [email protected]
MEGA
MECANIQUE, ENERGETIQUE, GENIE CIVIL, ACOUSTIQUE M. Jean Louis GUYADER Secrétariat : M. LABOUNE PM : 71.70 –Fax : 87.12
M. Jean Louis GUYADER INSA de Lyon Laboratoire de Vibrations et Acoustique Bâtiment Antoine de Saint Exupéry 25 bis avenue Jean Capelle 69621 VILLEURBANNE Cedex Tél :04.72.18.71.70 Fax : 04 72 18 87 12 [email protected]
SSED
SCIENCES DES SOCIETES, DE L’ENVIRONNEMENT ET DU DROIT Mme Claude-Isabelle BRELOT Insa : J.Y. TOUSSAINT
Mme Claude-Isabelle BRELOT Université Lyon 2 86 rue Pasteur 69365 LYON Cedex 07 Tél : 04.78.69.72.76 Fax : 04.37.28.04.48 [email protected]
Abstract
This dissertation deals with watermarking, compression, and their combination for three-
dimensional (3-D) triangular meshes. We first propose algorithms individually in order to
watermark static meshes and to compress mesh sequences. Finally we derive a combined
system for joint compression and watermarking.
Firstly, we propose two oblivious (or blind) watermarking techniques for 3-D static
meshes. They mainly use statistical features of vertex norms to embed watermark; the
first proposed method shifts the mean value of the distribution and the second proposed
method changes its variance. Histogram mapping functions are introduced to modify
the distribution. These mapping functions are devised in order to reduce the visibility
of watermark as much as possible. Since the statistical features of vertex norms are
less sensitive to signal alterations, the proposed methods can be robust against general
attacks. In addition, our methods employ a blind watermark detection scheme, which can
extract the watermark without referring to the original mesh model. Through simulations,
we demonstrate that the proposed approaches are robust against several attacks such as
adding binary noise, smoothing, uniform quantization, simplification, sub-division, vertex
re-ordering, and similarity transform.
Next, we present two compression methods for 3-D mesh sequences with constant
connectivity. The proposed methods mainly use an exact integer spatial wavelet analy-
sis (SWA) technique to efficiently decorrelate the spatial coherence of each mesh frame
and also to promptly transmit mesh frames with various spatial resolutions under differ-
ent bandwidth conditions (spatial scalability). To reduce the temporal redundancy, the
first proposed method applies multi-order differential coding (MDC) to the 1-D temporal
sequences after SWA of each mesh frame. MDC determines the optimal order of the dif-
ferential coder by analyzing the variance of prediction errors. Compared to the first-order
differential coding (FDC) scheme, the method can improve the compression performance.
The second proposed method applies temporal wavelet analysis (TWA) to the 1-D tem-
poral sequences. In particular, this method offers spatiotemporal multi-resolution coding.
Through simulations, we prove that our approaches enable efficient lossy-to-lossless com-
pression for 3-D mesh sequences.
Finally, we present a joint watermarking and compression method for 3-D mesh se-
quences. Our approach is based on the proposed compression method using SWA and
TWA. For robust and invisible watermark, a new watermarking technique derived from our
second watermarking scheme is applied to the intermediate step of the compression process.
Watermark embedding is carried out by the histogram mapping function which modifies
the variance of spatiotemporal wavelet coefficients belonging to specific sub-bands. The
hidden watermark is robust against several attacks such as additive binary noise, smooth-
ing, and frame dropping, because the employed watermark carrier is a statistical feature
of spatiotemporal wavelet coefficients. Through simulations, we prove that our approach
enables to efficiently compress 3-D mesh sequences and to strictly protect its ownership
in a single framework.
Keywords
Watermarking, compression, joint compression and watermarking, 3-D static meshes, 3-D
mesh sequences, and constant connectivity
Resume
Cette these contribue au tatouage, a la compression et a la combinaison de ces deux
techniques pour des objets 3-D representes par leur maillage surfacique. Dans un premier
temps, nous traitons individuellement ces deux problemes, puis, dans un deuxieme temps
nous les combinons.
Dans une premiere partie, nous proposons deux methodes de tatouage aveugle pour des
maillages statiques 3-D. Ces propositions utilisent les proprietes statistiques, de la norme
des vecteurs associes aux coordonnees des sommets, pour incorporer le tatouage. Une
premiere methode modifie la moyenne de la distribution de la norme des sommets et une
deuxieme methode change sa variance. Ces operations sont effectuees par transformations
non lineaires de la distribution de la norme des sommets (transformations d’histogramme).
Ces transformations sont concues dans le but de reduire la visibilite du tatouage. Comme
les proprietes statistiques des normes des sommets sont peu sensibles a des modifications
geometriques ou topologiques du maillage, nos propositions sont robustes aux attaques.
De plus, nos methodes emploient une extraction aveugle du tatouage, c’est a dire sans le
maillage original. Nous demontrons, par des simulations, que nos approches sont robustes
aux attaques telles que: l’addition de bruit binaire, le lissage, la quantification uniforme,
la simplification, la subdivision, le reordonnancement des sommets, et des transformations
affines.
Dans une deuxieme partie, nous proposons des algorithmes de compression des sequenc-
es de maillages 3-D a connectivite constante. Ces propositions utilisent une analyse
en ondelettes spatiales pour decorreler la geometrie des trames et pour les transmettre
progressivement, avec une resolution croissante (echelonnage spatial) afin de permettre
une adaptation a la bande passante disponible. A chaque niveau de resolution du mail-
lage des trames on considere que les coordonnees d’un sommet sont trois signaux (1D)
temporels independants. Dans une premiere methode nous appliquons a ces signaux un
codage differentiel, avec un ordre multiple, afin de reduire la redondance temporelle. Nous
determinons l’ordre optimal de prediction par celui qui conduit a la variance de l’erreur de
prediction la plus faible. En effet, nous montrons que l’entropie de l’erreur de prediction
decroıt lorsque sa variance decroıt. Dans une deuxieme methode nous appliquons une
analyse en ondelettes temporelles a ces signaux 1-D. Cette methode permet un codage
multi-resolution dans l’espace et le temps. Nous montrons, experimentalement, que nos
approches permettent, non seulement la compression avec pertes, mais aussi la compres-
sion sans pertes des sequences de maillages 3-D.
Finalement, nous presentons une methode combinant la compression et de tatouage
des sequences de maillages 3-D. Cette proposition s’appuie sur notre deuxieme methode de
compression qui utilise les analyses en ondelettes spatiales et temporelles. Afin d’obtenir un
tatouage robuste et invisible, une nouvelle approche, qui decoule de la deuxieme methode
de tatouage, est appliquee a l’etape intermediaire de la methode de compression. La vari-
ance des coefficients d’ondelettes spatio-temporelles qui appartiennent a certaines sous
bandes est modifiee par transformation d’histogramme. Le tatouage est robuste aux at-
taques telles que: l’addition de bruit binaire, le lissage, la suppression de trames. Ces
performances sont dues aux proprietes statistiques des coefficients d’ondelettes spatio-
temporelles employees comme porteur du tatouage. Par les simulations, nous montrons
que notre approche permet de compresser efficacement les sequences de maillages 3-D,
tout en protegeant leur proprietaire de copies frauduleuses, avec une methode combinant
compression et tatouage.
Mots cles
Tatouage, compression, compression et tatouage combines, maillages statiques 3-D, seque-
nces de maillages 3-D et connectivite constante
요약문 본 학위 논문은 3차원 삼각 메쉬 데이터(3-D triangular meshes)를 위한 워터마킹(watermarking), 압축(compression), 그리고 이들간의 통합 시스템을 다룬다. 워터마킹 및
압축 통합 시스템을 본 학위 논문의 최종 목표로 하여 각각의 연구 주제를 고찰한 뒤,
두 연구 주제로부터 하나의 통합된 시스템을 도출해 내기로 한다.
먼저, 3차원 정지 메쉬(3-D static mesh)를 위한 두 가지 블라인드(blind) 워터마킹 기법을 제안한다. 제안하는 방법은 워터마크(watermark)를 삽입하기 위해 통계적 특성(statistical feature)을 이용한다. 즉, 제안하는 첫 번째 방법은 확률 분포(probability
distribution)의 평균 값(mean value)을, 두 번째 방법은 확률 분포의 분산(variance)을 수정함으로써 워터마크를 삽입한다. 이를 위해 히스토그램 대응 함수(histogram mapping
function)가 워터마크의 비지각성(invisibility)을 극대화하기 위해 고안되었다. 일반적으로 좌표 벡터(vertex norm)의 통계적 특성은 신호 변형에 둔감하기 때문에 제안하는 방법은 다양한 신호처리 공격에 강인하다. 게다가 제안하는 방법은 원본 신호의 참조 없이 삽입된 워터마크 검출(watermark extraction)이 가능한 블라인드 기법이다. 모의 실험을 통하여 제안하는 방법이 이진 잡음 첨가(adding binary noise), 스무딩(smoothing), 균일 양자화(uniform quantization), 간략화(simplification), 세분화(subdivision), 좌표 재배열(vertex re-ordering), 유사 변환(similarity transform)과 같은 다양한 공격에 강인함을 증명한다.
다음으로 고정된 연결 정보(constant connectivity)를 가지는 3차원 메쉬 시퀀스(3-D
mesh sequence)를 위한 두 가지 압축 기법을 제안한다. 제안하는 방법은 효율적으로 각각의 메쉬 프레임의 공간 중복성(spatial redundancy)을 제거할 수 있을 뿐만 아니라 시시각각 변화하는 네트워크 환경에 대비하여 최고 해상도(highest resolution)로부터 최저
해상도(lowest resolution)까지 다양한 공간 해상도(spatial multi-resolutions)를 가지는 메쉬
프레임(mesh frame)을 전송하는 것이 가능한 정수형 공간 웨이블릿 분해 기법(exact
integer spatial wavelet analysis)을 주로 사용한다. 시간 중복성(temporal redundancy)을 제거하기 위한 방법으로서 제안하는 첫 번째 방법은 공간 웨이블릿 분해 후 얻어지는 1차원 신호 열(1-D temporal sequence)에 다차 차분 부호화 기법(multi-order differential coding
scheme)을 적용한다. 이 다차 차분 부호화 기법은 예측 오차(prediction error)의 분산을
분석함으로써 차분 부호화기의 최적 차수(optimal order)를 구할 수 있으며, 1차 차분 부호화기(first-order differential coder)와 비교 했을 때 압축 효율을 높일 수 있다. 제안하는
두 번째 방법은 공간 웨이블릿 분해 후 얻어지는 1차원 신호 열에 시간 축 웨이블릿
분해 기법(temporal wavelet analysis scheme)을 적용한다. 특히 이 방법은 시/공간 다 해상도(spatiotemporal multi-resolutions) 전송을 가능하게 한다. 모의 실험을 통하여 제안된
두 가지 방법이 손실 및 무손실 압축(lossy-to-lossless)이 하나의 단일 프레임워크에서
이루어질 수 있음을 증명한다.
마지막으로 3차원 메쉬 시퀀스를 위한 워터마킹 및 압축 통합 시스템을 제안한다.
제안하는 방법은 앞서 제안된 시/공간 웨이블릿 변환을 이용한 압축 기법에 기반한다.
삽입될 워터마크의 강인성 및 비지각성을 위해서 앞서 제안된 3차원 정지 메쉬 워터마킹 기법으로부터 확장된 새로운 방법이 압축의 중간 과정에 적용된다. 이 때, 워터마크 정보는 히스토그램 대응 함수를 이용하여 특정 부대역(sub-band)에 속하는 시/공간 웨이블릿 계수의 분산을 수정함으로써 삽입된다. 제안된 방법은 시/공간 웨이블릿
계수의 통계적 특성을 이용하기 때문에 삽입된 워터마크는 이진 잡음 첨가, 스무딩,
프레임 제거(frame dropping) 등과 같은 다양한 공격에 강인하다. 모의 실험을 통하여
제안된 방법이 하나의 통합된 시스템에서 3차원 메쉬 시퀀스를 위한 효율적인 압축
및 저작권 보호가 가능함을 입증한다.
핵심어 워터마킹, 압축, 압축 및 워터마킹의 통합 시스템, 3차원 정지 메쉬, 3차원 메쉬 시퀀스, 고
정 연결 정보
Contents
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Watermarking for 3-D Static Meshes 5
2.1 Introduction and State of the Arts . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Proposed Watermarking Methods . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 The Proposed Watermarkig Method Using Mean Modification . . . 12
2.2.2 The Proposed Watermarking Method Using Variance Modification . 17
2.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Attack Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2 Parameters for Robustness . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.3 ROC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4 Summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Compression for 3-D Mesh Sequences 43
3.1 Introduction and State of the Arts . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Wavelet-based Multi-resolution Analysis . . . . . . . . . . . . . . . . . . . . 47
3.2.1 SWA (Spatial Wavelet Analysis) and Its Synthesis . . . . . . . . . . 47
3.2.2 TWA (Temporal Wavelet Analysis) and Its Synthesis . . . . . . . . . 50
3.3 Proposed Compression Methods . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.1 The Proposed Compression Method Using SWA and MDC . . . . . 52
ii CONTENTS
3.3.2 The Proposed Compression Method Using SWA and TWA . . . . . 58
3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.1 SWA+MDC Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4.2 SWA+TWA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5 Summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4 Joint Watermarking and Compression 73
4.1 Introduction and State of the Arts . . . . . . . . . . . . . . . . . . . . . . . 74
4.2 Proposed Joint Watermarking and Compression Method . . . . . . . . . . . 78
4.2.1 Encoding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.2 Decoding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.1 Attack Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.2 Parameters for Robustness . . . . . . . . . . . . . . . . . . . . . . . 98
4.4 Summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5 Conclusions and Perspectives 103
A Histogram Mapping Function 107
A.1 For Shifting Mean Value of Uniform Distribution . . . . . . . . . . . . . . . 107
A.2 For Changing Variance of Uniform Distribution . . . . . . . . . . . . . . . . 109
A.3 For Changing Variance of Laplacian Distribution . . . . . . . . . . . . . . . 110
B Estimation of Entropy 113
C Finding the Optimal Order 115
Bibliography 117
List of Figures
2.1 Proposed watermarking method by shifting the mean of the distribution . . 10
2.2 Proposed watermarking method by changing the variance of the distribution 10
2.3 Distribution of vertex norms obtained from the bunny model, where dashed
vertical lines indicate the border of each bin. . . . . . . . . . . . . . . . . . 12
2.4 (a) Block diagrams of the watermark embedding for the proposed water-
marking method shifting the mean value of vertex norms (continued on next
page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 (b) Block diagrams of the watermark extraction for the proposed water-
marking method shifting the mean value of vertex norms (continued from
previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 (a) Block diagrams of the watermark embedding for the proposed water-
marking method changing the variance of vertex norms (continued on next
page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 (b) Block diagrams of the watermark extraction for the proposed water-
marking method changing the variance of vertex norms (continued from
previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Original mesh models (a) buddha, (b) bunny, (c) dragon (continued on next
page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 (d) cow, (e) face, and (f) fandisk (continued from previous page) . . . . . . 25
2.7 Watermarked mesh models, where (a)-(f) are watermarked by mean mod-
ification method and (g)-(l) by variance modification method. (continued
on next page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
iv LIST OF FIGURES
2.7 Watermarked mesh models, where (a)-(f) are watermarked by mean mod-
ification method and (g)-(l) by variance modification method. (continued
from previous page and contined on next page) . . . . . . . . . . . . . . . . 27
2.7 Watermarked mesh models, where (a)-(f) are watermarked by mean mod-
ification method and (g)-(l) by variance modification method. (continued
from previous page and contined on next page) . . . . . . . . . . . . . . . . 28
2.7 Watermarked mesh models, where (a)-(f) are watermarked by mean mod-
ification method and (g)-(l) by variance modification method. (continued
from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.8 Bunny model watermarked by mean modification method and attacked by
(a) multiplicative binary noise with error ratio of 0.5%, (b) 7bits/coordinate
quantization, (c) smoothing with iteration of 50 and relaxation of 0.03 and
(d) simplification with reducing 90.65% of vertices . . . . . . . . . . . . . . 30
2.9 (a) Relationship between the strength factor and the correlation. As an
example, a smoothing attack with iteration 30 and relaxation 0.03 is applied.
(continued on next page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.9 (b) Relationship between the number of bins and the correlation. As an
example, a smoothing attack with iteration 30 and relaxation 0.03 is applied.
(continued from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.10 ROC curves of bunny model (a) watermarked by mean modification method
and attacked by multiplicative noise, (b) watermarked by mean modification
method and attacked by simplification (continued on next page) . . . . . . 41
2.10 (c) watermarked by variance modification method and attacked by multi-
plicative noise, and (d) watermarked by variance modification method and
attacked by simplification (continued from previous page) . . . . . . . . . . 42
3.1 (a) SWA (Spatial Wavelet Analysis) and (b) its synthesis processes . . . . . 48
3.2 2-channel (a) TWA (Temporal Wavelet Analysis) and (b) its synthesis pro-
cesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
LIST OF FIGURES v
3.3 The encoding process of the proposed method using SWA and MDC tech-
niques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Variances (σ2) of prediction errors of Face model according to different
orders (m) of MDC. The x-coordinate of the first base mesh vertex sequence
of this model is designated for a practical example. . . . . . . . . . . . . . . 56
3.5 Prediction error distributions of Face model in terms of (a) FDC and (b)
MDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6 The encoding process of the proposed method using SWA and TWA tech-
niques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.7 Distributions of wavelet coefficients of the x-axis of the first base mesh
sequence of Face model using (a) Haar (2/2 tap) filters, (b) Le Gall (5/3
tap) filters (continued on next page) . . . . . . . . . . . . . . . . . . . . . . 60
3.7 (c) Daubechies (9/7 tap) filters (continued from previous page) . . . . . . . 61
3.8 Original mesh sequences, (a)-(c) Cow models (continued on next page) . . . 63
3.8 (d)-(f) Face models (continued from previous page) . . . . . . . . . . . . . . 64
3.9 Distributions of practical optimal orders of the differential coder in SWA+MDC
for (a) Cow and (b) Face models . . . . . . . . . . . . . . . . . . . . . . . . 65
3.10 R-D curves of SWA, SWA+FDC and SWA+MDC methods for (a) Cow and
(b) Face models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.11 R-D curves of SWA+TWA method at different spatial resolutions where
three temporal wavelet filter-banks are used for (a) Cow and (b) Face models 70
3.12 R-D curves of SWA+TWA method at different spatiotemporal resolutions,
where the temporal sequences are decomposed into five levels using Daubechies
filter banks for (a) Cow and (b) Face models . . . . . . . . . . . . . . . . . 71
4.1 Proposed watermarking method by changing the variances of high frequency
sub-band signal: (a) distributions of two subsets, A and B, of high fre-
quency sub-band signal, the modified distributions of the two subsets for
embedding watermark (b) +1 and (c) −1, where, we assume that the initial
two subsets have the same Laplacian distributions for the simple illustration. 80
vi LIST OF FIGURES
4.2 The encoding process of the proposed joint watermarking and compression
scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 The watermark embedding process . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 The decoding process of the proposed joint watermarking and compression
scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5 The watermark extraction process . . . . . . . . . . . . . . . . . . . . . . . 88
4.6 Watermarked mesh sequences, (a)-(c) Cow models (continued on next page) 91
4.6 (d)-(f) Face models (continued from previous page) . . . . . . . . . . . . . . 92
4.7 Cow model attacked by (a)-(c) multiplicative binary noise with error ratio
of 1% (continued on next page) . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.7 (d)-(f) 6bits/coordinate quantization (continued from previous page and
continued on next page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.7 (g)-(i) smoothing with iteration of 120 and relaxation of 0.03 (continued
from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
A.1 Histogram mapping function, Y = Xk, for different parameters of k . . . . 108
A.2 Expectation of the output random variable via histogram mapping function
with different k, assuming that the input random variable is uniformly
distributed over unit range [0, 1]. . . . . . . . . . . . . . . . . . . . . . . . . 109
A.3 Histogram mapping function, sign (X) |X|k, for different parameter of k . . 110
A.4 Variance of the output random variable via histogram mapping function
with different k, assuming that the input random variable is uniformly
distributed over the normalized range [−1, 1]. . . . . . . . . . . . . . . . . . 111
A.5 Second moment (variance) of the output random variable via histogram
mapping function with different k, assuming that the input variable has
Laplacian distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
B.1 Relationship between the entropy and the variance according to different σ 114
List of Tables
2.1 Evaluation of watermarked meshes when no attack . . . . . . . . . . . . . . 23
2.2 Evaluation of robustness against multiplicative binary noise attacks . . . . . 32
2.3 Evaluation of robustness against uniform quantization attacks . . . . . . . . 33
2.4 Evaluation of robustness against smoothing attacks . . . . . . . . . . . . . . 34
2.5 Evaluation of robustness against simplification attacks (continued on next
page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 (Continued from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6 Evaluation of robustness against 1:4 sub-division attacks . . . . . . . . . . . 36
3.1 The lossless compression results of SWA+MDC method compared with
SWA and SWA+FDC methods . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2 The lossless compression results of SWA+TWA method compared with
TWA scheme according to temporal wavelet decomposition levels and three
temporal wavelet filter-banks: Haar (2/2 tap), Le Gall (5/3 tap) and Daubechies
(9/7 tap) filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.1 Parameters used in the simulations . . . . . . . . . . . . . . . . . . . . . . . 90
4.2 Evaluation of compression performance and watermark robustness when no
attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3 Evaluation of robustness against intra-frame attacks . . . . . . . . . . . . . 98
4.4 Adjusted parameters to improve robustness (Face) . . . . . . . . . . . . . . 99
4.5 Evaluation of compression performance and watermark robustness in terms
of different threshold α and different β (When no attack) . . . . . . . . . . 99
viii LIST OF TABLES
4.6 Evaluation of robustness according to different threshold α and different β
(After intra-frame attacks applied to Face) . . . . . . . . . . . . . . . . . . . 100
Chapter 1
Introduction
1.1 Background
The information revolution has more and more led to convenient and interesting lives since
the end of the twentieth century. We are not unfamiliar with many digital devices, such as
laptop, PDA, MP3 player, and portable multimedia player, any longer. Wherever we are,
the Internet connected to the World Wide Web enables to know what happened on the
whole parts of the globe. DMB (Digital Multimedia Broadcasting) service providers, from
the last three or four years, have already offered live broadcasts with various channels via
digital personal devices such as mobile phone and PDA at every where and time that we
want. In the near future, human beings would live in the Ubiquitous environment as we
have seen in a new prospective life model such as Cool Town presented by the Hewlett-
Packard Corporation. All electronic and mechanical equipments would be linked together
by an integrated network, and therefore someone who lives in the city might access, control
and communicate with another terminal wherever and whenever he/she wants.
