Image Repairing: Robust Image Synthesis by Adaptive ND Tensor Voting

IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Jiaya Jia, Chi-Keung TangJiaya Jia, Chi-Keung Tang

Computer Science DepartmentComputer Science DepartmentThe Hong Kong University of The Hong Kong University of

Science and TechnologyScience and Technology

Motivation

• Main difficulties to repair a severely damaged image of natural scene– Mixture of texture and colors– Inhomogeneity of patterns– Regular object shapes

Motivation

• Given as few as one image without additional knowledge, we address:– How much color and shape information in the

existing part is needed to seamlessly fill the hole?– How good can we achieve in order to reduce

possible visual artifact when the information available is not sufficient.

• Robust Tensor Voting method is adopted

Tensor Voting Review• Tensors: compact representation of information • Tensor encoding:

3D tensor

3

1 2Ball tensor: uncertainty

in all directions

Plate tensor: certainty of directions in a plate

Stick tensor: certainty along two opposite directions

Tensor Voting Review

• Voting process is to propagate local information

P

Osculating circle

Image repairing system

Input Damaged Image

Texture-based Segmentation

Statistical Region Merging

Curve Connection

Adaptive Scale Selection

NND Tensor Voting

Output Repaired Image

Complete Segmentation

Image synthesis

SegmentationSegmentation

• JSEG [Deng and Manjunath 2001] – color quantization – spatial segmentation

• Mean shift [Comanicu and Meer 2002]

• Deterministic Annealing Framework [Hofmann et al 1998]

Texture-based SegmentationTexture-based Segmentation

Statistical Region Merge

• (M + 1)D intensity vector for each region Pi,

where M is the maximum color depth in the whole image.

0

20

40

60

80

100

1 2 … M M+1

PiPk

histogram gradient

if

1MiV

( 1) || ||i

ij Pi

V M jN

i kP P P

, || ||i k i ks V V Threshold

Why Region Merge?

• Decrease the complexity of region topology

• Relate separate regions

P1

P5

P3 P4

Damaged area

P2

Curve Connection

• 2D tensor voting method

P1

P5

P3 P4

P2

Z

XP2 P4

Why Tensor Voting?

• The parameter of the voting field can be used to control the smoothness of the resulting curve.

• Adaptive to various hole shapes

Small ScaleSmall Scale

Large ScaleLarge Scale

Without hole constraint

Without hole constraint

With hole constraint

With hole constraint

P4

Connection Sequence• Topology of surrounding area of the hole can be

very complex• Greedy algorithm

– Always connect the most similar regions

P1

P5

P3

Damaged area

P2

P2 and P4

P3 and P5

P1

Complete Segmentation

Image repairing system

Input Damaged Image

Texture-based Segmentation

Statistical Region Merging

Curve Connection

Adaptive Scale Selection

NND Tensor Voting

Output Repaired Image

Complete Segmentation

Image synthesis

ND Tensor Voting• Tensor encoding

– Each pixel is encoded as a ND stick tensor

5

5

Stick tensorScale N=26

ND Tensor Voting

• Voting process in ND space– An osculating circle becomes an osculating

hypersphere.– ND stick voting field is uniform sampling of normal

directions in the ND space.

sample sample

Adaptive Scaling

• texture inhomogeneity in images gives difficulty to assign only one global scale N [Lindeberg et al 1996].

• For each pixel i in images, we calculate:

{( )( ) }i i

TN N

M AVG I I {( )( ) }i i

N N

TM AVG I I {( )( ) }i i

TN N

M IAVG I • trace(M) measures the

average strength of the square of the gradient magnitude in the window of size Ni

Adaptive Scaling

• For each sample seed:– Increase its scale Ni from the lower bound to the

upper bound– If trace( ) < trace( ) - α where α is a

threshold to avoid small perturbation or noise interference, set Ni - 1 → Ni and return

– Otherwise, continue the loop until maxima or upper bound is reached

iNM 1iNM

Results

Results

Results

Results

Results

Limitations

• Lack of samples.

• Meaningful and semi-regular objects.

Conclusion

• An automatic image repairing system.

• Region partition and merging.

• Curve connection by 2D tensor voting.

• ND tensor voting based image synthesis.

• Adaptive scale.