With these remarkable breakthroughs of the digital information and the network tech-
nologies, the requirements of high quality multimedia data have gradually become con-
spicuous and concurrently encouraged the investigation of data compression in order to
compactly store and to promptly transmit a huge source data. Several international stan-
dardization working groups such as JPEG (Joint Photographic Experts Group) 1 and
1JPEG is a collaboration between ISO (International Organization for Standardization) standard and
2 Introduction
MPEG (Moving Picture Experts Group) 2, since 1980’s, have devoted commendable en-
deavors to establish competent frameworks for compression and transmission of audios,
2-D still images, 2-D videos and 3-D meshes.
Such facilities of the information and communication technologies, however, have not
always done make salutary results acting up to the social morality, owing to the essen-
tial characteristics: digitalized data could be exactly copied, easily modified and illegally
distributed without any effort. Besides, the World Wide Web fundamentally offers infor-
mation sharing services to end users. For those reasons, over the last decade, illegal use of
copyrighted data has been posed a serious problem on digital industrial fields. Many peer
to peer systems such as Napster and eDonkey have instigated to share copyrighted digital
data, and caused great financial damages of ownership holders. As a part of exploring
ways toward copyright protection, very recently, watermarking has been highlighted as a
good way out. It supplies information hiding scheme, and also enables to trace routes
of illegal distribution. Some international standards and associations such as JPEG2000
part 8 - JPSEC 3 and SDMI (Secure Digital Music Initiative) 4, from the last few years,
have tried to provide systematic mechanisms for ownership protection.
Until now, most studies on watermarking and compression have proceeded with each
separate framework. It is caused by the fact that watermarking within compressed bit-
stream could seriously affect the auditory or visual quality of decompressed data and
conversely that lossy compression based on quantization might interfere with the ownership
assertion of watermarked data. Nevertheless, it is clear that these two research topics
CCITT (International Telegraph and Telephone Consultative Committee) recommendation. It is the first
international standard for 2-D still images represented as grayscale and color. The outline of the standard-
ization has been considerably summarized in [Wallace, 1992].2MPEG was established by the joint ISO and IEC (International Electrotechnical Commission) technical
committee in order to develop efficient coding standards of moving pictures, associated audio and their
combination. An overview of the principal issues has been substantially recapitulated in [Sikora, 1997].3JPEG2000 is a wavelet transform based image coding standard expanded from JPEG. The part 8,
so-called JPSEC, of the standard provides security maintenance methodologies including security of trans-
action, protection of contents and so on. An overview of JPSEC has been quite obviously summarized
in [F. Dufaux, 2004].4SDMI is an international forum formed in 1998 for the protection of digital music resources focused
on on-line delivering.
1.2 Main Contributions 3
should be simultaneously treated for prompt and also secure transmission of multimedia
data over network. Although some parts of international coding standards, which were
previously mentioned, have strived to develop a combined system of two technologies,
researches on joint watermarking and compression are still in its early stages. Therefore,
it should be expedited to investigate this undeveloped research area.
1.2 Main Contributions
This dissertation deals with watermarking, compression, and their combination for three
dimensional (3-D) data. 3-D data, a new type of multimedia data, has been more and more
widely used in many applications including on/off-line video games, animation movies,
medical images, and so on. Triangular meshes and their temporal sequences have been
regarded as very appropriate means for efficient representation of 3-D objects. However,
since they require enormous costs in order to be stored and to be transmitted as well
as to be created, they should be efficiently compressed and strictly protected. Pursuing
to design a joint watermarking and compression scheme for 3-D mesh sequences as the
final goal of this dissertation, we primarily discuss two individual research topics and then
derive a combined system from both of them.
Watermarking We propose two watermarking schemes for 3-D static meshes
using distribution of vertex norms. The probability distribution of vertex norms would
not be sensitive to intentional or non-intentional alterations. Therefore, the first and
second proposed methods embed copyright owner’s information, so-called watermark, by
means of modifying mean or variance of vertex norms, respectively. The mean or variance,
in our methods, is changed into desired values via histogram mapping functions which
are newly designed in this dissertation. Both methods could be robust against general
attacks. Besides, they employ oblivious schemes which do not require the original data at
the watermark extraction side.
Compression We propose two compression methods for 3-D mesh sequences.
Our approaches basically utilize a SWA (Spatial Wavelet Analysis) not only to efficiently
de-correlate spatial coherence but also to transmit 3-D mesh sequences with various spa-
4 Introduction
tial resolutions. The first and second methods reduce temporal redundancy by adopting
a MDC (Multi-order Differential Coding) and TWA (Temporal Wavelet Analysis) tech-
niques, respectively. The first proposed method can improve compression performance of
FDC (the First-order Differential Coding) technique. Note that we could easily determine
the optimal order via an estimation of entropy coding efficiency using variance of tempo-
ral sequence. The second compression method, for temporal geometry coding, employs
several lossless wavelet filter banks including Haar (2/2 taps), Le Gall (5/3 taps), and
Daubechies (9/7 taps) filters. Our schemes enable lossy-to-lossless compression for 3-D
mesh sequences.
Joint Watermarking and Compression The proposed joint watermarking and
compression technique is based on the proposed compression method using SWA and TWA
schemes. For robust and invisible watermark, a new watermarking technique derived from
our 3-D static mesh watermarking scheme which modifies the variance of vertex norms
to embed watermark is applied to the intermediate step of the compression process. The
variance of spatiotemporal wavelet coefficients belonging to specific sub-band, to embed
watermark, is modified by a histogram mapping function. The hidden watermark can be
quite robust against several possible attacks because a statistical feature is employed as the
watermark carrier in our proposed method. Our scheme realizes a combined compression
system towards copyright protection for 3-D mesh sequences in a single framework.
1.3 Organization of the Dissertation
This dissertation is organized as follows. Chapter 2, Chapter 3, and Chapter 4 respectively
treat of three main research topics: watermarking, compression, and their combination.
Each chapter firstly introduces the overview and the state of the arts of pertinent research
area, and describes the proposed methods in detail. After that, the proposed methods are
evaluated in terms of the criterions required for individual application. The summaries
of each proposed technique are provided in the end of each chapter. Finally, we conclude
this dissertation with final remarks and perspectives in Chapter 5.
Chapter 2
Watermarking for 3-D Static
Meshes
This chapter presents two oblivious (or blind) watermarking techniques for 3-D static
meshes. Although it has been known that oblivious watermarking schemes are less robust
than non-oblivious ones, they are more useful for various applications where a host sig-
nal is not available in the watermark detection procedure. From a viewpoint of oblivious
watermarking for a 3-D polygonal mesh model, distortion-less attacks, such as similarity
transforms and vertex re-ordering, might be more serious than distortion attacks including
multiplicative noise, smoothing, simplification, re-meshing, clipping and so on. Clearly,
it is required to develop an oblivious watermarking that is robust against distortion-less
as well as distortion attacks. In this chapter, we propose two oblivious watermarking
methods for 3-D polygonal mesh models, which modify the distribution of vertex norms
according to the watermark bit to be embedded. One method is to shift the mean value
of the distribution and another is to change its variance. Histogram mapping functions
are introduced to modify the distribution. These mapping functions are devised to reduce
the visibility of watermark as much as possible. Since the statistical features of vertex
norms are invariant to the distortion-less attacks, the proposed methods are robust against
such attacks. In addition, our methods employ an oblivious watermark detection scheme,
which can extract the watermark without referring to the original mesh model. Through
simulations we demonstrate that the proposed approaches are remarkably robust against
6 Watermarking for 3-D Static Meshes
distortion-less attacks. Besides, they are also fairly robust against various distortion at-
tacks.
2.1 Introduction and State of the Arts
With the remarkable growth of the network technology such as WWW (World Wide
Web), digital media enables us to copy, modify, store, and distribute digital data without
effort. As a result, it has become a new issue to research schemes for copyright protection.
Traditional data protection techniques such as encryption are not adequate for copyright
enforcement, because the protection cannot be ensured after the data is decrypted. Water-
marking provides a mechanism for copyright protection by embedding information, called
a watermark, into host data [Praun et al., 1999]. Unlike encryption, digital watermarking
does not restrict access to the host data but ensures the hidden data remain inviolate and
recoverable. Note that so-called fragile or semi-fragile watermarking techniques have also
been widely used for content authentication and tamper proofing [Cayre and Macq, 2003].
Here, we address only watermarking technique for copyright protection, namely robust
watermarking.
Most previous research has focused on general types of multimedia data including text
data, audio stream [Bender et al., 1996,Gruhl and Bender, 1996,Cho et al., 2004], still
images [Seo et al., 2003,Cox et al., 1997,Lin et al., 2000], and video stream [Hartung and
Girod, 1998]. Recently, with the interest and requirement of 3-D models such as VRML
(Virtual Reality Modeling Language), CAD (Computer Aided Design), polygonal mesh
models and medical objects, several watermarking techniques for 3-D mesh models have
been developed [Ohbuchi et al., 2001, Ohbuchi et al., 1998, Yu et al., 2003b, Yu et al.,
2003a,Benedens, 1999,Kanai et al., 1998,Yin et al., 2001,Praun et al., 1999,Cayre and
Macq, 2003,Wagner, 2000,Lee et al., 2003,Jian-qiu et al., 2004,Cho et al., 2005,Cho et al.,
2006a].
Since 3-D mesh watermarking techniques were introduced in [Ohbuchi et al., 1998],
there have been several attempts to improve the performance in terms of transparency
and robustness. R. Ohbuchi et al. [Ohbuchi et al., 1998] proposed three watermarking
2.1 Introduction and State of the Arts 7
schemes: TSQ (Triangle Similarity Quadruple), TVR (Tetrahedral Volume Ratio), and
a visible mesh watermarking method. These schemes can be regarded as oblivious tech-
niques that can extract the watermark without reference of original mesh model, but they
are not sufficiently robust against various attacks. For example, TVR is very vulnerable
to re-meshing, simplification and re-ordering attacks. Beneden [Benedens, 1999] proposed
a watermark embedding method that modifies the local distribution of vertex directions
from the center point of model. The method is robust against simplification attack, be-
cause the local distribution is not sensitive to such operations. An extended scheme was
also introduced in [Lee et al., 2003] to overcome a weakness to cropping attack. However,
the method still requires pre-processing for re-orientation during the process of watermark
detection, as the local distribution essentially varies with the degree of rotation. Z. Yu et
al. [Yu et al., 2003b,Yu et al., 2003a] proposed a vertex norm modification method that
perturbs the distance between the vertices to the center of model according to watermark
bit to be embedded. It employs, before the modification, scrambling of vertices for the
purpose of preserving the visual quality. Note that it is not an oblivious technique and
also requires pre-processing such as registration and re-sampling. Some multi-resolution
based methods have also been introduced [Ohbuchi et al., 2001, Kanai et al., 1998, Yin
et al., 2001]. S. Kanai et al. [Kanai et al., 1998] proposed a watermarking algorithm based
on wavelet transform. Similar approaches, using Burt-Adelson style pyramid and mesh
spectral analysis were also published in [Yin et al., 2001] and [Ohbuchi et al., 2001], respec-
tively. The multi-resolution techniques could achieve a highly transparency of watermark,
but have yet to overcome various attacks such as vertex re-ordering and simplification,
since the connectivity information of vertices must be exactly known for multi-resolution
analysis and reconstruction. In addition, they are categorized as non-oblivious schemes.
In this dissertation, our interests focus on developing an oblivious watermarking.
3-D polygonal mesh models have serious difficulties for watermark embedding. While
image data is represented by brightness (or amplitudes of RGB components in the case of
color images) of pixels sampled over a regular grid in two dimension, 3-D polygonal models
have no unique representation, i.e., no implicit order and connectivity of vertices [Yu et al.,
2003b, Yu et al., 2003a]. This creates synchronization problem during the watermark
8 Watermarking for 3-D Static Meshes
extraction, which makes it difficult to develop robust watermarking techniques. For this
reason, most techniques developed for other types of multimedia are not effective for 3-D
meshes. Furthermore, a variety of complex geometrical and topological operations could
disturb the watermark extraction for assertion of ownership [Yu et al., 2003a].
The geometrical attacks include adding noise, smoothing and so on. Vertex re-ordering,
simplification and re-meshing fall into the category of topological attacks. These attacks
can be re-classified into two categories: distortion and distortion-less attacks [Cho et al.,
2005]. Distortion attacks include adding noise, simplification, smoothing, re-meshing,
clipping, and so on, which may cause visual deformation of the watermarked mesh model.
Most conventional watermarking techniques of 3-D polygonal mesh models have been de-
veloped to be robust mainly against the distortion attacks [Ohbuchi et al., 2001,Benedens,
1999,Kanai et al., 1998,Yin et al., 2001,Lee et al., 2003, Jian-qiu et al., 2004]. On the
other hand, distortion-less attacks include similarity transform and vertex re-ordering.
Note that the distortion-less attacks are more serious attacks on 3-D mesh watermarking
as they could fatally destroy the hidden watermark without any perceptual changes of
watermarked mesh model. Clearly, it is required to develop a watermarking technique
that is robust against distortion-less as well as distortion attacks.
In this chapter, we propose a statistical approach that modifies the distribution of
vertex norms to hide watermark information into host 3-D meshes. The distribution of
vertex norms is modified by two methods. One is to shift the mean value of the distribution
according to the watermark bit to be embedded and another to change its variance. A
similar approach has been used to shift the mean value in our previous work [Cho et al.,
2005], where a constant is added to vertex norms. Note that more sophisticated skills
are introduced in this chapter. In particular, histogram mapping functions are newly
introduced and used for the purpose of elaborate modification. Since the statistical features
are invariant to distortion-less attacks and less sensitive to various kinds of distortion ones,
robustness of watermark can be easily achieved. In addition, the proposed methods employ
a blind watermark detection scheme.
The rest of this chapter is organized as follows. In Section 2.2, the proposed water-
marking methods are described in detail, including the main idea behind the statistical
2.2 Proposed Watermarking Methods 9
approach, their embedding and extracting procedures. Here, histogram mapping functions
are also introduced to efficiently change the mean value and variance of the vector norm
distribution. Section 2.3 shows the simulation results of the proposed against various
distortion and distortion-less attacks. Finally, Section 2.4 summarizes this chapter.
2.2 Proposed Watermarking Methods
In order to achieve robustness of watermark against distortion-less attacks, it is very
important to find a watermark carrier, also called primitive in [Ohbuchi et al., 1998], that
can effectively preserve watermark from such attacks. For example, if vertices arranged in
a certain order are used as the watermark carrier, the hidden watermark bit stream cannot
be retrieved after vertex re-ordering. This is caused by the fact that 3-D polygonal meshes
do not have implicit order and connectivity of vertices. For the same reason, pre-processing
such as registration and re-sampling is required like as in [Yu et al., 2003b,Yu et al., 2003a]
or the robustness against distortion-less attacks cannot be guaranteed [Ohbuchi et al.,
2001,Ohbuchi et al., 1998,Kanai et al., 1998,Yin et al., 2001]. Clearly, statistical features
can be promising watermark carriers as they are generally less sensitive to these kinds
of attacks. Several features can be obtained directly from 3-D meshes, particularly, the
distribution of vertex directions and distribution of vector norms. Distribution of vertex
directions has been used as a watermark carrier in [Benedens, 1999, Lee et al., 2003],
where vertices are grouped into distinct sets according to their local direction and the
distribution of vertex direction is altered in each set separately. The distribution does not
change by vertex re-ordering operation, but it varies in essence with rotation operation.
Thus, it requires re-orientation processing before watermark detection [Benedens, 1999,Lee
et al., 2003]. On the other hand, the distribution of vertex norms does not change either
by vertex re-ordering or rotation operations. This is the reason why the distribution of
vertex norms is used as a watermark carrier in our methods.
We propose two watermarking methods that embed watermark into the 3-D mesh
model by modifying the distribution of vertex norms. Fig. 2.1 and 2.2 show the main
idea of each method, respectively. The first method is to make the mean value of vertex
10 Watermarking for 3-D Static Meshes
Figure 2.1: Proposed watermarking method by shifting the mean of the distribution
Figure 2.2: Proposed watermarking method by changing the variance of the distribution
2.2 Proposed Watermarking Methods 11
norms greater or smaller than a reference value according to watermark bit that we want to
insert. Assume that the vertex norms of original meshes are mapped into the interval [0, 1]
and have a uniform distribution over the interval as shown in Fig. 2.1(a). In this figure,
an arrow indicates the mean value of the vertex norms. To embed a watermark bit of
+1, the distribution is modified so that its mean value is greater than a reference value as
shown in Fig. 2.1(b). To embed −1, the distribution is modified so that it is concentrated
on the left side, and the mean value becomes smaller than a reference as shown in Fig.
2.1(c). The watermark extraction process is quite simple if the reference value is known.
The hidden watermark bit can be easily retrieved by simple comparison of the reference
with the mean value of vertex norms obtained from watermarked meshes. The second
proposed method is to change the variance of vertex norms to be greater or smaller than a
reference. Assume that the vertex norms are mapped into the interval [−1, 1] and have a
uniform distribution over the interval as shown in Fig. 2.2(a), where its standard deviation
is indicated by bi-directional arrow. To embed a watermark bit of +1, the distribution is
modified to concentrate on both margins. This leads to increase the standard deviation
as shown in Fig. 2.2(b). To embed −1, the distribution is altered to concentrate on the
center so that the standard deviation becomes smaller than a reference deviation as shown
in Fig. 2.2(c). Similar to the first proposed, the watermark can be extracted by comparing
the reference variance and variance taken from watermarked meshes.
Starting from the main idea of modifying the distribution of vertex norms, we introduce
some techniques to enhance watermark capacity and transparency. The distribution is
divided into distinct sections, hereafter referred to as bins, each of which is used as a
watermark embedding unit to embed one bit of watermark. The number of watermark
bits to be embedded can be properly selected by taking account the transparency. As an
example, Fig. 2.3 shows the distribution of a bunny model, which is divided into bins by
dashed vertical lines. It also shows that the distribution of each bin is close to uniform.
In addition, we introduce histogram mapping functions that can effectively modify the
distribution. The mapping functions are devised to reduce the visibility of the watermark
as much as possible.
12 Watermarking for 3-D Static Meshes
Figure 2.3: Distribution of vertex norms obtained from the bunny model, where dashed
vertical lines indicate the border of each bin.
2.2.1 The Proposed Watermarkig Method Using Mean Modification
This method embeds watermark information into 3-D polygonal mesh model by shifting
the mean value of each bin according to assigned watermark bit. All of the vertex norms
in each bin are modified by a histogram mapping function. Fig. 2.4 depicts the watermark
embedding and extraction processes, which are described in detail in the followings.
Fig. 2.4(a) shows the watermark embedding process. First, Cartesian coordinates of a
vertex vi = (xi, yi, zi) on the original mesh model V (vi ∈ V) are converted into spherical
coordinates (ρi, θi, φi) by means of
ρi =√
(xi − xg)2 + (yi − yg)2 + (zi − zg)2
θi = tan−1 (yi − yg)(xi − xg)
for 0 ≤ i ≤ L− 1 (2.1)
φi = cos−1 (zi − zg)√(xi − xg)2 + (yi − yg)2 + (zi − zg)2
where L is the number of the vertex, (xg, yg, zg) is the center of gravity of the mesh
model, and ρi is the i-th vertex norm. The vertex norm represents the distance between
2.2 Proposed Watermarking Methods 13
(a)
Fig
ure
2.4:
(a)
Blo
ckdi
agra
ms
ofth
ew
ater
mar
kem
bedd
ing
for
the
prop
osed
wat
erm
arki
ngm
etho
dsh
iftin
gth
em
ean
valu
eof
vert
ex
norm
s(c
onti
nued
onne
xtpa
ge)
14 Watermarking for 3-D Static Meshes
(b)
Figure
2.4:(b)
Block
diagrams
ofthe
waterm
arkextraction
forthe
proposedw
atermarking
method
shiftingthe
mean
valueof
vertex
norms
(continuedfrom
previouspage)
2.2 Proposed Watermarking Methods 15
each vertex and the center of gravity. The proposed method uses only vertex norms for
watermarking and keeps the other two components, θi and φi, intact. Note that the
distribution of vertex norms is invariant to vertex re-ordering and similarity transforms.
Second, vertex norms are divided into N distinct bins with equal range, according to
their magnitude. Each bin is used independently to hide one bit of watermark. If every bin
is processed for watermark embedding, we can insert at maximum N bits of watermark.
To classify the vertex norms into N bins, maximum and minimum vertex norms, ρmax
and ρmin, are calculated in advance. The n-th bin Bn is defined as follows.
Bn =ρn,j
∣∣∣∣ρmin +ρmax − ρmin
N· n < ρi
< ρmin +ρmax − ρmin
N· (n+ 1)
(2.2)
for 0 ≤ n ≤ N − 1, 0 ≤ i ≤ L− 1 and 0 ≤ j ≤Mn − 1
where Mn is the number of vertex norms belonging to the n-th bin and ρn,j is the j-th
vertex norm of the n-th bin.
Third, vertex norms belonging to the n-th bin are mapped into the normalized range
of [0, 1] by
ρn,j =ρn,j −minρn,j∈Bn ρn,j
maxρn,j∈Bn ρn,j −minρn,j∈Bn ρn,j(2.3)
where maxρn,j∈Bn ρn,j is the maximum vertex norm of the n-th bin and minρn,j∈Bn ρn,j
is the minimum vertex norm. ρn,j is the normalized, j-th vertex norm of the n-th bin.
Note that each bin now has a distribution very close to uniform over the unit interval as
mentioned in the previous section.
The fourth step of the proposed watermark embedding is to shift the mean value of
each bin via transforming vertex norms by the histogram mapping function as presented
in Appendix A.1. To embed a watermark bit of +1 (ωn = +1), vertex norms ρn,j are
transformed in order to shift the mean of the distribution by a factor, α (0 < α < 12).
Alternatively, to embed ωn = −1, vertex norms are transformed in order to shift the mean
by a factor −α. Then the mean of each bin, µ′n, is changed by
µ′n =
12 + α if ωn = +1
12 − α if ωn = −1
(2.4)
16 Watermarking for 3-D Static Meshes
where α is the strength factor that can control the robustness and the transparency of
watermark. The exact parameter kn can be found directly from Eq. (A.3).
kn =
1−2α1+2α if ωn = +1
1+2α1−2α if ωn = −1
(2.5)
Note that kn exists in the range of ]0, 1[ when the watermark bit is +1, and kn does in
the range of ]1,∞[ when watermark bit is −1.
The real vertex norm distribution in each bin is neither continuous nor uniform. Then
the parameter kn cannot be calculated by Eq. (2.5). To overcome this difficulty we use
an iterative approach as follow.
For embedding ωn = +1 into the n-th bin:
1) Initialize the parameter kn as 1;
2) Transform normalized vertex norms by ρ′n,j = (ρn,j)kn ;
3) Calculate mean of transformed vertex norms through
µ′n = 1Mn
∑Mn−1j=0 ρ′n,j ;
4) If µ′n <12 + α, decrease kn (kn = kn −∆k) and go back to 2);
5) Replace normalized vertex norms with transformed norms using ρn,j = ρ′n,j ;
6) End.
For embedding ωn = −1 into the n-th bin:
4) If µ′n >12 − α, increase kn (kn = kn + ∆k) and go back to 2);
The fifth step is inverse processing of the third step. Transformed vertex norms of each
bin are mapped onto the original range by
ρ′n,j = ρ′n,j ·(
maxρn,j∈Bn
ρn,j − minρn,j∈Bn
ρn,j)
+ minρn,j∈Bn
ρn,j (2.6)
where maxρn,j∈Bn ρn,j and minρn,j∈Bn ρn,j are the same as those used in the step
three.
Finally, the watermark embedding process is completed by combining all of the bins
and converting the spherical coordinates to Cartesian coordinates. Let ρ′i be a vertex norm
2.2 Proposed Watermarking Methods 17
in the combined bin. A watermarked mesh model V′ consisting of vertices v′i = (x′i, y′i, z
′i)
represented in Cartesian coordinate is obtained by
x′i = ρ′i cos θi sinφi + xg
y′i = ρ′i sin θi sinφi + yg for 0 ≤ n ≤ L− 1 (2.7)
z′i = ρ′i cosφi + zg
where θi, φi, and the center of gravity are the same as those calculated in the first step.
The watermark extraction process is quite simple as shown in Fig. 2.4(b). Similar
to embedding process, the watermarked mesh model is first converted to spherical coor-
dinates. After finding the maximum and minimum vertex norms, the vertex norms are
classified into N bins and mapped onto the normalized range of [0, 1]. Then, the mean of
each bin, µ′′n is calculated and compared to the reference value, 12 . The watermark hidden
in the n-th bin, ω′′n, is extracted by means of
ω′′n =
+1, if µ′′n >12
−1, if µ′′n <12
(2.8)
Note that the watermark detection process does not require the original meshes.
2.2.2 The Proposed Watermarking Method Using Variance Modifica-
tion
In this method, the variance of vertex norm distribution is changed to hide one bit of
watermark in each bin. Again, a histogram mapping function is introduced and applied.
Both the watermark embedding and extraction processes of the method are quite similar
to mean modification method, as introduced in previous section and shown in Fig. 2.5.
Fig. 2.5(a) shows the watermark embedding process. As the first two steps and the last
step of this watermark embedding process are identical to those mentioned in Sub-section
2.2.1, only the unique steps of this method are described in details. Note that notations
have not been changed from the previous section for the sake of simplicity.
In the first and second steps, vertices of original meshes are represented in spherical
coordinate, and vertex norms are divided into N bins such as ρn,j ∈ Bn for 0 ≤ n ≤ N −1
and 0 ≤ j ≤Mn − 1.
18 Watermarking for 3-D Static Meshes
(a)
Figure
2.5:(a)
Block
diagrams
ofthe
waterm
arkem
beddingfor
theproposed
waterm
arkingm
ethodchanging
thevariance
ofvertex
norms
(continuedon
nextpage)
2.2 Proposed Watermarking Methods 19
(b)
Fig
ure
2.5:
(b)B
lock
diag
ram
sof
the
wat
erm
ark
extr
acti
onfo
rth
epr
opos
edw
ater
mar
king
met
hod
chan
ging
the
vari
ance
ofve
rtex
norm
s
(con
tinu
edfr
ompr
evio
uspa
ge)
20 Watermarking for 3-D Static Meshes
In the third step, vertex norms of each bin are mapped into a normalized range similar
to the mean modification method. However, the range [−1, 1] is now mapped by
ρn,j = 2 ·(ρn,j −minρn,j∈Bn ρn,j
)maxρn,j∈Bn ρn,j −minρn,j∈Bn ρn,j
− 1 (2.9)
where ρn,j is the j-th vertex norm of the n-th bin represented in the normalized range.
Note that each bin has a nearly uniform distribution over the interval [−1, 1].
The fourth step of the watermark embedding process is to change variance of each
bin via transforming vertex norms by the histogram mapping function as presented in
Appendix A.2. To embed ωn = +1, vertex norms ρn,j are transformed in order to change
the variance of the distribution by a strength factor, α (0 < α < 13). To embed ωn = −1,
vertex norms are transformed in order to change the variance by a factor −α. Then the
variance of each bin, σ2′n , is changed by
σ2′n =
13 + α if ωn = +1
13 − α if ωn = −1
(2.10)
The exact parameter can be found directly from Eq. (A.4).
kn =
1−3α1+3α if ωn = +1
1+3α1−3α if ωn = −1
(2.11)
Note that kn exists in the range of ]0, 1[ when the watermark bit is +1, and kn does in
the range of ]1,∞[ when watermark bit is −1.
As mentioned in Sub-section 2.2.1, Eq. (2.11) is not useful for the real vertex norm
distribution. Thus we use an iterative approach as follow.
For embedding ωn = +1 into the n-th bin:
1) Initialize the parameter kn as 1;
2) Transform normalized vertex norms by ρ′n,j = sign (ρn,j) |ρn,j |kn ;
3) Calculate the variance of transformed vertex norms through
σ2′n = 1
Mn
∑Mn−1j=0 ρ′2n,j ;
4) If σ2′n < 1
3 + α, decrease kn (kn = kn −∆k) and go back to 2);
5) Replace normalized vertex norms with transformed norms using ρn,j = ρ′n,j ;
2.3 Simulation Results 21
6) End.
For embedding ωn = −1 into the n-th bin:
4) If σ2′n > 1
3 − α, increase kn (kn = kn + ∆k) and go back to 2);
The fifth step is to map each bin onto the original range using
ρ′n,j =12·(ρ′n,j + 1
)·(
maxρn,j∈Bn
ρn,j − minρn,j∈Bn
ρn,j)
+ minρn,j∈Bn
ρn,j (2.12)
Finally, the watermark embedding process is completed by combining all of the bins
and converting the spherical coordinates to Cartesian coordinates using Eq. (2.7).
Watermark extraction process for this method is also quite simple as illustrated in Fig.
2.5(b). The variance of each bin, σ2′′n is calculated and compared with the reference value,
13 . The watermark hidden in n-th bin, ω′′n, is extracted by means of
ω′′n =
+1, if σ2′′n > 1
3
−1, if σ2′′n < 1
3
(2.13)
Note that this watermark extraction process is performed without the original mesh model.
2.3 Simulation Results
Simulations were carried out on six 3-D triangular mesh models, a buddha (with 543 652
vertices and 1 087 716 cells), a bunny (with 35 947 vertices and 69 451 cells), a dragon
(with 15 574 vertices and 29 999 cells), a cow (with 2 903 vertices and 5 804 cells), a face
(with 539 vertices and 1 042 cells) and a fandisk (with 6 475 vertices and 12 946 cells) as
shown in Fig. 2.6.
To measure the quality distortion between the original mesh model and watermarked
one, we use Metro [Cignoni et al., 1998] which provides the HD (Hausdorff Distance)
between two static surfaces modeled by triangular meshes. It first evaluates two one-sided
distances, e (V,V′) and e (V′,V) (V and V′ represent the original and deformed surfaces
of meshes, respectively). Note that there exist surfaces such that e (V,V′) 6= e (V′,V).
22 Watermarking for 3-D Static Meshes
For that reason, the HD, E (V,V′), is obtained by taking the maximum value of two
one-sided distances:
E(V,V′) = max
e(V,V′) , e (
V′,V)
(2.14)
The robustness of the watermark is measured in terms of correlation between the
original watermark and the extracted one.
Corr =∑N−1
n=0 (ω′′n −$
′′)(ωn −$)√∑N−1
n=0 (ω′′n −$′′)2 ×
∑N−1n=0 (ωn −$)2
(2.15)
where $ indicates the average of the watermark and Corr is on the range of [−1, 1].
In the simulations, we embedded 64 bits of watermark into a mesh model considering
the trade-off between the robustness and the transparency of watermark. Then, vertex
norms were divided into 64 bins and one bit of watermark was hidden in each bin. For
comparison of the two proposed methods, the strength factor of watermark was determined
experimentally so that both methods have very similar quality for each model in terms of
HD. Fig. 2.7 shows the watermarked mesh models, of which the performance are listed
in Table 2.1 in terms of HD and Corr when no attack. Here, the strength factor of
each watermark is also listed. The table shows that the statistical approach employed in
the proposed methods cannot embed a watermark bit into every bin in the case of very
small size models such as face. This is mainly caused by the fact that some of the bins
are empty or do not contain enough number of vertices. For this reason, the proposed
methods are not recommended to be applied to such small size models (approximately
having under 2 000 vertices). However, the hidden watermark can be extracted perfectly
from all watermarked models except for the smallest size model. This means the proposed
methods guarantee to hide a watermark bit into every bin for models with a sufficient
number of vertices. From the viewpoint of watermark transparency, mean modification
method maintains better visual quality than variance modification method. Some artifacts
appear in smooth regions such as in the lower belly of buddha and the rump of bunny
as shown in Fig. 2.7(g) and Fig. 2.7(h). In particular, the artifacts are conspicuous in
flat regions of fandisk, even when small strength factor is applied. This is mainly due to
the fact that every vertex is modified without considering local curvature of models. It
2.3 Simulation Results 23
Table 2.1: Evaluation of watermarked meshes when no attack
Method ModelStrength
factorHD Corr
Mean
Modification
buddha 0.03 0.38×10−4 1.00
bunny 0.03 0.40×10−4 1.00
dragon 0.04 0.45×10−4 1.00
cow 0.16 5.84×10−3 1.00
face 0.16 1.41×10−2 0.43
fandisk 0.01 7.32×10−4 1.00
Variance
Modification
buddha 0.06 0.35×10−4 1.00
bunny 0.07 0.41×10−4 1.00
dragon 0.11 0.48×10−4 1.00
cow 0.26 5.91×10−3 1.00
face 0.28 1.27×10−2 0.49
fandisk 0.05 7.85×10−4 1.00
is also caused by discontinuities in the boundaries of neighbor bins when the distribution
is modified. As results, the proposed methods are not applicable to CAD models with
flat region. Consequently, attack simulations have been performed with buddha, bunny,
dragon and cow.
2.3.1 Attack Simulations
To evaluate the robustness of the watermark, various distortion and distortion-less attacks
were performed on the watermarked meshes. Each attack was applied with varying at-
tack strengths. Distortion attacks including multiplicative binary random noise, uniform
quantization, smoothing, simplification and sub-division were carried out. As examples,
the watermarked bunny models deformed by various distortion attacks are shown in Fig.
2.8.
For evaluating the resistance to noise attack, binary random noise was added to each
24 Watermarking for 3-D Static Meshes
(a)
(b)
(c)
Figure
2.6:O
riginalm
eshm
odels(a)
buddha,(b)
bunny,(c)
dragon(continued
onnext
page)
2.3 Simulation Results 25
(d)
(e)
(f)
Fig
ure
2.6:
(d)
cow
,(e
)fa
ce,an
d(f
)fa
ndis
k(c
onti
nued
from
prev
ious
page
)
26 Watermarking for 3-D Static Meshes
(a)
(b)
(c)
Figure
2.7:W
atermarked
mesh
models,w
here(a)-(f)
arew
atermarked
bym
eanm
odificationm
ethodand
(g)-(l)by
variancem
odification
method.
(continuedon
nextpage)
2.3 Simulation Results 27
(d)
(e)
(f)
Fig
ure
2.7:
Wat
erm
arke
dm
esh
mod
els,
whe
re(a
)-(f
)ar
ew
ater
mar
ked
bym
ean
mod
ifica
tion
met
hod
and
(g)-
(l)
byva
rian
cem
odifi
cati
on
met
hod.
(con
tinu
edfr
ompr
evio
uspa
gean
dco
ntin
edon
next
page
)
28 Watermarking for 3-D Static Meshes
(g)
(h)
(i)
Figure
2.7:W
atermarked
mesh
models,w
here(a)-(f)
arew
atermarked
bym
eanm
odificationm
ethodand
(g)-(l)by
variancem
odification
method.
(continuedfrom
previouspage
andcontined
onnext
page)
2.3 Simulation Results 29
(j)
(k)
(l)
Fig
ure
2.7:
Wat
erm
arke
dm
esh
mod
els,
whe
re(a
)-(f
)ar
ew
ater
mar
ked
bym
ean
mod
ifica
tion
met
hod
and
(g)-
(l)
byva
rian
cem
odifi
cati
on
met
hod.
(con
tinu
edfr
ompr
evio
uspa
ge)
30 Watermarking for 3-D Static Meshes
(a) (b)
(c) (d)
Figure 2.8: Bunny model watermarked by mean modification method and attacked by (a)
multiplicative binary noise with error ratio of 0.5%, (b) 7bits/coordinate quantization, (c)
smoothing with iteration of 50 and relaxation of 0.03 and (d) simplification with reducing
90.65% of vertices
2.3 Simulation Results 31
vertex norm 1 in watermarked model with three different error rates: 0.1%, 0.3% and
0.5% [Yu et al., 2003b]. Here, the error rate represents the noise amplitude as a fraction
of the maximum vertex norm of the object. We perform each noise attack five times
using different random seeds and report the median as shown in Table 2.2. The effect
of the noise attack is shown in Fig. 2.8(a). The performance of variance modification
method decreases faster than that of mean modification method as increasing the error
rate. Both methods are fairly resistant to the noise attacks under an error rate of 0.3,
but good watermark detection cannot be expected for higher error rates. This is due to
the fact that the multiplicative noise essentially alters the distribution of vertex norms
in the divided bins. In addition, more vertex norms exceed the range of each bin as the
noise error rate increases. Similar tendency was observed in quantization and smoothing
attacks. For such reasons, the robustness cannot be enhanced beyond a certain level even
when the strength factor α increases. The robustness can also be improved by widening
the size (width) of bin, but the transparency of watermark and the number of bits to be
embedded should be considered.
To evaluate the robustness against uniform quantization attacks, three different quanti-
zation rates are applied to watermarked meshes. Each coordinate of vertices is represented
with 7bits, 8bits and 9bits. Table 2.3 shows the robustness against the quantization attack.
An example is shown in Fig. 2.8(b). Both methods are fairly robust up to 8bits quan-
tization. Similar to the case of noise attack, variance modification has relatively abrupt
diminution of the robustness as the quantization step size increases.
Table 2.4 shows the performance of the watermarking schemes after smoothing attacks
[Field, 1988]. Three different pairs of iteration and relaxation were applied. An example
of the attack is also shown in Fig. 2.8(c), where the effect can be seen in the rounded
edges. The robustness depends on the smoothness of the original meshes. Buddha and
bunny are relatively less sensitive to smoothing attacks.
To evaluate the robustness of our methods against simplification attacks, we utilized
a simplification method [Shroder et al., 1992]. Watermarked models were simplified by
various reduction ratios. Table 2.5 demonstrates that the proposed methods are robust
1It is multiplicative noise in the coordinates.
32 Watermarking for 3-D Static Meshes
Table 2.2: Evaluation of robustness against multiplicative binary noise attacks
Method Model Error rate HD Corr
Mean
Modification
buddha
0.1% 0.54×10−4 0.94
0.3% 1.26×10−4 0.73
0.5% 1.96×10−4 0.41
bunny
0.1% 0.59×10−4 0.87
0.3% 1.47×10−4 0.51
0.5% 2.38×10−4 0.18
dragon
0.1% 0.68×10−4 1.00
0.3% 1.49×10−4 0.55
0.5% 2.37×10−4 0.21
cow
0.1% 6.27×10−3 0.97
0.3% 8.95×10−3 0.91
0.5% 1.27×10−2 0.41
Variance
Modification
buddha
0.1% 0.54×10−4 1.00
0.3% 1.26×10−4 0.81
0.5% 1.96×10−4 −0.29
bunny
0.1% 0.59×10−4 1.00
0.3% 1.47×10−4 0.53
0.5% 2.38×10−4 −0.39
dragon
0.1% 0.70×10−4 1.00
0.3% 1.49×10−4 0.65
0.5% 2.37×10−4 −0.34
cow
0.1% 6.30×10−3 1.00
0.3% 8.74×10−3 0.50
0.5% 1.29×10−2 0.22
2.3 Simulation Results 33
Table 2.3: Evaluation of robustness against uniform quantization attacks
Method Model Quantization HD Corr
Mean
Modification
buddha
9bits 0.64×10−4 0.87
8bits 1.21×10−4 0.78
7bits 2.42×10−4 0.47
bunny
9bits 0.69×10−4 0.94
8bits 1.26×10−4 0.88
7bits 2.46×10−4 0.39
dragon
9bits 0.75×10−4 0.94
8bits 1.30×10−4 0.84
7bits 2.48×10−4 0.43
cow
9bits 6.43×10−3 0.91
8bits 7.81×10−3 0.94
7bits 1.22×10−2 0.51
Variance
Modification
buddha
9bits 0.64×10−4 1.00
8bits 1.21×10−4 0.97
7bits 2.42×10−4 0.19
bunny
9bits 0.73×10−4 1.00
8bits 1.28×10−4 0.97
7bits 2.46×10−4 −0.01
dragon
9bits 0.82×10−4 1.00
8bits 1.34×10−4 1.00
7bits 2.49×10−4 0.72
cow
9bits 6.56×10−3 1.00
8bits 8.07×10−3 0.72
7bits 1.23×10−2 0.11
34 Watermarking for 3-D Static Meshes
Table 2.4: Evaluation of robustness against smoothing attacks
Method Model(# of iteration,
relaxation)HD Corr
Mean
Modification
buddha
(10,0.03) 0.32×10−4 1.00
(30,0.03) 0.33×10−4 1.00
(50,0.03) 0.36×10−4 0.94
bunny
(10,0.03) 0.41×10−4 0.75
(30,0.03) 0.80×10−4 0.57
(50,0.03) 1.21×10−4 0.46
dragon
(10,0.03) 0.76×10−4 0.62
(30,0.03) 1.85×10−4 0.39
(50,0.03) 2.88×10−4 0.24
cow
(10,0.03) 1.03×10−2 0.69
(30,0.03) 2.43×10−2 0.23
(50,0.03) 3.67×10−2 0.17
Variance
Modification
buddha
(10,0.03) 0.31×10−4 1.00
(30,0.03) 0.31×10−4 1.00
(50,0.03) 0.33×10−4 1.00
bunny
(10,0.03) 0.42×10−4 0.97
(30,0.03) 0.81×10−4 0.87
(50,0.03) 1.22×10−4 0.75
dragon
(10,0.03) 0.79×10−4 0.97
(30,0.03) 1.89×10−4 0.27
(50,0.03) 2.92×10−4 0.18
cow
(10,0.03) 1.00×10−2 0.42
(30,0.03) 2.40×10−2 0.11
(50,0.03) 3.64×10−2 0.11
2.3 Simulation Results 35
Table 2.5: Evaluation of robustness against simplification attacks (continued on next page)
Method Model Reduction ratio HD Corr
Mean
Modification
buddha
30.02% 0.38×10−4 1.00
50.02% 0.39×10−4 0.94
70.03% 0.41×10−4 0.84
90.10% 1.05×10−4 0.75
bunny
32.11% 0.44×10−4 0.94
51.44% 0.52×10−4 0.77
70.79% 0.70×10−4 0.58
90.65% 3.44×10−4 0.38
dragon
30.36% 0.98×10−4 0.76
50.97% 1.91×10−4 0.75
63.74% 3.43×10−4 0.44
82.46% 7.47×10−4 0.22
cow
30.01% 1.02×10−2 0.46
44.54% 2.09×10−2 0.46
58.77% 4.31×10−2 0.46
75.41% 6.83×10−2 0.17
against simplification attacks. In addition, variance modification method is more robust
than mean modification method. In this table, the percentage represents the number of
vanished vertices as a fraction of total number of vertices. Fig. 2.8(d) shows an example
of the simplification attack. Sub-division attacks were also carried out. Each triangle
was uniformly divided into four cells. The performance is listed in Table 2.6. The results
show that the proposed methods are robust against sub-division attacks, similar to attacks
using simplification. The results demonstrate that the distribution of vertex norms is less
sensitive to changes in the number of vertices. Clearly, this is an additional advantage of
the statistical approach. However, clipping attack simulation shows that the proposed are
very vulnerable to such attacks that cause severe alteration to the center of gravity of the
model.
36 Watermarking for 3-D Static Meshes
Table 2.5: (Continued from previous page)
Variance
Modification
buddha
30.02% 0.35×10−4 1.00
50.02% 0.35×10−4 1.00
70.46% 0.37×10−4 1.00
90.01% 0.92×10−4 0.97
bunny
32.10% 0.44×10−4 1.00
51.43% 0.52×10−4 0.97
70.78% 0.70×10−4 0.94
89.71% 3.35×10−4 0.79
dragon
30.42% 0.99×10−4 1.00
50.97% 1.96×10−4 1.00
63.81% 3.48×10−4 0.71
81.70% 8.52×10−4 0.53
cow
30.01% 1.08×10−2 1.00
43.62% 2.13×10−2 0.51
58.63% 2.13×10−2 0.37
76.34% 2.13×10−2 0.25
Table 2.6: Evaluation of robustness against 1:4 sub-division attacks
Method Model # of cells HD Corr
Mean
Modification
buddha 4,350,864 0.38×10−4 1.00
bunny 277,804 0.34×10−4 0.87
dragon 119,996 2.80×10−4 0.62
cow 11,609 5.78×10−3 0.58
Variance
Modification
buddha 4,350,864 0.35×10−4 1.00
bunny 277,804 0.41×10−4 0.94
dragon 119,996 2.82×10−4 1.00
cow 11,609 5.29×10−3 0.61
2.3 Simulation Results 37
To evaluate the robustness of our methods against distortion-less attacks, vertex re-
ordering and similarity transforms were carried out. Vertex re-ordering attack was per-
formed iteratively 100 times, also changing the seed of random number generator for each
iteration. Similarity transforms were carried out with many combinations of rotation,
uniform scaling, and translation factors. It is not necessary to tabulate watermark detec-
tion performance because both proposed perfectly extracted the hidden watermark infor-
mation. As intended, the proposed watermarking methods are perfectly robust against
distortion-less attacks.
2.3.2 Parameters for Robustness
In this section, we analyze two parameters that can be adjusted to improve the robustness
of the proposed methods. One is the watermark strength factor α, another is the size of
bin. For these analyses, bunny model and mean modification method were used. Smooth-
ing operation with iteration of 30 and relaxation of 0.03 was applied as an example attack.
To analyze the effect of watermark strength factor, bunny model was watermarked with
varying the strength factor and underwent the smoothing attack. Here, 64 bits of wa-
termark were embedded. Fig. 2.9(a) shows the correlation of watermark detection along
different strength factors. Corresponding HD of watermarked meshes is also plotted. It
shows that the robustness can be improved to a certain limited level as the strength factor
increases. However, the watermark transparency should be carefully considered, as HD
increases linearly. Fig. 2.9(b) shows the relationship between the size of bin and the
correlation, where the strength factor is used as α = 0.03. Note that the size of bin is
inversely proportional to the number of bins. This shows that the robustness can also be
improved as the size of bin increases. In other words, this means that the use of larger
bins reduces the probability that vector norms exceed the corresponding bin when be-
ing attacked by smoothing operations. However, watermark transparency should be also
carefully considered. Note that the use of larger bins limits the number of watermark bits.
38 Watermarking for 3-D Static Meshes
(a)
Figure 2.9: (a) Relationship between the strength factor and the correlation. As an
example, a smoothing attack with iteration 30 and relaxation 0.03 is applied. (continued
on next page)
2.3 Simulation Results 39
(b)
Figure 2.9: (b) Relationship between the number of bins and the correlation. As an
example, a smoothing attack with iteration 30 and relaxation 0.03 is applied. (continued
from previous page)
40 Watermarking for 3-D Static Meshes
2.3.3 ROC Analysis
The proposed methods were analyzed by ROC (Receiver Operating Characteristic) curve
that represents the relation between probability of false positives Pfp and probability of
false negatives Pfn by varying the decision threshold TCorr for declaring the watermark
present [Praun et al., 1999]. The probability density functions for Pfp and Pfn were mea-
sured experimentally with 100 correct and 100 wrong keys, and approximated to Gaussian
distribution. In these simulations, we used the same watermarked model of bunny as used
in Sub-section 2.3.1. Fig. 2.10 shows the ROC curves when multiplicative binary noise and
simplification attacks are respectively applied into the watermarked model of bunny. EER
(Equal Error Rate) is also indicated in this figure. As shown in the figure, the proposed
methods have fairly good performance in terms of watermark detection for both attacks.
2.4 Summaries
In this chapter, we proposed two statistical watermarking methods for 3-D polygonal mesh
models that modify the distribution of vertex norms via changing respectively the mean
and the variance of each bin by histogram mapping function. Through the simulations,
we proved that both proposed methods are perfectly robust against distortion-less attack
such as vertex re-ordering and similarity transforms. Moreover, they are fairly robust
against various kinds of distortion attacks, in particular, simplification and sub-division
operations. However, there are some drawbacks. Our proposals are not applicable to very
small size models and CAD models with flat regions, and are very vulnerable to clipping
attacks that cause severe alteration to the center of gravity of the model. Nevertheless,
the simulation results demonstrate a possible, oblivious watermarking method based on
statistical approach for 3-D polygonal mesh model.
2.4 Summaries 41
(a)
(b)
Fig
ure
2.10
:R
OC
curv
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odel
(a)
wat
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42 Watermarking for 3-D Static Meshes
(c)(d
)
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2.10:(c)
waterm
arkedby
variancem
odificationm
ethodand
attackedby
multiplicative
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(d)w
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Chapter 3
Compression for 3-D Mesh
Sequences
In this chapter, we present two compression methods for irregular three-dimensional (3-
D) mesh sequences with constant connectivity. The proposed methods mainly use an
exact integer spatial wavelet analysis (SWA) technique to efficiently decorrelate the spatial
coherence of each mesh frame and also to adaptively transmit mesh frames with various
spatial resolutions. To reduce the temporal redundancy, the first proposed method applies
multi-order differential coding (MDC) to the temporal sequences obtained from SWA.
MDC determines the optimal order of the differential coder by analyzing the variance of
prediction errors. Comparing with the first-order differential coding (FDC) scheme, the
method can improve the compression performance. The second proposed method applies
temporal wavelet analysis (TWA) to the temporal sequences. In particular, this method
offers spatiotemporal multi-resolution coding. Through simulations, we prove that our
approaches not only have better coding efficiency than some methods but also enable
efficient lossy-to-lossless compression for 3-D mesh sequences.
3.1 Introduction and State of the Arts
With the remarkable progress of multimedia and information technologies, 3-D data has
been more and more widely used in various applications such as virtual reality, video
44 Compression for 3-D Mesh Sequences
games, animation movies and medical images.
Polygonal meshes provide an efficient representation of 3-D objects, since they can be
rapidly rendered by existing graphics hardware. Like as the categorization of 2-D still
images and motion pictures, they can be classified into static meshes and mesh sequences.
Static meshes contain two kinds of principal information, the locations of vertices and
their topological connections – geometry and connectivity, respectively. Similar to mo-
tion pictures, a 3-D mesh sequence consists of consecutive static meshes. The motion of
meshes is usually represented by vertex displacements. These kinds of mesh sequences
have constant connectivity information over all mesh frames. On the other hand, some
mesh sequences might have variable connectivity over all or partial mesh frames. In this
chapter, we address only mesh sequences with constant connectivity.
Generally, mesh sequences obtained by 3-D scanners or mesh design tools such as 3-D
Studio MAX require huge capacity or enormous bandwidth to be stored or transmitted.
For that reason, it has become an important issue to develop efficient compression methods
for 3-D mesh sequences. Similar to 2-D motion picture compression, spatial and temporal
redundancies are mainly exploited to minimize data size. To reduce the spatial redundancy,
the geometry and connectivity information of a single mesh frame can be modeled for
entropy coding. The geometrical coherence in temporal direction between consecutive
mesh frames can be used to reduce the temporal redundancy. Clearly, other attributes such
as normal vectors or texture information could be also regarded as important components
to be compressed. Note that we focus on geometry coding in this chapter.
Since Lengyel [Lengyel, 1999] proposed a geometry compression method for 3-D mesh
sequences, there have been several attempts to reduce the spatial and geometry redundan-
cies [Yang et al., 2002,Lengyel, 1999,Zhang and Owen, 2005,Alexa and Muller, 2000,Karni
and Gotsman, 2004,Ibarria and Rossignac, 2003,Ahn et al., 2002,Guskov and Khodakovsky,
2004,Cho et al., 2006b,Payan and Antonini, 2005]. In [Lengyel, 1999], the original meshes
are segmented into small rigid body meshes. The motion of each rigid body mesh is rep-
resented by affine transform coefficients, then the coefficients and residuals are quantized
and encoded by an entropy coder. This algorithm uses temporal coherence of rigid body
meshes to reduce temporal redundancy. However, this method has difficulties to obtain
3.1 Introduction and State of the Arts 45
precise segmentation and cannot have good coding performance for the mesh sequences
with high geometrical complexity. A quantization based method was also presented by
Zhang and Owen [Zhang and Owen, 2005]. They proposed a hybrid compression method
combining delta and octree coding schemes. For each mesh frame, the geometry informa-
tion is encoded by using selectively one of two coding schemes which has smaller prediction
errors. This technique requires high processing time, because it iterates the encoding pro-
cesses until the predetermined visual quality of the decoded mesh sequences. Some PCA
(Principal Component Analysis) based methods have been presented [Alexa and Muller,
2000,Karni and Gotsman, 2004]. Alexa and Muller [Alexa and Muller, 2000] represented
3-D mesh sequences using several principal bases obtained by PCA. Karni and Gots-
man [Karni and Gotsman, 2004] expanded it to a hybrid method combining PCA and
LPC (Linear Prediction Coding). However, these methods essentially require high com-
putational complexity to calculate the eigenvectors. Ibarria and Rossignac [Ibarria and
Rossignac, 2003] introduced an efficient compression method which can simultaneously
reduce the temporal and spatial redundancies by using a space-time replica predictor.
Some methods [Yang et al., 2002,Ahn et al., 2002,Guskov and Khodakovsky, 2004,Cho
et al., 2006b] applied the motion picture coding techniques, which have been widely used
in MPEG (Motion Pictures Experts Group) and H.26x, to 3-D mesh sequence compres-
sion. Yang et al. [Yang et al., 2002] used two-stage vertex-wise motion vector prediction.
In the first stage, they first define the topological neighborhood of a vertex and predict
the motion vector. To improve the compression performance, in the second stage, the pre-
diction errors are once more decorrelated by four optional modes – no prediction mode,
temporal prediction mode, spatial prediction mode, and spatiotemporal prediction mode
– applying R-D (Rate-Distortion) optimization. Ahn et al. [Ahn et al., 2002] proposed
a motion compensated coding scheme. The method extracts triangle strips using the
connectivity of the first mesh frame, and then divides each triangle strip into several seg-
ments. The segments can be regarded as macro blocks in motion picture coding. Each
segment is independently motion estimated, and its motion vector is encoded. These two
algorithms [Yang et al., 2002,Ahn et al., 2002] enable both a simple and an efficient com-
pression via conventional 2-D video coding schemes. Recently, scalability has become an
46 Compression for 3-D Mesh Sequences
important issues in video coding, as it facilitates to adaptively manage bit-rates according
to different conditions of bandwidth or capacity [Sun et al., 2005]. From the viewpoint of
scalable coding, wavelet transform – SWA (Spatial Wavelet Analysis) and/or TWA (Tem-
poral Wavelet Analysis) – is suitable for 3-D mesh sequences. Some wavelet-based meth-
ods have been introduced [Payan and Antonini, 2005,Guskov and Khodakovsky, 2004,Cho
et al., 2006b]. Payan and Antonini [Payan and Antonini, 2005] used a TWA to reduce
temporal redundancy. Although they achieved good compression performance by using
their optimal bit allocation scheme, they did not consider the spatial redundancy. Guskov
and Khodakovsky [Guskov and Khodakovsky, 2004] introduced a SWA-based compression
algorithm. They encoded the differential errors between the wavelet coefficients of previ-
ous and current frames. Here, the wavelet coefficients are obtained from the Burt-Adelson
style pyramid scheme. The method can provide the spatial resolution scalability.
In this chapter, we propose two compression techniques of the mesh geometry for 3-
D mesh sequences with constant connectivity. To reduce the spatial redundancy, both
proposed methods use the SWA technique which employs an exact integer analysis and
synthesis filter bank [Valette and Prost, 2004a]. The filters can be directly applied to irreg-
ular meshes. Besides, they can easily achieve lossy-to-lossless compression 1. In order to
reduce the temporal redundancy, we consider two different techniques, MDC (Multi-order
Differential Coding) and TWA. The first method uses SWA and MDC schemes. In our pre-
vious work [Cho et al., 2006b], we used a FDC (First order Differential Coding) technique
employing IPPP frame pattern coding which combines Intra-mesh and Predicted-mesh
coding. To improve the coding efficiency, we introduce a more sophisticated approach
in which the variances of prediction errors are analyzed to find the optimal order. The
second method employs both SWA and TWA schemes. Although TWA scheme was ap-
plied in a previous algorithm [Payan and Antonini, 2005], there has been no attempt
to apply SWA and TWA, simultaneously. Both proposed methods can provide lossy-to-
lossless compression if input mesh sequences have integer coordinates. The first method
1In general, lossy compression gain is determined by quantization via R-D optimization. Note that, in
this chapter, we regard ‘multi-resolution transmission (or representation)’ as ‘lossy compression’ because
it could also reduce data size.
3.2 Wavelet-based Multi-resolution Analysis 47
can reconstruct mesh sequences with various spatial resolutions, and the second enables
temporal multi-resolution coding as well as spatial one.
The rest of this chapter is organized as follows. In Section 3.2, SWA and TWA tech-
niques, which are used in our compression schemes, are introduced. Two compression
methods using wavelet-based multi-resolution analysis are proposed in Section 3.3. Sec-
tion 3.4 shows the simulation results of the proposed methods in terms of lossless and
lossy compression performances. Finally, Section 3.5 summarizes this chapter.
3.2 Wavelet-based Multi-resolution Analysis
Early compression methods for multimedia data have been mainly concentrated on the
development of single-rate coding system [Peng et al., 2005]. Although single-rate cod-
ing has enough performance in a network environment with fixed bandwidth, it might
be difficult to be promptly applied to variable bandwidth conditions. For that reasons,
scalable coding techniques such as the annexed functionalities of MPEG (Motion Picture
Experts Group)-2 and -4 have been intensively researched. In general scalable decoding
frameworks, the coarsest version is first reconstructed from the base layer, and higher
resolution versions are adaptively produced from the enhancement layers depending on
channel conditions. It has been well-known that wavelet-based multi-resolution analysis
techniques are useful for scalable coding. Besides, they provide good coding performance,
as the PDF (Probability Density Function) of the wavelet coefficients can be approximated
to Laplacian distribution with a sharp peak [Cho et al., 2006b]. These are the reasons
why we use SWA and TWA in order to design efficient 3-D mesh sequence compression
systems. In the following sub-sections, SWA and TWA schemes are summarized.
3.2.1 SWA (Spatial Wavelet Analysis) and Its Synthesis
The wavelet-based multi-resolution scheme for 3-D static meshes was firstly introduced
by Lounsbery [Lounsbery, 1994]. Fig. 3.1 shows an example of SWA and its synthesis
processes. From the original mesh CJ , the SWA is performed by two analysis filters, Aj
48 Compression for 3-D Mesh Sequences
(a)
(b)
Figure 3.1: (a) SWA (Spatial Wavelet Analysis) and (b) its synthesis processes
3.2 Wavelet-based Multi-resolution Analysis 49
(low-pass filter) and Bj (high-pass filter) as follows,
Cj−1 = AjCj (3.1)
Dj−1 = BjCj for 0 ≤ j ≤ J (3.2)
where j is the spatial resolution level, and Cj is a vj × 3 matrix representing the vertex
coordinates (x-, y-, and z-coordinates) of the input mesh having vj vertices. A fine mesh
Cj is decomposed into a coarse mesh Cj−1 and wavelet coefficients Dj−1. The wavelet
coefficients represent the lost details. We obtain a hierarchy of meshes from the original
CJ to the simplest one, C0, so-called base mesh.
The reconstruction is done by two synthesis filters, P j and Qj . It is formulated as
Cj = P jCj−1 +QjDj−1 (3.3)
A fine mesh is reconstructed from the coarse one and the corresponding wavelet coefficients.
If the filter-banks satisfy the following constraint, we can achieve perfect reconstruction.[Aj
Bj
]=
[P j |Qj
]−1 (3.4)
Lounsbery’s scheme handles meshes with one-to-four (1:4) subdivision connectivity. The
mesh hierarchy can be considered as successive quadrisections of a base mesh (C0) faces
followed by deformation of edge midpoints to fit the surface to be approximated. The
vertices of coarse mesh have arbitrary valences while the subdivided mesh interiors and
boundary vertices have valence six and four, respectively. Conversely, four-to-one (4:1) face
coarsening in Eq. (3.1) is the inverse operation of quadrisection. The wavelets functions,
in this scheme, are hat functions associated with odd vertices of the mesh at resolution
j and linearly vanishing on the opposite edges. This wavelet is often called the ‘Lazy
wavelet’. The scaling functions are also hat function but with a twice wider support and
are associated with the even vertices. However, wavelets are not orthogonal to scaling
functions. Then a primal 2-ring lifting is used to construct new wavelets which are more
orthogonal to the scaling functions. These wavelets produce the coarse meshes with good
quality in terms of approximation.
Recently the wavelet multi-resolution analysis has been extended to irregular mesh
(vertices can have any valence) by Valette and Prost [Valette and Prost, 2004a]. In [Valette
50 Compression for 3-D Mesh Sequences
and Prost, 2004b], they also introduced an exact integer analysis and synthesis with the
lifting scheme based on Lazy filter-banks and the Rounding transform [Jung and Prost,
1998,Calderbank et al., 1998]. Now, the analysis is sequentially performed by the lifted
Lazy filter-banks.
Dj−1 =⌊Bj
lazyCj⌋
(3.5)
Cj−1 = AjlazyC
j +⌊αjDj−1
⌋(3.6)
where Ajlazy and Bj
lazy are Lazy analysis filters, and αj is a vj−1 ×(vj − vj−1
)matrix
chosen to ensure that Cj−1 is the best approximation of Cj . The synthesis is done by
Cj =⌈P j
lazy
(Cj−1 −
⌊αjDj−1
⌋)+Qj
lazyDj−1
⌉(3.7)
where P jlazy and Qj
lazy are Lazy synthesis filters, and b·c and d·e are the floor and ceiling
operators, respectively. These modified filter-banks make it possible to implement a loss-
less compression for the given meshes with integer coordinates. In addition, they can be
applied to irregular meshes by using an irregular subdivision scheme [Valette and Prost,
2004b]. Note that the Lounsbery’s method based on regular subdivision scheme [Louns-
bery, 1994] cannot work on irregular ones. These are the reasons why our methods use
this exact integer analysis/synthesis scheme and an irregular coarsening approach. The
notation ‘SWA’ indicates the exact integer spatial wavelet analysis in the rest of this dis-
sertation. For more details about the SWA, refer to [Valette and Prost, 2004a], [Valette
and Prost, 2004b] and [Valette, 2002].
3.2.2 TWA (Temporal Wavelet Analysis) and Its Synthesis
Fig. 3.2 shows an example of the TWA and its synthesis processes. In the wavelet
analysis process, the original signal x (n) (for 1 ≤ n ≤ N , and N is the number of
samples) is decomposed into low and high frequency band signals, y0 (n) and y1 (n), by an
analysis filter-bank, h0 (n) and h1 (n). Low and high frequency band signals correspond
to the coarse version of the original signal and its details, respectively. To obtain more
resolution levels, the analysis process can be repeatedly applied to the low frequency band
signal. In the wavelet synthesis process, the two sub-band signals are transformed into
3.2 Wavelet-based Multi-resolution Analysis 51
(a)
(b)
Figure 3.2: 2-channel (a) TWA (Temporal Wavelet Analysis) and (b) its synthesis pro-
cesses
52 Compression for 3-D Mesh Sequences
a reconstructed signal x (n) by a synthesis filter-bank, g0 (n) and g1 (n). Note that the
implementation allows lossless compression using a lifting scheme [Sweldens, 1996, Jung
and Prost, 1998,Adams and Kossentini, 2000].
In our second compression method (See Section 3.3.2), TWA is applied to whole tem-
poral sequences. Here, temporal movement of each coordinate is regarded as a 1-D signal
as in [Payan and Antonini, 2005].
3.3 Proposed Compression Methods
The proposed methods mainly use the exact integer SWA scheme [Valette and Prost,
2004b] introduced in Section 3.2.1. The SWA can efficiently reduce the spatial redundancy
and also offer a progressive transmission from the base mesh to the original one for static
irregular meshes. Clearly, this scheme can be applied to each frame of 3-D mesh sequences,
and therefore provide an adaptive transmission for mesh sequences when the bandwidth
is not fixed because it can produce mesh sequences with various spatial resolutions.
To reduce the temporal redundancy existing in the base mesh and spatial wavelet
coefficients of mesh sequences, two different techniques are used in our proposed methods.
The first proposed method employs the MDC which determines the optimal order of
the differential encoder by evaluating the variance of the prediction error. The MDC
provides simple and adaptive differential coding technique. The second employs the TWA
scheme. This approach allows spatiotemporal multi-resolution coding in a single frame
work. Although TWA was already used for geometry compression in temporal domain
[Payan and Antonini, 2005], there has been no attempt to use simultaneously both SWA
and TWA. In the following sub-sections, we describe our proposed methods in details.
3.3.1 The Proposed Compression Method Using SWA and MDC
Fig. 3.3 shows the encoding process of the proposed method using SWA and MDC tech-
niques. We assume the original mesh sequences are represented by integer coordinates.
First, each mesh frame is transformed by the exact integer SWA [Valette and Prost, 2004b].
Two kinds of major information are obtained from this transform for each frame, namely
3.3 Proposed Compression Methods 53
the connectivity and the geometry. The geometry information contains the coordinates of
the base mesh and of wavelet coefficients corresponding to each spatial resolution level.
The connectivity is the topological connections of the vertices.
The second step is connectivity coding. The connectivity information obtained from
the first step is entropy coded by an arithmetic coder [Schindler, 1998]. Note that this
process is performed only for the first frame, because the mesh sequence has constant
connectivity. The reader can refer to [Valette and Prost, 2004b] for more details of the
connectivity coding.
The third step is geometry coding to reduce the temporal redundancy. Each coordinate
of the base mesh vertices and of the spatial wavelet coefficients is processed independently
as 1-D signal with N samples along temporal direction. Here, N is the number of frames.
For a given r-th base mesh vertex c0r = (xr, yr, zr) (c0r ∈ C0 for 1 ≤ r ≤ R, and R is the
number of base mesh vertices), each coordinate is independently treated as ‘base mesh
vertex sequence’: xr (n), yr (n), and zr (n) (for 1 ≤ n ≤ N). Similarly, for a given s-
th wavelet coefficient of the j-th spatial resolution level djs =
(xj
s, yjs, z
js
)(dj
s ∈ Dj for
1 ≤ s ≤ S, and S is the number of wavelet coefficients in each spatial resolution level),
each coordinate is independently treated as ‘spatial wavelet coefficient sequence’: xjs (n),
yjs (n), and zj
s (n). Consequently, the ‘temporal sequences’ consist of the base mesh vertex
sequences and the spatial wavelet coefficient sequences. Note that MDC is applied to each
temporal sequence.
Before discussing MDC technique, the first order differential operation for the temporal
sequences is formulated by
∆(1)u (n) = u (n)− u (n− 1) , u ∈xr, yr, zr, x
js, y
js, z
js
(3.8)
The prediction errors obtained from Eq. (3.8) might still have some redundancy. Then, the
remaining redundancy could be reduced by repeatedly applying the differential operation
to the prediction errors. This is named MDC and given by
∆(m)u (n) = ∆(m−1)u (n)−∆(m−1)u (n− 1) (3.9)
where m (m ≥ 2) is the order of differential coding. Then this order can be easily deter-
mined by finding the optimal order with smaller entropy via analyzing the variance of the
54 Compression for 3-D Mesh Sequences
Figure
3.3:T
heencoding
processof
theproposed
method
usingSW
Aand
MD
Ctechniques
3.3 Proposed Compression Methods 55
prediction errors. In order to prove the correctness of our idea, we consider that the input
sequence is modeled as WSSMP (Wide Sense Stationary Markov Process). As proved
in Appendix, the first order predictor can be applied for a first order Markov process
(a first order autoregressive process, AR(1)) with a correlation coefficient existing in the
range of 0.5 < ρ < 1. The more the input samples are correlated (p-th order AR process,
AR(p)), the higher the efficiency of entropy coding is expected with higher order (p-th
order) differential coding.
To apply the MDC technique to practical 1-D temporal sequences, we use an iterative
approach as follows.
1) calculate the variance of input signal σ2u and let it be a reference variance such as
σ2ref = σ2
u;
2) initialize the parameter m as 1;
3) perform the m-th order differential operation via
∆(m)u(n) =
u(n)− u(n− 1) if m = 1;
∆(m−1)u(n)−∆(m−1)u(n− 1) if m ≥ 2;
4) calculate the variance of prediction errors through
σ2∆(m)u
= 1/N∑N
n=1
(∆(m)u(n)− µ∆(m)u
)2, where µ is mean value;
5) if σ2∆(m)u
< σ2ref , increase m (m = m+ 1), replace σ2
ref with σ2∆(m)u
and go back to
3);
6) or else stop and encode the (m− 1)-th order differential errors using the arithmetic
coder.
We can automatically find the optimal order by using this iterative approach. Note that
the entropy coding efficiency can be estimated using the variance of the prediction errors,
as mentioned in Appendix B. Fig. 3.4 shows the variances of prediction errors according
to different orders of MDC. Here, the x-coordinate of the first base mesh vertex sequence,
x1 (n) (1 ≤ n ≤ 1 024), of Face model is shown for a practical example. In this case,
the second order is selected for MDC, as its corresponding variance is the smallest. Fig.
56 Compression for 3-D Mesh Sequences
Figure 3.4: Variances (σ2) of prediction errors of Face model according to different orders
(m) of MDC. The x-coordinate of the first base mesh vertex sequence of this model is
designated for a practical example.
3.5 depicts the distributions of prediction error for the first order and the second order
differential coding. From this figure, we can easily estimate that MDC is more efficient
than FDC.
In the third step, the optimal order of each sequence should be also transmitted as
side-information whose bitrate is given by
dlog2omaxe × 3N
(bits/vertex/frame) (3.10)
where omax is the maximum optimal order. Note that the side-information is very negli-
gible.
The entropy coded connectivity and geometry including the side-information are finally
merged into the compressed bit-stream. Note that the transmitted bit-stream, in the
decoder side, can be sequentially reconstructed from the coarsest signals to finer ones with
various spatial resolutions. We call this approach SWA+MDC method.
3.3 Proposed Compression Methods 57
(a)
(b)
Figure 3.5: Prediction error distributions of Face model in terms of (a) FDC and (b) MDC
58 Compression for 3-D Mesh Sequences
3.3.2 The Proposed Compression Method Using SWA and TWA
Fig. 3.6 shows the encoding process of the proposed compression method using SWA and
TWA techniques. As the first two steps of this encoding process are identical to those
mentioned in Section 3.3.1, the peculiar steps of this scheme are described in detail. Note
that the same notations with the previous section are used for the sake of simplicity.
Up to the second step, each frame of the original mesh sequence is transformed by the
exact integer SWA [Valette and Prost, 2004b], and the connectivity information for only
the first frame is entropy coded by the arithmetic coder.
The third step performs the geometry coding to reduce the temporal redundancy.
For geometry coding, the proposed method applies TWA to the temporal sequences of
the base mesh vertices (xr (n), yr (n), and zr (n)) and of the spatial wavelet coefficients
(xjs (n), yj
s (n), and zjs (n)). Note that the efficiency of entropy coding depends on the
performance of frequency decomposition according to temporal wavelet filter-banks. Many
analysis and synthesis filter-banks have been developed [Adams and Kossentini, 2000].
We consider three well-known filter-banks such as Haar (2/2 tap), Le Gall (5/3 tap) and
Daubechies (9/7 tap) filters. These filter-banks can be applied for lossless compression of
3-D mesh sequences by implementing in integer lifting form, because the input sequences
have integer coordinates. Fig. 3.7 shows the distributions of temporal wavelet coefficients.
Here, the x-coordinate of the first base mesh vertex sequence, x1 (n) (1 ≤ n ≤ 1024), of
Face model is chosen for a practical example. From this figure, we can expect Le Gall and
Daubechies filters to be more efficient than Haar filter. We experimentally evaluate the
coding efficiency according to these filters in Section 3.4.2.
In the third step, the low and high frequency band signals obtained from both SWA
and TWA are entropy coded by the arithmetic coder.
The entropy coded connectivity and geometry information are finally merged into the
compressed bit-stream. Note that the transmitted bit-stream, in the decoder side, can be
sequentially reconstructed from the coarsest signals to finer ones with various spatial and
temporal resolutions, simultaneously. We call the approach, SWA+TWA method.
3.3 Proposed Compression Methods 59
Fig
ure
3.6:
The
enco
ding
proc
ess
ofth
epr
opos
edm
etho
dus
ing
SWA
and
TW
Ate
chni
ques
60 Compression for 3-D Mesh Sequences
(a)
(b)
Figure 3.7: Distributions of wavelet coefficients of the x-axis of the first base mesh sequence
of Face model using (a) Haar (2/2 tap) filters, (b) Le Gall (5/3 tap) filters (continued on
next page)
3.4 Simulation Results 61
(c)
Figure 3.7: (c) Daubechies (9/7 tap) filters (continued from previous page)
3.4 Simulation Results
Simulations are carried out on two 3-D irregular triangle mesh sequences, Cow (with 204
frames and 2 904 vertices/frame) and Face (with 10 002 frames and 539 vertices/frame).
The number of vertices and their connectivity information are fixed over all frames. To
apply TWA to mesh sequences, the number of frames should be an integer power of two.
Therefore, we use only the first 128 and 1 024 frames of Cow and Face, respectively.
Each coordinate is uniformly quantized, coded to 12 bits, and used for the original like
as in [Karni and Gotsman, 2004]. Fig. 3.8 shows several frames of the original mesh
sequences as examples.
To measure the quality distortion between the original mesh sequence and decom-
pressed one, we use the average of HD (Hausdorff Distance) (See Eq. (2.14)) over all
frames, called AHD (Average HD), E (Vn,V′n):
E(Vn,V′
n
)=
1N
N−1∑n=0
En
(Vn,V′
n
)(3.11)
where, Vn and V′n represent the original and decompressed surfaces of meshes at the
62 Compression for 3-D Mesh Sequences
Table 3.1: The lossless compression results of SWA+MDC method compared with SWA
and SWA+FDC methods
Method ModelBitrate
(bits/vertex/frame)
SWACow 22.40
Face 30.04
SWA+FDCCow 14.22
Face 11.49
SWA+MDCCow 13.57
Face 10.52
n-th frame, respectively.
3.4.1 SWA+MDC Method
To evaluate the coding efficiency of the proposed SWA+MDC method, we perform also
two other methods, SWA method and SWA+FDC method. Here, the SWA method does
not consider the temporal redundancy. Table 3.1 shows the lossless compression results.
As shown in this table, both SWA+FDC and SWA+MDC methods achieve quite high
compression performance comparing to SWA method, because they exploit the temporal
coherence. SWA+MDC method is more efficient than SWA+FDC method. It shows that
the first order of differential coder is not good enough to reduce the temporal redundancy.
Fig. 3.9 shows the distribution of practical optimal orders. Actually, 56% and 55%
of the temporal sequences obtained from SWA need second or third order differential
coding in Cow and Face models, respectively. Although the proposed method requires
side information to transmit the optimal order of each sequence, the amount is so small as
to be negligible. In this simulation, two bits per temporal sequence are assigned to transmit
the order. Cow and Face models need 4.69 × 10−2 and 5.86 × 10−3 (bits/vertex/frame)
for the side information, respectively.
The lossy-to-lossless compression performances according to various spatial resolutions
are evaluated in terms of AHD and bitrates. Fig. 3.10 depicts the R-D (Rate-Distortion)
3.4 Simulation Results 63
(a)
1-s
tfr
am
e(b
)64-t
hfr
am
e(c
)128-t
hfr
am
e
Fig
ure
3.8:
Ori
gina
lm
esh
sequ
ence
s,(a
)-(c
)C
owm
odel
s(c
onti
nued
onne
xtpa
ge)
64 Compression for 3-D Mesh Sequences
(d)
1-st
fram
e(e)
512-th
fram
e(f)
1024-th
fram
e
Figure
3.8:(d)-(f)
Facem
odels(continued
fromprevious
page)
3.4 Simulation Results 65
(a)
(b)
Figure 3.9: Distributions of practical optimal orders of the differential coder in
SWA+MDC for (a) Cow and (b) Face models
66 Compression for 3-D Mesh Sequences
(a)
(b)
Figure 3.10: R-D curves of SWA, SWA+FDC and SWA+MDC methods for (a) Cow and
(b) Face models
3.4 Simulation Results 67
curves of SWA, SWA+FDC and SWA+MDC methods. Cow and Face models are decom-
posed into 19 and 11 spatial levels. Here, we present the results of five highest resolution
levels. As shown in Fig. 3.10, the proposed method enables to reconstruct the mesh se-
quences at various spatial resolutions. Similar to lossless compression results, SWA+MDC
method has better coding efficiency than the others.
3.4.2 SWA+TWA Method
For the evaluation of SWA+TWA method, three different temporal wavelet filter-banks
– Haar, Le Gall and Daubechies filters – are applied to the temporal sequences obtained
from SWA. Each temporal sequence is decomposed into several sub-bands in the dyadic
form using lifting scheme [Daubechies and Sweldens, 1998]. The lossless coding efficiency is
evaluated according to different temporal wavelet decomposition levels as shown in Table
3.2. For comparison, we also present the compression results of the method which applies
only TWA to original mesh sequences. We denote it TWA method. As shown in this table,
TWA method has poor performance. It means that the spatial redundancy should also be
exploited. In particular, Cow model have relatively high spatial redundancy. SWA+TWA
method has lower bitrates than TWA method. The coding efficiency depends on the kind
of temporal wavelet filter-banks. Le Gall and Daubechies filter-banks are more efficient
than Haar filter-banks. The bitrate decreases as a function of the decomposition level.
However the performance of SWA+TWA is slightly lower than that of SWA+MDC.
Lossy-to-lossless compression performances are evaluated by R-D curves. Fig. 3.11
shows the R-D curves according to different spatial resolutions and three temporal wavelet
filter-banks. Here, temporal sequences are reconstructed in full temporal resolution. As
shown in Fig. 3.11, Le Gall and Daubechies filters have similar coding efficiency and are
more efficient than Haar filter at all spatial resolutions. Although SWA+TWA method has
slightly lower performance than SWA+MDC, it provides both spatial and temporal scal-
ability. Fig. 3.12 shows the R-D curves according to different spatiotemporal resolutions.
Here, temporal sequences are decomposed into five levels using Daubechies filter-banks.
This figure demonstrates that we can properly select the bitrates at various spatiotempo-
ral resolutions. However, the bitrates should be carefully selected for the mesh sequences
68 Compression for 3-D Mesh Sequences
Table 3.2: The lossless compression results of SWA+TWA method compared with TWA
scheme according to temporal wavelet decomposition levels and three temporal wavelet
filter-banks: Haar (2/2 tap), Le Gall (5/3 tap) and Daubechies (9/7 tap) filters
# of TWA
LevelsTWA Filter Model
Bitrate (bits/vertex/frame)
Method
TWA SWA+TWA
1
HaarCow 32.78 18.21
Face 24.84 20.77
Le GallCow 30.19 16.39
Face 22.05 19.01
DaubechesCow 29.93 16.53
Face 22.13 19.44
3
HaarCow 30.60 16.30
Face 17.52 14.99
Le GallCow 27.16 13.92
Face 13.86 12.58
DaubechiesCow 26.49 13.93
Face 13.47 12.95
5
HaarCow 30.43 16.11
Face 16.06 13.83
Le GallCow 27.08 13.79
Face 12.52 11.54
DaubechiesCow 26.34 13.73
Face 12.12 11.83
3.5 Summaries 69
having large movement such as Cow model.
3.5 Summaries
In this chapter, we proposed two geometry compression methods for irregular 3-D mesh
sequences with constant connectivity. To reduce the spatial redundancy, both methods
employ an exact integer spatial wavelet analysis (SWA). Temporal redundancy is reduced
by multi-order differential coding (MDC) and temporal wavelet analysis (TWA), respec-
tively, in two proposed methods. The method SWA+MDC offers spatial scalability and
the method SWA+TWA provides spatiotemporal multi-resolution coding. In addition,
both methods enable lossy-to-lossless compression. The method SWA+MDC has slightly
better performances than SWA+TWA method in both lossless and lossy compressions.
70 Compression for 3-D Mesh Sequences
(a)
(b)
Figure 3.11: R-D curves of SWA+TWA method at different spatial resolutions where three
temporal wavelet filter-banks are used for (a) Cow and (b) Face models
3.5 Summaries 71
(a)
(b)
Figure 3.12: R-D curves of SWA+TWA method at different spatiotemporal resolutions,
where the temporal sequences are decomposed into five levels using Daubechies filter banks
for (a) Cow and (b) Face models
72 Compression for 3-D Mesh Sequences
Chapter 4
Joint Watermarking and
Compression for 3-D Mesh
Sequences
This chapter presents a joint watermarking and compression method for 3-D mesh se-
quences. Our approach is mainly based on the SWA (Spatial Wavelet Analysis) + TWA
(Temporal Wavelet Analysis) compression scheme proposed in Section 3.3.2. This com-
pression scheme allows us not only to efficiently compress mesh sequences but also to
promptly transmit them as various versions with spatiotemporal multi-resolutions. For
the copyright protection of mesh sequences, a watermarking technique expanded from our
3-D static mesh watermarking scheme proposed in Section 2.2.2 is applied to the interme-
diate step of the compression process. The variance of spatiotemporal wavelet coefficients
belonging to specific spatial and temporal sub-bands, to embed watermark, is modified by
the same histogram mapping function used in Section 2.2.2. The hidden watermark can
be quite robust against several intra-frame and inter-frame attacks because a statistical
feature is employed as the watermark carrier in the proposed method. Through simula-
tions, we prove that our approach enables to efficiently compress 3-D mesh sequences and
to strictly protect their ownership in a single framework.
74 Joint Watermarking and Compression
4.1 Introduction and State of the Arts
Watermarking and data compression have been mainly treated on independent frame-
works. Their combination has not been briskly studied due to an opposition of two tech-
nologies; watermarking within compressed domain could seriously affect the auditory or
visual quality of reconstructed data, and conversely lossy compression might be an attack
which interferes with the ownership assertion of watermarked data. Nevertheless, digital-
ized data is usually distributed through a network channel with limited bandwidth, and
at the same time the owner of this data never wants that it is illegally used by pirates.
Consequently, these two research topics should be simultaneously considered.
Joint watermarking and compression system can be designed by two major strategies.
One is to sequentially perform compression after watermarking (and vice versa) [Denis
et al., 2005], and the other is to embed watermark in the intermediate process of compres-
sion [Wang et al., 2004,Xu et al., 2001,Siebenhaar et al., 2001,Wong and Au, 2002,Suhail
and Obaidat, 2001,Seo et al., 2001,Li and Zhang, 2003,Su et al., 2001,Hartung and Girod,
1998,Kang et al., 2004,Wang et al., 2005,Wang and Pearmain, 2006]. The former allows
an easy and simple implementation because any existing compression (or watermarking)
algorithm can be combined with any existing watermarking (or compression) algorithm.
However, it could be inefficient from the viewpoint of system complexity since the time
and computational costs for entire processes are nearly same as the sum of each cost which
is produced by watermarking and compression. Clearly, the latter is more efficient than
the former because the watermark embedding can be completed before the compressed
bit-stream is entirely generated.
Several joint watermarking and compression techniques for audio clips [Wang et al.,
2004,Xu et al., 2001,Siebenhaar et al., 2001], two-dimensional (2-D) still images [Wong
and Au, 2002, Suhail and Obaidat, 2001, Seo et al., 2001, Li and Zhang, 2003, Su et al.,
2001], and 2-D video sequences [Hartung and Girod, 1998,Kang et al., 2004,Wang et al.,
2005,Wang and Pearmain, 2006] have been introduced, being encouraged by some inter-
national coding standards such as JPEG (Joint Photographic Experts Group)/JPEG-2000
and MPEG (Moving Picture Experts Group). Wang and Chao [Wang et al., 2004] pre-
4.1 Introduction and State of the Arts 75
sented an audio watermarking method which embeds watermark into the low frequency
coefficients of MDCT (Modified Discrete Cosine Transform) obtained from the analysis
filter-bank of MP3 (MPEG-1 Layer-3) coder. In [Xu et al., 2001], another audio water-
marking scheme was proposed. It first extracts several frames from compressed bit-stream,
then selects specific frames according to the features of audio content and the masking
threshold of HAS (Human Auditory System). The watermark is embedded into the se-
lected frames via bit hopping and hiding techniques. Siebenhaar et al. [Siebenhaar et al.,
2001] also designed an audio watermarking system for MPEG-2/4 AAC coding. It embeds
watermark into the transform coefficients before quantization step by using the spread
spectrum technique [Cox et al., 1997]. Although these schemes [Wang et al., 2004, Xu
et al., 2001, Siebenhaar et al., 2001] are robust against MP3 or AAC compression with
various bit-rates, the robustness against other common attacks, for example, adding noise,
down sampling, band-pass filtering, echo addition, equalization and so on, was not vali-
dated. Wong and Au [Wong and Au, 2002] proposed a blind watermarking method for
JPEG compressed image. Their algorithm embeds watermark into a vector set obtained
from the coefficients of 8×8 block DCT by using spread spectrum technique. It also used
an iterative watermark embedding technique for the purpose of robustness. In [Suhail
and Obaidat, 2001,Seo et al., 2001,Su et al., 2001], some JPEG-2000 based watermarking
schemes were introduced. Suhail and Obaidat [Suhail and Obaidat, 2001] used the spread
spectrum technique for watermark embedding. They implanted the watermark into low
frequency coefficients of DWT (Discrete Wavelet Transform) by using a β function which
represents the characteristics of HVS (Human Visual System). On the other hand, Seo
et al. [Seo et al., 2001] proposed a method to embed watermark on the intermediate step
of lifting. Their method can achieve a quite secure system as it allows us to choose a
certain sub-band as well as lifting step. In [Su et al., 2001], Su et al. presented another
JPEG-2000-based approach which embeds watermark into some significant wavelet coef-
ficients. This algorithm can extract watermark from a progressive decoding step or from
a ROI (Region of Interest) by properly grafting their watermark embedding scheme into
the EBCOT (Embedded Block Coding with Optimized Truncation) technique. Hartung
and Girod [Hartung and Girod, 1998] proposed a watermarking method for uncompressed
76 Joint Watermarking and Compression
video and compressed MPEG-2 video. Concentrating on compressed video, the watermark
is embedded into 8×8 DCT-block by using the spread spectrum technique. Their method
causes distortion propagation due to the watermark embedded in every I(Intra)-frames.
Although it applies a drift compensation technique to cope with this problem, the addi-
tional processing increases the system complexity. Kang et al. [Kang et al., 2004] proposed
a robust watermarking scheme for MPEG video. This algorithm embeds watermark into
I-frame and P(Predicted)-/B(Bi-directional)-frames by applying different methods, re-
spectively. For I-frame watermarking, it used the RCOB (Relative Complexity of a Block)
from quantized DCT coefficients and the QP (Quantization Parameter) from rate control
as watermark carrier. For P-/B-frames watermarking, the method directly altered VLC
(Variable Length Coding) stream. The authors experimentally demonstrated that their
algorithm is robust against additive Gaussian noise, low-pass filtering, median filtering,
and histogram equalization as well as MPEG re-encoding. Another MPEG-based video
watermarking method [Wang et al., 2005] embeds watermark by modifying the direction
of motion vector obtained from half-pixel accuracy on the basis of one-pixel accuracy. This
method could not be robust against frame dropping attack because it utilizes the motion
vectors as the watermark carrier. Most of MPEG video watermarking are performed by
altering the 8×8 block DCT coefficients [Hartung and Girod, 1998, Kang et al., 2004].
Clearly, these algorithms are very fragile to synchronization attack such as cropping. To
cope with this problem, Wang and Pearmain [Wang and Pearmain, 2006] introduced a
MPEG-2 video watermarking methods which embeds repeatedly the same watermark bit
into the same row (or the same column) of coefficients belonging to 8×8 DCT-block.
In [Wang and Pearmain, 2006], the authors also proposed two other techniques which are
robust against down-sampling and frame dropping, respectively. The second scheme em-
beds watermark by altering only the low frequency coefficients obtained from full DCT.
This method allows the hidden watermark to be robust against down-sampling attack
because the spatial down-scaling of a frame has roughly equivalent effect to the trunca-
tion of high frequency band in its full DCT domain. For the robustness against frame
dropping attack, the third scheme first segments the picture frames into several groups
and embeds the same watermark into the same group. Their techniques provide good
4.1 Introduction and State of the Arts 77
solutions to cope with major attacks which should be considered for robust video wa-
termarking. Unlike the cases of universal multimedia data such as audio clips, 2-D still
images and 2-D video sequences, the investigations of joint watermarking and compression
schemes for 3-D graphics data have hardly proceeded. Denis et al. [Denis et al., 2005]
presented a watermarking method for compressed 3-D static meshes. Their algorithm first
compresses original meshes by using a sub-division-based coding technique [Lavoue et al.,
2005] and embeds watermark by modifying the transform coefficients obtained from the
spectral analysis [Karni and Gotsman, 2000]. This method could not be efficient since
watermarking and compression are individually performed in different domains.
In this chapter, we address a joint watermarking and compression technique for 3-D
mesh sequences. To our knowledge, there have been no attempts for this kind of 3-D
graphics data. From the view point of joint watermarking and compression, the following
requirements should be considered: low complexity, compression gain, invisibility and
robustness.
• Low complexity : As previously mentioned, a watermark embedding process should
be included to the intermediate step of a compression procedure for the purpose of
low system complexity.
• Compression gain : Clearly, the compression module should be effectively able to
reduce the spatial and temporal redundancies. The compression ratio is generally
dependent on the prediction model to be encoded by an entropy coder. Consequently,
the watermarking scheme should not disturb the well-produced prediction model.
• Invisibility (low distortion of visual quality): A joint system should embed
watermark information and control the compression ratio minimizing the distortion
of visual quality.
• Robustness: The watermark hidden into 3-D sequences could suffer from two kinds
of attacks: intra-frame and inter-frame attacks. The former includes whole attacks
which are considered in 3-D static mesh watermarking, i.e., distortion attacks such
as adding noise, uniform quantization, smoothing, simplification and sub-division,
and distortion-less attacks such as vertex re-ordering and similarity transforms (See
78 Joint Watermarking and Compression
Section 2.1). The latter includes frame dropping. The watermarking scheme should
be designed to be robust against intra-frame and inter-frame attacks.
Considering the above requirements, we propose a joint watermarking and compres-
sion method for 3-D mesh sequences. The proposed scheme is mainly based on the SWA
(Spatial Wavelet Analysis) + TWA (Temporal Wavelet Analysis) compression scheme
presented in Section 3.3.2. This compression method allows us not only to efficiently
compress mesh sequences but also to promptly transmit them as various versions with
spatiotemporal multi-resolutions. The proposed method embeds watermark, before en-
tropy coding, into the spatiotemporal wavelet coefficients obtained from SWA and TWA.
For the robustness and invisibility of watermark, specific sub-bands are selected in spatial
and temporal wavelet domain, respectively, and their corresponding signals are modified.
To embed a watermark bit, the proposed method changes the variance of a selected 1-D
temporal sequence which consists of spatiotemporal wavelet coefficients belonging to the
same vertex index and the same axis over all mesh frames by using the same histogram
mapping function used in Section 3.3.2. The proposed method can reduce the system
complexity because this watermark embedding scheme is performed at the intermediate
step of compression. Besides, the watermark can be quite robust against intra-frame and
inter-frame attacks since a statistical feature is employed as the watermark carrier. The
watermark is extracted by an oblivious watermark detection technique.
The rest of this chapter is organized as follows. The proposed joint watermarking and
compression method is presented in Section 4.2. Section 4.3 shows the simulation results
in terms of compression performances and robustness against intra-frame and inter-frame
attacks. Finally, Section 4.4 summarizes this chapter.
4.2 Proposed Joint Watermarking and Compression Method
for 3-D Mesh Sequences
To provide an efficient combined watermarking and compression system for 3-D mesh
sequences, we apply a watermarking method expanded from our 3-D mesh watermarking
technique proposed in Section 2.2.2 to an intermediate step of SWA+TWA compression
4.2 Proposed Joint Watermarking and Compression Method 79
scheme presented in Section 3.3.2.
SWA+TWA scheme can efficiently reduce the spatial and temporal redundancies. It
uses wavelet coefficients as good prediction models for entropy coding; the spatial and
temporal wavelet coefficients can be approximated to Laplacian distribution with sharp
peak [Cho et al., 2006b]. In addition, SWA+TWA scheme enables a flexible transmission
at different conditions of bandwidth because it is able to reconstruct mesh sequences with
various spatiotemporal resolutions. From the viewpoint of watermarking, wavelet-based
multi-resolution analysis provides a suitable watermark carrier for robust and invisible
watermarking since we can embed the watermark with relatively high energy into a specific
sub-band [Cox et al., 2001]. This is the reason why we employ SWA+TWA technique as
the base framework of our proposed method.
To guarantee the robustness against intra-frame and inter-frame attacks, a watermark-
ing technique which uses statistical feature of signals is applied to the intermediate step of
the compression process. This watermarking method implants watermark by altering the
distribution of specific sub-band (high or middle frequency bands) signals after SWA and
TWA steps of the compression scheme. The main idea is as follows. We first translate the
distribution of low frequency coefficients in order that its mean value is mapped onto zero.
It means that the translated coefficients can be divided into two subsets which have nearly
same number of positives (+) and negatives (−), respectively. Next, the high (or middle)
frequency band signals are selectively classified into two subsets referring to the corre-
sponding low frequency coefficients. Since wavelet transform simultaneously provides the
time (or spatial) and frequency information, we can easily determine the high frequency
coefficient that corresponds to a low frequency coefficient. Note that the low frequency
coefficients are used just to determine two subsets of high frequency coefficients and the
selected high frequency coefficients are employed to embed watermark. This is caused
by the facts that the low frequency sub-band is hardly changed through common signal
processing, and that HVS is very sensitive to small alterations in the low frequency. The
high frequency coefficients in two subsets are modified by using the histogram mapping
function, such that one subset has bigger (or smaller) variance than the other according
to the watermark bit to be embedded. Fig. 4.1 illustrates how to modify the distributions
80 Joint Watermarking and Compression
Figure 4.1: Proposed watermarking method by changing the variances of high frequency
sub-band signal: (a) distributions of two subsets, A and B, of high frequency sub-band
signal, the modified distributions of the two subsets for embedding watermark (b) +1 and
(c) −1, where, we assume that the initial two subsets have the same Laplacian distributions
for the simple illustration.
of the two subsets. As the proposed method modifies the high frequency band coefficients
that correspond to the low frequency coefficients, it can achieve good performances both
in terms of the robustness and invisibility of watermark. In the following sub-sections,
we describe on the entire procedure of our joint watermarking and compression system
according to the functional blocks.
4.2.1 Encoding Process Including Compression and Watermark Embed-
ding
Fig. 4.2 shows the encoding process including compression and watermark embedding.
The same notations with Section 2.2 and Section 3.3 are used for the sake of simplicity.
First, each mesh frame is transformed by the exact integer SWA. Two kinds of major
information – geometry and connectivity – are obtained from this transform for each frame.
4.2 Proposed Joint Watermarking and Compression Method 81
Fig
ure
4.2:
The
enco
ding
proc
ess
ofth
epr
opos
edjo
int
wat
erm
arki
ngan
dco
mpr
essi
onsc
hem
e
82 Joint Watermarking and Compression
The geometry information contains the coordinates of the base mesh and of wavelet coef-
ficients corresponding to each spatial resolution level. The connectivity is the topological
connections of the vertices.
The second step is connectivity coding. The connectivity information obtained from
the first step is entropy coded by an arithmetic coder [Schindler, 1998]. Note that this
process is performed only for the first frame because we assume that the mesh sequence
has a constant connectivity. The reader can refer to [Valette and Prost, 2004b] for more
details of the connectivity coding.
The third step performs TWA. Each coordinate of the base mesh and of the spatial
wavelet coefficients is processed independently as 1-D signal with N samples along tem-
poral direction [Payan and Antonini, 2005]. Here, N is the number of frames. For a given
r-th base mesh vertex c0r = (xr, yr, zr) (c0r ∈ C0 for 1 ≤ r ≤ R, and R is the number of base
mesh vertices), each coordinate is independently treated as ‘base mesh vertex sequence’:
xr (n), yr (n), and zr (n) (for 1 ≤ n ≤ N). Similarly, for a given s-th wavelet coefficient
of the j-th spatial resolution level djs =
(xj
s, yjs, z
js
)(dj
s ∈ Dj for 1 ≤ s ≤ S, and S is
the number of the wavelet coefficients in each spatial resolution level), each coordinate is
independently treated as a ‘spatial wavelet coefficient sequence’: xjs (n), yj
s (n), and zjs (n).
Note that TWA is applied to each temporal sequence u (n) (u ∈ xr, yr, zr, xjs, y
js, z
js). In
the third step, the temporal sequence u (n) is decomposed into low and high frequency
band signals, v0 (n) and v1 (n) (where v is a representative vector to denote the temporal
wavelet coefficients of u (that is, ‘spatiotemporal wavelet coefficient sequences’), by TWA
scheme, assuming that only two-channel sub-band decomposition is applied for the sim-
plicity. Clearly, more temporal resolutions can be produced by repeatedly applying TWA
to the low frequency band.
The fourth step performs the watermark embedding. In this step, specific spatiotempo-
ral wavelet coefficient sequences vp (vp0 , v
p1 ∈ vp ∈ v) are firstly selected to guarantee the
invisibility of watermark and only the selected sequences vp are used to embed watermark.
Fig. 4.3 shows the watermark embedding process in detail. This process is independently
applied to each selected temporal sequence. It means that we can embed a watermark bit
into a single temporal sequence. The high frequency band signals vp1 (n) are mapped into
4.2 Proposed Joint Watermarking and Compression Method 83
Fig
ure
4.3:
The
wat
erm
ark
embe
ddin
gpr
oces
s
84 Joint Watermarking and Compression
the normalized range of [−1, 1]. It is denoted by vp1 (n). As reported in 3, the PDF of
vp1 (n) is modeled by Laplaian distribution. Then, the high frequency coefficients vp
1 (n) is
selectively classified into two subsets A and B referring to vp0 (n), as follows.
A =vp1 (l) |l ∈ Ω+
for Ω+ =
l|vp
0 (l)− µvp0> α · σvp
0
B =
vp1 (l) |l ∈ Ω−
for Ω− =l|vp
0 (l)− µvp0< −α · σvp
0
(4.1)
where, the distribution of low frequency coefficients is translated by means of vp0 (l)− µvp
0
in order that two subsets Ω+ and Ω− (equivalently A and B) have nearly same number of
coefficients1, and α · σvp0
is a threshold value to select the high frequency band coefficients
of which the corresponding low frequency band coefficients have high energy. Assuming
that low frequency band has Gaussian distribution, about 31.7% of high frequency band
coefficients are selected for α = 1. That is, the trade-off between robustness and trans-
parency of watermark can be adjusted by determining α. Note that two subsets A and
B now have the same distribution very close to Laplacian over the interval [−1, 1]. The
coefficients in each subset are transformed by the histogram mapping function proposed
in Section 2. In Section 2, this function has been originally used to modify the variance
of uniform distribution. We prove that it can be also applied to Laplacian distribution
in Appendix A.3. The variance of the two subsets is modified according to watermark
bit. To embed watermark ω = 1 (or ω = −1), the variances of subsets A and B, σ2A and
σ2B, become respectively greater (or smaller) and smaller (or greater) than that of whole
normalized high frequency coefficients σ2vp1:
σ2A > (1 + β) · σ2
vp1
and σ2B < (1− β) · σ2
vp1
if ω = +1
σ2A < (1− β) · σ2
vp1
and σ2B > (1 + β) · σ2
vp1
if ω = −1 (4.2)
where β(0 < β < 1) is the watermark strength factor that can control the trade-off between
robustness and the transparency of watermark. To change the variance to the desired level,
the parameter k in Eq. (A.9) cannot be exactly calculated in practical environments. For
such reasons, we use an iterative approach to find proper k as follow.
1After the classification of two subsets A and B, the low frequency coefficients returns to the original
values using vp0 (l) + µv
p0.
4.2 Proposed Joint Watermarking and Compression Method 85
For embedding ω = +1 into a temporal sequence:
1) Calculate the variance of vp1 through σ2
vp1
= 1L
∑Ll=1 v
p1 (l)2, where L is the
number of coefficients in vp1 ;
2) Initialize the parameter k as 1;
3) Transform the high frequency band signals belonging to two subsets A and B
by vp′
1 = sign (vp1) |v
p1 |
k;
4) Calculate the variance of A′ and B′ through
σ2A′ = 1
LA
∑LAl=1
vp′
1 (l)2
, where vp′
1 (l) ∈ A′ and LA is the number of coeffi-
cients in A′
σ2B′ = 1
LB
∑LBl=1
vp′
1 (l)2
, where vp′
1 (l) ∈ B′ and LB is the number of coeffi-
cients in B′;
5) If σ2A′ < (1 + β) · σ2
vp1, decrease k (k = k −∆k) and go back to 3);
6) If σ2B′ > (1− β) · σ2
vp1, increase k (k = k + ∆k) and go back to 3);
7) Replace the high frequency band signals with transformed ones using vp1 = vp′
1 ;
8) End.
For embedding ω = −1 into a temporal sequence:
5) If σ2A′ > (1− β) · σ2
vp1, increase k (k = k + ∆k) and go back to 3);
6) If σ2B′ < (1 + β) · σ2
vp1, decrease k (k = k −∆k) and go back to 3);
All high frequency band coefficients including modified coefficients vp′
1 are mapped onto
the original range. Note that the low frequency band coefficients vp0 are kept intact in the
watermark embedding process.
In the sixth step, the watermarked spatiotemporal wavelet coefficient sequences are
entropy coded by the arithmetic encoder.
The entropy coded connectivity and geometry information are finally merged into the
compressed bit-stream.
86 Joint Watermarking and Compression
4.2.2 Decoding Process Including Decompression and Watermark Ex-
traction
Fig. 4.4 shows the decoding process including decompression and watermark extraction.
This process is performed by the inverse procedure of the encoding. The compressed bit-
stream is entropy decoded and the spatiotemporal wavelet coefficient sequences on which
the watermark is embedded are obtained in the first and second steps. From the first step,
connectivity information is also decompressed.
The third step extracts the hidden watermark from the spatiotemporal wavelet co-
efficient sequences. Fig. 4.5 shows the watermark extraction process. Similar to the
watermark embedding process, two subsets of high frequency band coefficients, A′′ and
B′′, are obtained from each watermarked temporal sequence. And then, the variances
of the two subsets, σ2A′′ and σ2
B′′ , are respectively calculated and compared. The hidden
watermark ω′′ is extracted by means of
ω′′ =
+1, if σ2A′′ > σ2
B′′
−1, if σ2A′′ < σ2
B′′
(4.3)
Note that the watermark detection process does not require the original signal.
In the fourth step, all spatiotemporal wavelet coefficient sequences are inversely trans-
formed by the TWS (Temporal Wavelet Synthesis) process. From this step, the temporal
sequences of the base mesh vertex and of the spatial wavelet coefficients are obtained.
Finally, the reconstructed mesh sequence is obtained by applying the SWS (Spatial
Wavelet Synthesis) process.
4.3 Simulation Results
Simulations were carried out on two 3-D irregular triangle mesh sequences, Cow (with 128
frames and 2 904 vertices/frame) and Face (with 1 024 frames and 539 vertices/frame)
which were used in Section 3.4. The number of vertices and their connectivity information
are fixed over all frames.
To measure the quality distortion between the original mesh sequence and decom-
pressed one, we use AHD (Average Hausdorff Distance), E (Vn,V′n) (See Eq. (3.11)).
4.3 Simulation Results 87
Fig
ure
4.4:
The
deco
ding
proc
ess
ofth
epr
opos
edjo
int
wat
erm
arki
ngan
dco
mpr
essi
onsc
hem
e
88 Joint Watermarking and Compression
Figure
4.5:T
hew
atermark
extractionprocess
4.3 Simulation Results 89
The robustness of the watermark is measured in terms of correlation between the original
watermark and the extracted one (See Eq. (2.15)).
Table 4.1 shows parameters used in our simulations. As mentioned in Section 4.2,
the proposed method can embed watermark into specific sub-bands in both spatial and
temporal wavelet domain. Cow and Face are decomposed into 19 and 11 levels using the
exact integer SWA scheme [Valette and Prost, 2004b] and Le Gall (5/3 tap) filter bank with
6 decomposition levels is applied for TWA and its synthesis. Assuming that we transmit
the original mesh sequences with full spatiotemporal resolutions, middle frequency bands
can be a good watermark embedding region in terms of robustness and imperceptibility
[Cox et al., 2001]. For that reason, to embed watermark information, we selected three sub-
bands in spatial wavelet domain and one sub-band in temporal wavelet domain as listed in
Table 4.1. In our method, the number of watermark bits is dependent on the number of 1-D
temporal sequences: base mesh vertex sequences and spatial wavelet coefficient sequences.
It means that the amount of watermark can be increased by embedding watermark into
multiple sub-bands in the spatial wavelet domain. This is the reason why we selected
three middle frequency bands to embed watermark. However, the candidate sub-band to
embed watermark should be selected towards lower frequency bands in order to guarantee
robustness of hidden watermark when the original mesh sequence is transmitted in worse
condition of bandwidth. The threshold α to produce subsets A and B was differently
determined according to the frame lengths of two test mesh sequences. Note that bigger α
can be used for watermark transparency when the low frequency band in temporal wavelet
domain has more coefficients. Cow and Face respectively have 4 and 32 coefficients in
each low frequency band. In Table 4.1, we also listed the average numbers of coefficients
belonging to two subsets Ω+ and Ω−. In these simulations, the numbers of coefficients in
A and B are exactly equal to eight times of those in Ω+ and Ω−, respectively. Considering
visual quality, the strength factors of watermark β were properly determined according
to the spatial resolution levels, that is, we embedded more robust watermark into higher
frequency band because most energy of signals concentrates around the low frequency
band. Fig. 4.6 depicts several frames of the watermarked mesh sequences as examples.
The evaluation results of compression performance and watermark robustness when
90 Joint Watermarking and Compression
Table
4.1:Param
etersused
inthe
simulations
Model
SWA
levelsto
embed
waterm
ark
(#of
waterm
ark)
TW
Alevel
to
embed
waterm
ark
Threshold
α
(Avg.
#of
Ω+,
Avg.
#of
Ω−)
Strength
factorβ
(SWA
level)
Cow
8th,9th,
10th(105bits)
5th0.00
(2.04,1.96)
0.25(8th),
0.30(9th),
0.35(10th)
Face5th,
6th,7th
(75bits)5th
1.00(5.12,
5.17)0.35
(5th),0.40
(6th),0.45
(7th)
4.3 Simulation Results 91
(a)
1-s
tfr
am
e(b
)64-t
hfr
am
e(c
)128-t
hfr
am
e
Fig
ure
4.6:
Wat
erm
arke
dm
esh
sequ
ence
s,(a
)-(c
)C
owm
odel
s(c
onti
nued
onne
xtpa
ge)
92 Joint Watermarking and Compression
(d)
1-st
fram
e(e)
512-th
fram
e(f)
1024-th
fram
e
Figure
4.6:(d)-(f)
Facem
odels(continued
fromprevious
page)
4.3 Simulation Results 93
Table 4.2: Evaluation of compression performance and watermark robustness when no
attack
Model AHD
Compression performance Watermark
robustness(bits/vertex/frame)
SWA+TWA Joint method Corr
Cow 9.89 13.79 13.82 1.00
Face 1.22 11.54 11.53 1.00
no attacks are listed in Table 4.2 2. As shown in this table, the quality distortions caused
by embedding watermark are very small. Besides, the hidden watermark can be extracted
perfectly from all watermarked models. From the viewpoint of compression performance,
our watermarking method might affect the coding efficiency since it changes the variance
of the prediction models. It means that the bitrate could increase (or decrease) when the
variance of prediction models decreases (or increases). However, as the binary watermark
information is generated such that it has nearly uniform distribution, we can prevent
the hidden watermark from degrading the compression performance. Comparing with
SWA+TWA scheme in which only compression is performed, the compression performance
is nearly same although the prediction models (spatiotemporal wavelet coefficients) for
entropy coding are modified by watermark embedding process.
4.3.1 Attack Simulations
To evaluate the robustness of watermark against intra-frame attacks, some distortion and
distortion-less attacks (See Section 2.1) were applied to each frame of the watermarked
mesh sequences. Table 4.3 shows the performances of watermark extraction after intra-
frame attacks. For evaluating the resistance to distortion attacks, multiplicative binary
random noise, uniform quantization and smoothing were carried out. Binary random noise
was added to each vertex norm in each watermarked mesh frame with three different error
2Detailed lossy-to-lossless compression results are reported in Section 3.4. SWA+TWA method origi-
nally enables lossless compression. However, this joint watermarking and compression method can provide
near-lossless compression due to the watermark embedding.
94 Joint Watermarking and Compression
rates: 1%, 5% and 10% [Yu et al., 2003b]. Here, the error rate represents the noise ampli-
tude as a fraction of the maximum vertex norm of each mesh frame. We performed each
noise attack five times using different random seeds and reported the median. To evalu-
ate the robustness against uniform quantization attacks, three different quantization rates
were applied to each watermarked mesh frame; each coordinate of vertices was represented
with 8bits, 6bits and 4bits. For evaluating the robustness against smoothing attacks [Field,
1988], three different pairs of iteration and relaxation were applied. We denote these fairs
as (# of iteration,relaxation) in Table 4.3. The effects of these distortion attacks are shown
in Fig. 4.7. The proposed method is fairly resistant to the noise, quantization and smooth-
ing attacks. This is due to the fact that low frequency band signals to be used to classify
middle frequency band signals into two subsets are not easily changed by these attacks
and also that the proposed method uses statistical feature as watermark carrier. However,
the robustness for Face is not as good as that of Cow. Note that it can be improved by
adjusting the threshold α and the strength factor β. In Section 4.3.2, we discuss this topic
in more detail. To evaluate the robustness of our methods against distortion-less attacks,
vertex re-ordering and similarity transforms were carried out. Vertex re-ordering attack
was performed iteratively 100 times, also changing the seed of random number generator
in each iteration. Here, the constant connectivity over all frames was kept intact by ap-
plying the same seed to whole frames in each iteration. Similarity transforms were carried
out with many combinations of rotation, uniform scaling and translation factors. Similar
to vertex re-ordering, the same factors were applied to whole frames in each trial. It is not
necessary to tabulate watermark detection performances because the hidden watermark
information was perfectly extracted after these distortion-less attacks.
To evaluate the robustness against inter-frame attack, we applied frame dropping with
three different ratios, 1/10, 1/5 and 1/2, to watermarked mesh sequences. Here, a ratio
1/10, 1/5 and 1/2 means that one frame is dropped per 10, 5 and 2 frames, respectively. For
watermark extraction, dropped frame was interpolated by bilinear interpolation technique.
It is also not necessary to tabulate watermark detection performances because the hidden
watermark information was perfectly extracted after this inter-frame attack. These results
are caused by the fact that the proposed method employ statistical feature to embed
4.3 Simulation Results 95
(a)
1-s
tfr
am
e(b
)64-t
hfr
am
e(c
)128-t
hfr
am
e
Fig
ure
4.7:
Cow
mod
elat
tack
edby
(a)-
(c)
mul
tipl
icat
ive
bina
ryno
ise
wit
her
ror
rati
oof
1%(c
onti
nued
onne
xtpa
ge)
96 Joint Watermarking and Compression
(d)
1-st
fram
e(e)
64-th
fram
e(f)
128-th
fram
e
Figure
4.7:(d)-(f)
6bits/coordinatequantization
(continuedfrom
previouspage
andcontinued
onnext
page)
4.3 Simulation Results 97
(g)
1-s
tfr
am
e(h
)64-t
hfr
am
e(i
)128-t
hfr
am
e
Fig
ure
4.7:
(g)-
(i)
smoo
thin
gw
ith
iter
atio
nof
120
and
rela
xati
onof
0.03
(con
tinu
edfr
ompr
evio
uspa
ge)
98 Joint Watermarking and Compression
Table 4.3: Evaluation of robustness against intra-frame attacks
Intra-frame
attackAttack intensity
Model
Cow Face
AHD Corr AHD Corr
Multiplicative
binary noise
1% 17.29 1.00 13.60 1.00
5% 57.56 0.94 63.11 0.49
10% 107.48 0.81 115.16 0.17
Uniform
quantization
8bits 739.16 1.00 1924.09 1.00
6bits 803.13 1.00 1108.52 0.89
4bits 826.51 0.96 1143.99 0.49
Smoothing
(120,0.03) 1452.24 0.96 2136.67 0.81
(360,0.03) 1479.37 0.79 2181.46 0.60
(600,0.03) 1500.57 0.68 2204.75 0.49
Average 775.92 0.90 1210.15 0.66
watermark.
4.3.2 Parameters for Robustness
In this section, we analyze two parameters that can be adjusted to improve the watermark
robustness of the proposed method. One is the threshold α, and the other is the watermark
strength factor β. In order to enhance the performance reported in Section 4.3.1, Face was
watermarked with several fairs of α and β. Table 4.4 shows the fairs of two parameters.
Case I and II (or Case III and IV) adjust only the thresholds (or the strength factors)
keeping the strength factors (or the thresholds) used in 4.3.1 intact, and Case V does
both of them. These adjustments were carefully considered because they could produce
serious visual distortion. As listed in Table 4.5, new parameters were properly determined
considering the watermark transparency. In addition, they hardly affect the compression
performances.
To analyze the effect of new parameters for robustness of watermark, the watermarked
Face underwent the intra-frame attacks – multiplicative binary random noise, uniform
4.3 Simulation Results 99
Table 4.4: Adjusted parameters to improve robustness (Face)
Threshold α Strength factor β (SWA level)
Case I 0.50 0.35 (5th), 0.40 (6th), 0.45 (7th)
Case II 0.00 0.35 (5th), 0.40 (6th), 0.45 (7th)
Case III 1.00 0.50 (5th), 0.55 (6th), 0.60 (7th)
Case IV 1.00 0.70 (5th), 0.75 (6th), 0.80 (7th)
Case V 0.00 0.70 (5th), 0.75 (6th), 0.80 (7th)
Table 4.5: Evaluation of compression performance and watermark robustness in terms of
different threshold α and different β (When no attack)
AHDCompression performance Watermark robustness
(bits/vertex/frame) Corr
Case I 1.83 11.55 1.00
Case II 2.26 11.56 1.00
Case III 1.62 11.54 1.00
Case IV 2.19 11.55 1.00
Case V 4.19 11.59 1.00
100 Joint Watermarking and Compression
Table 4.6: Evaluation of robustness according to different threshold α and different β
(After intra-frame attacks applied to Face)
Intra-frame
attackAttack intensity
Corr
Case I Case II Case III Case IV Case V
Multiplicative
binary noise
1% 0.95 1.00 0.97 1.00 1.00
5% 0.69 0.79 0.73 0.63 0.77
10% 0.31 0.33 0.33 0.42 0.55
Uniform
quantization
8bits 1.00 1.00 1.00 1.00 1.00
6bits 0.92 0.92 0.92 0.97 0.97
4bits 0.47 0.47 0.55 0.55 0.60
Smoothing
(120,0.03) 0.76 0.84 0.81 0.79 0.87
(360,0.03) 0.66 0.74 0.63 0.65 0.76
(600,0.03) 0.58 0.60 0.55 0.66 0.66
Average 0.70 0.74 0.72 0.74 0.80
quantization and smoothing – having same intensities with Section 4.3.1. Table 4.6 shows
watermark extraction results in terms of several parameter pairs. Firstly, when the thresh-
old α is close to zero, the robustness can be improved as reported in the results of Case
I and II. This is mainly due to the fact that whole signals in the specific sub-band can
be referred (low frequency band signals) and modified (middle frequency band signals) to
embed watermark when α = 0. We can also improve the robustness via increasing the
strength factor, as higher strength factor enables to embed watermark with higher energy
(See the results of Case III and IV in this table). Taking advantage of adjusting both the
threshold and the strength factor, Case V has the best performance in these simulations.
4.4 Summaries
In this chapter, we proposed a joint watermarking and compression method for 3-D mesh
sequences. Based on SWA (Spatial Wavelet Analysis) + TWA (Temporal Wavelet Anal-
ysis) compression scheme, the proposed method embeds watermark into an intermediate
4.4 Summaries 101
step of compression. To embed watermark, the variances of spatiotemporal wavelet coef-
ficient sequences belonging to specific sub-bands are modified by the histogram mapping
function. Through the simulations, we proved that the proposed watermarking scheme can
be properly combined with the efficient compression method which provides spatiotem-
poral scalability. Moreover, it is quite robust against inter-frame attack including frame
dropping, as well as several intra-frame attacks including multiplicative binary noise, uni-
form quantization, smoothing, similarity transform and vertex re-ordering. However, there
are some drawbacks. Our proposal can not extract the hidden watermark after some syn-
chronization attacks such as simplification since spatial wavelet coefficients after these
kinds of attacks could have entirely different distribution from that of the watermarked
ones. Nevertheless, the proposed method presented a possibility to realize a well-designed
joint watermarking and compression system for 3-D mesh sequences.
102 Joint Watermarking and Compression
Chapter 5
Conclusions and Perspectives
This dissertation dealt with three major research topics – watermarking, compression and
their combination – for three-dimensional (3-D) graphics data. Pursuing to develop an
efficient joint watermarking and compression system for 3-D mesh sequences as the final
goal of this dissertation, we have discussed two individual research topics and then derive
a combination system from both of them.
In Chapter 2, two oblivious watermarking methods for 3-D static meshes were pre-
sented. This chapter first re-classified general geometrical and topological attacks into
distortion and distortion-less attacks, and emphasized that distortion-less attacks is more
serious attacks on 3-D mesh watermarking because they could fatally destroy the hidden
watermark without any perceptual changes of watermarked mesh model. To effectively
cope with distortion-less as well as distortion attacks, two proposed methods use the sta-
tistical features of vertex norms to embed watermark. The first method shifts the mean
value of the distribution of vertex norms according to the watermark bit to be embedded
and the second method changes its variance. In our methods, histogram mapping func-
tions were newly introduced and used for the purpose of elaborate modification. Since
the statistical features are invariant to distortion-less attacks and less sensitive to various
kinds of distortion ones, robustness of watermark can be easily achieved. In addition, the
proposed methods employ a blind watermark detection scheme. Through the simulations,
we proved that both proposed methods are perfectly robust against distortion-less attacks
such as vertex re-ordering and similarity transforms. Moreover, they are fairly robust
104 Conclusions and Perspectives
against various kinds of distortion attacks, in particular, simplification and sub-division
operations. However, there are some drawbacks. Our proposals are not applicable to very
small size models and CAD models with flat regions, and are very vulnerable to clipping
attacks that cause severe alteration to the center of gravity of the model. Nevertheless,
the simulation results demonstrate a possible, oblivious watermarking method based on
statistical approach for 3-D polygonal mesh model.
In Chapter 3, two possible compression methods for 3-D mesh sequences were proposed:
SWA (Spatial Wavelet Analysis) + MDC (Multi-order Differential Coding) method and
SWA + TWA (Temporal Wavelet Analysis) method. Both proposed methods use the
SWA technique which employs an exact integer analysis and synthesis filters to reduce
the spatial redundancy. The filters have a powerful advantage that they can be directly
applied to irregular meshes. Besides, they provide spatial scalability. In order to reduce
the temporal redundancy, we employed two different techniques, MDC and TWA. Through
simulations, we verified that the SWA+MDC method has slightly better performances than
the SWA+TWA method in terms of both lossless and lossy compressions. On the other
hand, the SWA+TWA method offers spatiotemporal scalability while the SWA+MDC
does only spatial one.
As the final destination of this dissertation, a joint watermarking and compression
method was proposed in Chapter 4. This chapter first defined some requirements – low
complexity, compression gain, invisibility and robustness – and re-classified possible at-
tacks – intra-frame and inter-frame attacks – which should be guaranteed on 3-D mesh se-
quence watermarking. For the robustness and invisibility of watermark, specific sub-bands
are respectively selected in spatial and temporal wavelet domain and its corresponding sig-
nals are modified. To embed a watermark bit, the proposed method changes the variance
of a selected sequence of spatiotemporal wavelet coefficients by using a histogram mapping
function. The proposed method can reduce the system complexity because this watermark
embedding scheme is performed at the intermediate step of compression. Besides, the wa-
termark can be quite robust against intra-frame and inter-frame attacks since a statistical
feature is employed as the watermark carrier. The watermark is extracted by an oblivious
watermark detection technique. Through the simulations, we proved that the proposed
105
watermarking scheme can be well combined with the efficient compression method which
provides spatiotemporal scalability. Moreover, it is very robust against frame dropping
which is classified into inter-frame attacks, as well as several intra-frame attacks includ-
ing multiplicative binary noise, uniform quantization, smoothing, similarity transform and
vertex re-ordering. However, there are some drawbacks. Our proposal can not extract the
hidden watermark after some synchronization attacks such as simplification since spatial
wavelet coefficients after these kinds of attacks could have entirely different distribution
from that of the watermarked ones. Nevertheless, the proposed method presented a pos-
sibility to realize the well designed joint watermarking and compression system for 3-D
mesh sequences.
An interesting application on which the proposed methods can be used is medical image
protection and transmission systems. The medical images containing the affected parts
of patients should be strictly protected from unauthorized persons except few authorized
ones such as doctors and nurses. In addition, sometimes, these kinds of data should be
transmitted from a hospital to another. In this case, quality distortion might confuse for
doctor to accurately judge the condition of patient; it means that only lossless compression
should be used for the transmission systems of medical images assuming that the band-
width is enough guaranteed to avoid transmission problems such as packet loss and delay.
The proposed joint watermarking and compression method can be directly applied to these
kinds of systems if the medical images are represented as triangular mesh sequences. It
is caused by the fact that our method enables not only lossless compression to promptly
transmit medical images but also invisible and robust watermarking to effectively protect
its personal information. In addition to these systems, our watermarking, compression,
and their combination methods can be appropriately employed in many applications such
as 3-D movies, video games, cultural assets reconstructed as 3-D objects and so on.
106 Conclusions and Perspectives
Appendix A
Histogram Mapping Function
In this appendix, we show how to modify the mean value or variance of input signal into
desired one.
A.1 For Shifting Mean Value of Uniform Distribution
Let’s consider a continuous random variable X with uniform distribution over the interval
[0, 1]. Clearly, the expectation of the random variable E [X] is given by
E [X] =∫ 1
0xpX (x) dx =
12
(A.1)
where pX (x) is the PDF (Probability Density Function) of X. This expectation will be
used as a reference value when moving the mean of each bin to a certain level in the next
step. In our method, vertex norms in each bin are modified to shift the mean value. It
is very important to assure that the modified vertex norms also exist within the range of
each bin. Otherwise, vertex norms belonging to a certain bin could shift into neighbor
bins, which may have a serious impact on the watermark extraction. We now propose
a histogram mapping function, which can shift the mean to the desired level through
modifying the value of vertex norms while staying within the proper range. The use
of a mapping function is inspired from the histogram equalization techniques often used
in image enhancement processing [Gonzalez and Woods, 1992]. For a given continuous
random variable X, the mapping function is defined as
Y = Xk for 0 < k <∞ and k ∈ < (A.2)
108 Histogram Mapping Function
Figure A.1: Histogram mapping function, Y = Xk, for different parameters of k
where Y is the transformed variable, and the parameter k is a real value for 0 < k < ∞.
Fig. A.1 shows curves of the mapping function for different values of k. When the
parameter k is selected in the range 1 < k <∞, input variables are mapped into relatively
small values. Moreover, increases in k decrease the value of the transformed variable. It
means the reduction of mean value. On other hand, the mean value increases for decreasing
k when 0 < k < 1. Expectation of output random variable, E[Y ], is represented as
E [Y ] = E[Xk
]=
∫ 1
0xkpX (x) dx =
1k + 1
(A.3)
Fig. A.2 shows the expectation value of the output of the mapping function over
k. The expectation value decreases monotonically with the parameter k. Therefore, we
can easily adjust the mean value of the distribution by selecting a proper parameter. In
particular, the mapping function does not only guarantee to alter the variable within the
limited range, but also allows shifting of the mean value to the desired level.
A.2 For Changing Variance of Uniform Distribution 109
Figure A.2: Expectation of the output random variable via histogram mapping function
with different k, assuming that the input random variable is uniformly distributed over
unit range [0, 1].
A.2 For Changing Variance of Uniform Distribution
Now, let X be a continuous random variable with uniform distribution over [−1, 1]. As X
has a mean of zero, its variance is given by
E[X2
]=
∫ 1
−1x2pX (x) dx =
13
(A.4)
where E[X2] denotes the second moment of the random variable X. A variance of 13 will
be used as a reference when changing the variance of each bin according to the watermark
bit to be embedded. To change the variance, vertex norms in each bin should be modified
within the normalized range of [−1, 1]. For this purpose, we use a histogram mapping
function, which can change the variance to the desired level by modifying vertex norms
while staying within the specified range. For a given X, the mapping function is defined
by
Y = sign (X) |X|k for 0 < k <∞ and k ∈ < (A.5)
110 Histogram Mapping Function
Figure A.3: Histogram mapping function, sign (X) |X|k, for different parameter of k
where Y is the transformed variable, and k is a real value for 0 < k < ∞. Fig. A.3
shows curves of the mapping function for different k. When the parameter is selected
for 1 < k < ∞, input variable is transformed into output variable with relatively small
absolute value while maintaining its sign. Moreover, the absolute value of transformed
variable becomes smaller as increasing k. It means a reduction of the variance. On the
other hand, variance increases for decreasing k on the range 0 < k < 1. The variance of
the output random variable E[Y 2
]is represented as
E[Y 2
]= E
[(sign (X) |X|k
)2]
=∫ 1
−1|x|2kpX (x) dx =
12k + 1
(A.6)
Fig. A.4 shows the variance of the output random variable over k of the mapping
function. Note that the variance decreases monotonically as k increases. Therefore, the
variance of the distribution can easily be adjusted by selecting a proper parameter.
A.3 For Changing Variance of Laplacian Distribution
Consider a continuous random variable X with Laplacian distribution, of which the PDF
is defined by
px(x) =λ
2e−λ|x| (A.7)
A.3 For Changing Variance of Laplacian Distribution 111
Figure A.4: Variance of the output random variable via histogram mapping function with
different k, assuming that the input random variable is uniformly distributed over the
normalized range [−1, 1].
Clearly, the second moment (variance) of the random variable E[X2
]is given by
E[X2
]=
∫ ∞
−∞x2pX (x) dx =
2λ2
(A.8)
If the random variable X is transformed using the histogram mapping function that is
defined by
y =
sign(x) · |x|k, for − 1 ≤ x ≤ 1
x, otherwise(A.9)
where sign (x) is the sign of x and k is a real value for 0 < k <∞, the second moment of
the output random variable E [Y ] is obtained as follows:
E[Y 2
]=
∫ 1
−1x2kpX (x) dx+
∫ −1
−∞x2kpX (x) dx+
∫ ∞
1x2kpX (x) dx
=∞∑
n=0
(−1)n · λn+1
(n+ 2k + 1) · n!+ 2e−λ
(12
+2λ
+2λ2
)(A.10)
where n! indicates the factorial of positive integer n. The first term of Eq. (A.10) represents
the second moment of the transformed variable for the input variable existing over the
112 Histogram Mapping Function
Figure A.5: Second moment (variance) of the output random variable via histogram map-
ping function with different k, assuming that the input variable has Laplacian distribution.
interval [−1, 1] and the second does that of the input variable being in intact outside
of the interval [−1, 1]. As results, the second moment of the output random variable is
represented by the summation of the two terms. The second term might be negligible,
if the variance of the input variable is smaller enough than one (λ >>√
2). Here, λ is
inversely proportional to the variance of the input variable. Fig. A.5 shows the second
moment of the output random variable over the parameter k of the mapping function, for
different λ. The output variance of output variable can be easily adjusted by selecting a
parameter k.
Appendix B
Estimation of Entropy Coding
Efficiency via Variance of Signal
In this appendix, we show that the entropy coding efficiency can be estimated using the
variance of prediction model.
To improve the entropy coding efficiency, there have been many trials to produce a good
prediction model whose distribution exhibits one sharp peak. The more the distribution
concentrates on a specific value, the better the coding efficiency can be expected. A good
statistical model for the prediction errors is a Laplacian distribution. The coding efficiency
can be estimated by using the variance of the distribution.
Consider a continuous random variable X with zero-mean Laplacian distribution for
which the PDF is defined by
pX (x) =λ
2e−λ|x|. (B.1)
Here, the sharpness of the distribution can be determined by the parameter λ. Clearly,
the entropy 1 of the random variable, H (X), is obtained as [A., 1965]
H (X) =∫ ∞
−∞pX (x) log2
1pX (x)
dx = log2
2λ
+1
ln2. (B.2)
1This type of entropy is named ‘continuous or differential entropy’. It could sometimes have negative
values and then be inefficient to measure the amount of information comparing with Shannon entropy. Note
that we just use continuous entropy to demonstrate the inter-relationship between entropy and variance
focusing on a statistical model, Laplacian distribution.
114 Estimation of Entropy
Figure B.1: Relationship between the entropy and the variance according to different σ
The variance, σ2, is given by the second moment E[X2
]:
σ2 = E[X2
]=
∫ ∞
−∞x2pX (x) dx =
2λ2. (B.3)
From Eq. (B.2) and (B.3), both the entropy and variance are functions of λ. Therefore
Eq. (B.2) can be rewritten as
H (X) = log2σ√
2 +1
ln2. (B.4)
Fig. B.1 shows a relationship between the entropy and the variance according to different
σ. As shown in this figure, the variance is highly correlated with the entropy. In our
approaches, the entropy coding efficiency is estimated using the variance of prediction
model.
Appendix C
Finding the Optimal Order of
MDC (Multi-order Differential
Coding)
In this appendix, we discuss the efficiency of the MDC (Multi-order Differential Coding)
according to the correlation coefficient of input signal.
Let an input data sequence u(n) (for 1 ≤ n ≤ N) be a WSSMP (Wide Sense Stationary
Markov Process) with zero mean.
The m-th order differential error sequence y(m) (n) can be expressed by
y(1) (n) = u (n)− u (n− 1)
y(2) (n) = y(1) (n)− y(1) (n− 1)
...
y(m) (n) = y(m−1) (n)− y(m−1) (n− 1) (C.1)
The impulse response of the differential coding system is defined as
h (n) = δ (n)− δ (n− 1) (C.2)
Using Eq. (C.1), the m-th order differential error sequence can be rewritten as
y(m) (n) = h (n) ∗ y(m−1) (n) (C.3)
116 Finding the Optimal Order
where, ∗ denotes the convolution operator.
The auto-correlation function of Eq. (C.3) can be calculated as
ϕy(m)(k) = ϕh(k) ∗ ϕy(m−1)(k) (C.4)
where,
ϕh(k) = h (k) ∗ h (−k) and ϕy(m−1)(k) = E[y(m−1)(k)y(m−1)(n+ k)
](C.5)
where, E [.] is expectation. According to Eq. (C.2), Eq. (C.5) is given by
ϕh(k) = −δ (k − 1) + 2δ (k)− δ (k + 1) (C.6)
Considering the first order differential coders, from Eq. (C.4)
ϕy(1)(k) = −ϕu(k − 1) + 2ϕu(k)− ϕu(k + 1) (C.7)
From Eq. (C.7):
ϕy(1)(0) = 2 (ϕu(0)− ϕu(1)) (C.8)
where ϕu (0) = σ2u and if we write the auto-correlation function of the input data sequence
as ϕu (k) = σ2uψ (k), (ψ (k) < 1, ∀k), ϕu (1) = σ2
uψ (1). Clearly, from Eq. (C.8), the
output variance of the first order differential coder is
σ2y(1) = ϕy(1)(0) = 2σ2
u (1− ψ (1)) (C.9)
If the input sequence u (n) is a first order stationary Markov process, ϕu(k) = E [u (n)u (n+ k)] =
σ2uψ (k) with ψ (k) = ρ|k|. Here, ρ (|ρ| ≤ 1) is the correlation coefficient. Therefore, Eq.
(C.9) can be rewritten as follow:
σ2y(1) = ϕy(1)(0) = 2σ2
u (1− ρ) (C.10)
From Eq. (C.10), σ2y(1) < σ2
u, if and only if 0.5 < ρ ≤ 1. Note that the WSSMP is a first
order autoregressive (AR(1)) process of the form:
u (n) = ρu (n− 1) +√
1− ρ2w (n) (C.11)
where w (n) is a white noise with zero mean and variance σ2u.
117
Clearly, for an AR(1) process, the optimal predictor is:
y1opt (n) = u (n)− ρu (n− 1) (C.12)
Then, its output variance is
σ2y1
opt= σ2
u (1− ρ)2 (C.13)
It follows that the output variance is more reduced for a predictor having larger corre-
lation coefficient. However, the (optimal) predictor requires both computational costs to
calculate the correlation factor and side information to be transmitted.
For an AR(1) process, it is easy to prove that the output variance of the MDC is
reduced if
0.7752 < ρ ≤ 1 for the second order
0.9199 < ρ ≤ 1 for the third order
0.9740 < ρ ≤ 1 for the fourth order
· · ·
Considering that the input sequence is modeled by a p-th order AR process (AR(p)), the
optimal differential coder has the order p:
y1opt (n) = u (n)−
p∑k=1
aku (n− 1) (C.14)
Clearly, the proposed m-th order MDC technique is a good alternative. In addition, the
method requires just to evaluate the optimal order of the differential coder in terms of
output variance and to transmit it.
118 Finding the Optimal Order
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Journals
[Cho et al., 2007a] Cho, J., Prost, R., Jung, H., An oblivious watermarking for 3-D
polygonal meshes using distribution of vertex norms, IEEE Transaction on Signal
Processing, volume 55, no. 1, (2007), pp. 142-155.
Conferences
[Cho et al., 2007b] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., A 3-D mesh
sequence coding using the combination of spatial and temporal wavelet analysis,
Lecture Note in Computer Science, volume 4418, (2007), pp. 389-399.
[Kim et al., 2006a] Kim, M., Cho, J., Prost, R., Jung, H., Wavelet analysis based
blind watermarking for 3-D surface meshes, Lecture Note in Computer Science,
volume 4283, (2006), pp. 123-137.
[Cho et al., 2006b] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D dynamic
mesh compression using wavelet-based multiresolution analysis, in: Proceedings of
ICIP 2006, Atlanta, GA, USA, Oct. 2006, (pp. 529-532).
[Kim et al., 2006c] Kim, M., Cho, J., Prost, R., Jung, H., A robust blind water-
marking for 3D meshes using distribution of scale coefficients based on irregular
wavelet analysis, in: Proceedings of ICASSP 2006, Toulouse, France, May. 2006,
(pp. 477-480).
[Cho et al., 2005] Cho, J., Kim, M., Prost, R., Chung, H., Jung, H., Robust water-
marking on polygonal meshes using distribution of vertex norms, Lecture Note in
Computer Science, volume 3304, (2005), pp. 283-293.
Submitted Journals
[Cho et al., 2007c] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D mesh se-
quence compression using wavelet-based multi-resolution analysis, IEEE Transaction
on Circuits and Systems for Video Technology.
Curriculum Vitae
Personal Information
• Name: Cho, Jae-Won
• Date of birth: May 6, 1979
Educations
• Mar. 2005 - Dec. 2007 : Department of Electronics, INSA-Lyon (Institut National
des Sciences Appliquees de Lyon), France (Ph.D.)
• Sep. 2004 - Feb. 2008 : Department of Information and Communication Engineering,
Yeungnam University, Rep. of Korea (Ph.D.)
• Sep. 2002 - Aug. 2004 : Department of Information and Communication Engineer-
ing, Yeungnam University, Rep. of Korea (M.S.)
• Mar. 1998 - Aug. 2002 : Department of Information and Communication Engineer-
ing, Yeungnam University, Rep. of Korea (B.S.)
Research Areas
• Multimedia signal processing including audio clips, 2-D still images, 2-D video
streams, 3-D meshes, 3-D mesh sequences
• Data compression
• Digital watermarking
• Quality measurement
Professional Experiences
• Dec. 2006 - Jan. 2007 : Reviewer, Computer Graphics Forum (a Journal of Euro-
graphics)
• Sep. 2004 - Feb. 2008 : Professional researcher, Graduate School of Yeungnam
University
• Jan. 2004 - Feb. 2004 : Visiting researcher, CREATIS of INSA-Lyon
• Sep. 2002 - Aug. 2006 : Assistant teacher, School of EECS (Electrical Engineering
and Computer Science) of Yeungnam University
Research Projects
• Dec. 2006 - Nov. 2007 : Director, “A study of efficient coding method for 3-D mesh
sequences,” KRF (Korea Research Foundation), Rep. of Korea
• Aug. 2003 - Aug. 2007 : Assistant researcher, “A study on the QoS-guaranteed traf-
fic engineering and multimedia service platform in the next generation wired/wireless
integrated networking environment,” MIC (Ministry of Information and Communi-
cation), Rep. of Korea
• Sep. 2003 - Sep. 2005 : Assistant researcher, “Joint watermarking and compres-
sion in 3-D irregular meshes via multi-resolution wavelet analysis,” CNRS (Centre
National de la Recherche Scientifique), France and KOSEF (Korea Science and En-
gineeriing Foundation), Rep. of Korea
Award
The prize of excellent paper presentation, ASK (Acoustical Society Korea), Rep. of Korea
(Jul. 2003)
Patents
• Cho, J., Kim, M., Jung, H., “Encoding and decoding method for watermarking using
statistical analysis (10-2006-0080755),” Aug. 24, 2006, Rep. of Korea (Applied)
• Cho, J., Park, H., Jung, H., “Method for generating digital watermark and detecting
digital watermark (10-2006-0080756),” Aug. 24, 2006, Rep. of Korea (Applied)
• Cho, J., Chung, H., Jung, H., “System and method for transformation of digital
signal for measuring quality and for measuring a transmission quality of digital
signal (10-2006-0080757),” Aug. 24, 2006, Rep. of Korea (Applied)
Publications
International Journals
[Cho et al., 2007a] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D mesh se-
quence compression using wavelet-based multi-resolution analysis, IEEE Transaction
on Circuits and Systems for Video Technology, (Submitted).
[Cho et al., 2007b] Cho, J., Prost, R., Jung, H., An oblivious watermarking for 3-D
polygonal meshes using distribution of vertex norms, IEEE Transaction on Signal
Processing, volume 55, no. 1, (2007), pp. 142-155.
[Park et al., 2004a] Park, H., Cho, J., Oh, I., Prost, R., Chung, H., Jung, H., Multi-
ple echo hiding in sub-band signals, GESTS International Transaction on Acoustic
Science and Engineering, volume 2, no. 1, (2004), pp. 122-131.
Lecture Notes in Computer Science
[Cho et al., 2007c] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., A 3-D mesh
sequence coding using the combination of spatial and temporal wavelet analysis,
Lecture Note in Computer Science, volume 4418, (2007), pp. 389-399.
[Cho et al., 2006a] Cho, J., Chung, H., Jung, H., A robust blind audio watermarking
using distribution of sub-band signals, Lecture Note in Computer Science, volume
4105, (2006), pp. 106-113.
[Kim et al., 2006b] Kim, M., Cho, J., Prost, R., Jung, H., Wavelet analysis based
blind watermarking for 3-D surface meshes, Lecture Note in Computer Science,
volume 4283, (2006), pp. 123-137.
[Cho et al., 2005a] Cho, J., Kim, M., Prost, R., Chung, H., Jung, H., Robust wa-
termarking on polygonal meshes using distribution of vertex norms, Lecture Note in
Computer Science, volume 3304, (2005), pp. 283-293.
[Cho et al., 2004b] Cho, J., Park, H., Huh, Y., Chung, H., Jung, H., Echo watermark-
ing in sub-band domain, Lecture Note in Computer Science, volume 2939, (2004),
pp. 447-455.
International Conferences
[Cho et al., 2006c] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D dynamic
mesh compression using wavelet-based multiresolution analysis, in: Proceedings of
ICIP 2006, Atlanta, GA, USA, Oct. 2006, (pp. 529-532).
[Kim et al., 2006d] Kim, M., Cho, J., Prost, R., Jung, H., A robust blind water-
marking for 3D meshes using distribution of scale coefficients based on irregular
wavelet analysis, in: Proceedings of ICASSP 2006, Toulouse, France, May. 2006,
(pp. 477-480).
[Oh et al., 2005b] Oh, I., Cho, J., Chung, H., Jung, H., Multiple echo watermarking
using wavelet transform, in: Proceeding of the Kyushu-Youngnam Joint Conference
2005, Busan, Rep. of Korea, Jan. 2005, (pp. 13-16).
[Cho et al., 2004c] Cho, J., Kim, M., Chung, H., Jung, H., Robust 3-D watermarking
against distortionless attacks, in: Proceeding of 2004 Joint Workshop of Tohoku
Univ. and Yeungnam Univ., Gyeongsan, Rep. of Korea, Nov. 2004, (pp. 33-34).
[Oh et al., 2004d] Oh, I., Cho, J., Prost, R., Chung, H., Jung, H., Audio watermark-
ing in sub-band signals using multiple echo kernels, in: Proceeding of ICSLP 2004,
Jeju, Rep. of Korea, Oct. 2004, (pp. 2453-2456).
[Cho et al., 2003a] Cho, J., Park, H., Chung, H., Jung, H., An evaluation of blind wa-
termarking based on fast fourier transform, in: Proceeding of the Kyushu-Youngnam
Joint Conference 2003, Kyushu, Japan, Jan. 2003, (pp. 81-84).
Korean Domestic Journals
[Cho et al., 2007d] Cho, J., Yoo, K., Jung, H., Quality measurement methods for
transmitted multimedia data using statistical characteristics of signals, Journal of
Korea Multimedia Society, volume 11, no. 1, (2007), pp. 76-84.
[Kim et al., 2007e] Kim, M., Cho, J., Prost, R., Jung, H., A blind watermarking for
3-D mesh sequence using temporal wavelet transform of vertex norms, Journal of
Korea Multimedia Society, volume 32, no. 3, (2007), pp. 256-268.
[Cho et al., 2002a] Cho, J., Kim, M., H., Jung, H., A blind watermarking based on
fast fourier transform, Journal of the Institute of Information and Telecommunica-
tion, volume 9, no. 1, (2002), pp. 41-46.
Korean Domestic Conferences
[Cho et al., 2006e] Cho, J., Kim, M., Chung, H., Jung, H., Statistical character-
istics based audio watermarking using discrete wavelet transform, in: Conference
Proceeding of Acoustical Society of Korea, Daegu, Rep. of Korea, Nov. 2006, (pp.
441-446).
[Kim et al., 2006f] Kim, M., Cho, J., Chung, H., Jung, H., A blind watermarking for
3-D mesh sequences using temporal wavelet transform, in: Conference Proceeding of
Acoustical Society of Korea, Daegu, Rep. of Korea, Nov. 2006, (pp. 447-452).
[Cho et al., 2005c] Cho, J., Park, H., Kim, M., Chung, H., Jung, H., Quality measure-
ment for transmitted audio data using variance of sub-band signals, in: Conference
Proceeding of Acoustical Society of Korea, Gangwon, Rep. of Korea, Nov. 2005, (pp.
191-194).
[Kim et al., 2005d] Kim, M., Park, H., Cho, J., Chung, H., Jung, H., A watermark-
ing method for 3D irregular meshes based on multi-resolution wavelet analysis, in:
Conference Proceeding of Acoustical Society of Korea, Gangwon, Rep. of Korea,
Nov. 2005, (pp. 195-198).
[Park et al., 2005e] Park, H., Cho, J., Chung, H., Jung, H., Audio watermarking in
sub-band signals using multiple echo kernals, in: Conference Proceeding of Acoustical
Society of Korea, Gangwon, Rep. of Korea, Nov. 2005, (pp. 199-202).
[Cho et al., 2003b] Cho, J., Park, H., Chung, H., Jung, H., Echo watermarking based
on sub-band signals, in: Conference Proceeding of Korean Institute of Communica-
tion Sciences, Seoul, Rep. of Korea, Dec. 2003, (p. 491).
[Cho et al., 2003c] Cho, J., Park, H., Chung, H., Jung, H., Echo watermarking based
on wavelet transform, in: Conference Proceeding of Acoustical Society of Korea,
Jinhae, Rep. of Korea, Oct. 2003, (pp. 31-34).
[Cho et al., 2003d] Cho, J., Park, H., Chung, H., Jung, H., Echo watermarking based
on descrete wavelet transform, in: Conference Proceeding of Acoustical Society of
Korea, Changwon, Rep. of Korea, Jul. 2003, (pp. 397-400).
[Suk et al., 2003e] Suk, S., Kim, C., Cho, J., Jung, H., Chung, H., Speech and
character combined recognition system for PDA in wireless network environment, in:
Conference Proceeding of Acoustical Society of Korea, Gyeongjoo, Rep. of Korea,
Oct. 2003, (pp. 19-20).
[Cho et al., 2002b] Cho, J., Kim, M., Ryu, K., Chung, H., Jung, H., An evaluation
of digital watermarking based on fast fourier transform, in: Conference Proceeding
of Acoustical Society of Korea, Andong, Rep. of Korea, Oct. 2002, (pp. 55-58).
[Park et al., 2002c] Park, H., Cho, J., Chung, H., Jung, H., An efficient operation on
wavelet transform, in: Conference Proceeding of Acoustical Society of Korea, Busan,
Rep. of Korea, Nov. 2002, (pp. 295-298).
FOLIO ADMINISTRATIF
THESE SOUTENUE DEVANT L'INSTITUT NATIONAL DES SCIENCES APPLIQUEES DE LYON
NOM : CHO DATE de SOUTENANCE : le 7 Décembre (avec précision du nom de jeune fille, le cas échéant) Prénoms : Jae-Won TITRE : Watermarking, Compression, and Their Combination for 3-D Triangular Meshes NATURE : Doctorat Numéro d'ordre : 2007-ISAL-0099 Ecole doctorale : ÉLECTRONIQUE, ÉLECTROTECHNIQUE, AUTOMATIQUE Spécialité : IMAGES ET SYSTÈMES Cote B.I.U. - Lyon : T 50/210/19 / et bis CLASSE : RESUME : This dissertation deals with watermarking, compression, and their combination for three-dimensional (3-D) triangular meshes. We first propose algorithms individually in order to watermark static meshes and to compress mesh sequences. Finally we derive a combined system for joint compression and watermarking. Firstly, we propose two oblivious (or blind) watermarking techniques for 3-D static meshes. They mainly use statistical features of vertex norms to embed watermark; the first proposed method shifts the mean value of the distribution and the second proposed method changes its variance. Histogram mapping functions are introduced to modify the distribution. These mapping functions are devised in order to reduce the visibility of watermark as much as possible. Since the statistical features of vertex norms are less sensitive to signal alterations, the proposed methods can be robust against general attacks. In addition, our methods employ a blind watermark detection scheme, which can extract the watermark without referring to the original mesh model. Through simulations, we demonstrate that the proposed approaches are robust against several attacks such as adding binary noise, smoothing, uniform quantization, simplification, sub-division, vertex re-ordering, and similarity transform. Next, we present two compression methods for 3-D mesh sequences with constant connectivity. The proposed methods mainly use an exact integer spatial wavelet analysis (SWA) technique to efficiently decorrelate the spatial coherence of each mesh frame and also to promptly transmit mesh frames with various spatial resolutions under different bandwidth conditions (spatial scalability). To reduce the temporal redundancy, the first proposed method applies multi-order differential coding (MDC) to the temporal sequences after SWA of each mesh frame. MDC determines the optimal order of the differential coder by analyzing the variance of prediction errors. Compared to the first-order differential coding (FDC) scheme, the method can improve the compression performance. The second proposed method applies temporal wavelet analysis (TWA) to the 1-D temporal sequences. In particular, this method offers spatiotemporal multi-resolution coding. Through simulations, we prove that our approaches enable efficient lossy-to-lossless compression for 3-D mesh sequences. Finally, we present a joint compression and watermarking method for 3-D mesh sequences. Our approach is based on the proposed compression method using SWA and TWA. For robust and invisible watermark, a new watermarking technique derived from our second watermarking scheme is applied to the intermediate step of the compression process. Watermark embedding is carried out by the histogram mapping function which modifies the variance of spatiotemporal wavelet coefficients belonging to specific sub-bands. The hidden watermark is robust against several attacks such as additive binary noise, smoothing, frame dropping, because the employed watermark carrier is a statistical feature of spatiotemporal wavelet coefficients. Through simulations, we prove that our approach enables to efficiently compress 3-D mesh sequences and strictly protect its ownership in a single framework. MOTS-CLES : Watermarking, compression, joint compression and watermarking, 3-D static meshes, 3-D mesh sequences, and constant connectivity Laboratoire (s) de recherche : CREATIS-LRMN (Centre de Recherche Et d’Applications en Traitement des Images et du Signal), UMR CNRS 5220, U630 Inserm Directeur de thèse: Cotutelle INSA-Lyon /Yeungnam University Korea : M. Rémy PROST et M. Ho-Youl JUNG Président de jury : Mme. Isabelle MAGNIN Composition du jury : M. Marc ANTONINI (rapporteur), M. Ki-Ryong KWON (rapporteur), Mme. Françoise PRETEUX (examinatrice), M. Hyun-Soo KANG (examinateur), M. Kook-Yeol YOO (examinateur), Mme. Isabelle MAGNIN (présidente), M. Rémy PROST (co-directeur) et M. Ho-Youl JUNG (co-directeur)