Post on 19-Mar-2020
A Classification Method for TCA-Images München September 15, 2005 - p. 1/15
A Classification Method for TCA-Images6. Kongress der Gesellschaft für Anthropologie e.V.
"Facetten der modernen Anthropologie"
Katy StresoMax Planck Institute for Demographic Research
www.demogr.mpg.de
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 2/15
Introduction
■ Introduction to Tooth Cementum Annulation (TCA) Methodand Images
■ The Statistical Model - HMRF■ Application
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 2/15
Introduction
■ Introduction to Tooth Cementum Annulation (TCA) Methodand Images
■ The Statistical Model - HMRF
■ Application
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 2/15
Introduction
■ Introduction to Tooth Cementum Annulation (TCA) Methodand Images
■ The Statistical Model - HMRF■ Application
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 3/15
Introduction to Tooth CementumAnnulation (TCA) Method and Images
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 4/15
TCA Method and Images
- --
■ age estimation method■ paleodemographers: want to reconstruct mortality profiles of
historical populations by counting tooth rings→ need of an objective and automatic evaluation (Diss)
■ TCAa images◆ ≈ 1016 x 1300 pixels◆ gray values [0, 28 − 1] or [0, 212 − 1]◆ tooth ring roughly 1-3 µm (5-20 pixel) thick
■ typical good quality TCA-image:
a[Hoppa and Vaupel, 2002]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 4/15
TCA Method and Images
-
--
■ age estimation method■ paleodemographers: want to reconstruct mortality profiles of
historical populations by counting tooth rings→ need of an objective and automatic evaluation (Diss)
■ TCAa images◆ ≈ 1016 x 1300 pixels◆ gray values [0, 28 − 1] or [0, 212 − 1]◆ tooth ring roughly 1-3 µm (5-20 pixel) thick
■ typical good quality TCA-image:
a[Hoppa and Vaupel, 2002]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 4/15
TCA Method and Images
- -
-
■ age estimation method
■ paleodemographers: want to reconstruct mortality profiles ofhistorical populations by counting tooth rings→ need of an objective and automatic evaluation (Diss)
■ TCAa images◆ ≈ 1016 x 1300 pixels◆ gray values [0, 28 − 1] or [0, 212 − 1]◆ tooth ring roughly 1-3 µm (5-20 pixel) thick
■ typical good quality TCA-image:
a[Hoppa and Vaupel, 2002]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 4/15
TCA Method and Images
- --
■ age estimation method■ paleodemographers: want to reconstruct mortality profiles of
historical populations by counting tooth rings→ need of an objective and automatic evaluation (Diss)
■ TCAa images◆ ≈ 1016 x 1300 pixels◆ gray values [0, 28 − 1] or [0, 212 − 1]◆ tooth ring roughly 1-3 µm (5-20 pixel) thick
■ typical good quality TCA-image:
a[Hoppa and Vaupel, 2002]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 4/15
TCA Method and Images
- --
■ age estimation method■ paleodemographers: want to reconstruct mortality profiles of
historical populations by counting tooth rings→ need of an objective and automatic evaluation (Diss)
■ TCAa images◆ ≈ 1016 x 1300 pixels◆ gray values [0, 28 − 1] or [0, 212 − 1]◆ tooth ring roughly 1-3 µm (5-20 pixel) thick
■ typical good quality TCA-image:
a[Hoppa and Vaupel, 2002]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 4/15
TCA Method and Images
- --
■ age estimation method■ paleodemographers: want to reconstruct mortality profiles of
historical populations by counting tooth rings→ need of an objective and automatic evaluation (Diss)
■ TCAa images◆ ≈ 1016 x 1300 pixels◆ gray values [0, 28 − 1] or [0, 212 − 1]◆ tooth ring roughly 1-3 µm (5-20 pixel) thick
■ typical good quality TCA-image:
a[Hoppa and Vaupel, 2002]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 5/15
TCA Image
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 6/15
TCA-Image Analysis
■ typical result after thresholding:
need to punish saw cuts, reinforce tooth rings
■ incorporate information about neighboring pixel◆ Fourier transformer
(applied on TCA-images by Czermak a)◆ set up statistical model to include spatial dependencies
aCzermak, A. (2004). Automatisierte Auszahlung von Zahnzementzuwachsringen
(TCA). Talk presented at the Appa-Tagung 2004 but not yet published. See
http://www.gfanet.de/docs/appa workshop 10 04 beitraege.pdf.
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
● TCA Method and Images
● TCA Image
● TCA-Image Analysis
The Statistical Model - HMRF
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 6/15
TCA-Image Analysis
■ typical result after thresholding:
need to punish saw cuts, reinforce tooth rings■ incorporate information about neighboring pixel
◆ Fourier transformer(applied on TCA-images by Czermak a)
◆ set up statistical model to include spatial dependenciesaCzermak, A. (2004). Automatisierte Auszahlung von Zahnzementzuwachsringen
(TCA). Talk presented at the Appa-Tagung 2004 but not yet published. See
http://www.gfanet.de/docs/appa workshop 10 04 beitraege.pdf.
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 7/15
The Statistical Model - HMRF
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
true, unknown label image
TCA-imageIobs
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
0 0 1 0 1 1 0
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
0 0 1 0 1 1 0
P (Itrue)
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
independent noiseInoise
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
independent noiseInoise
P (Inoise) ∼
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
independent noiseInoise
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
unknown label imageItrue
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
independent noiseInoise
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
= µ
+
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
independent noiseInoise
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
=
µ
+unknown label imageItrue
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
µ
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
independent noiseInoise
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
=
µ
+unknown label imageItrue
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
µ
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)
a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 8/15
Hidden Markov Random Field (HMRF) Model a
TCA-imageIobs
0 0 1 0 1 1 0
P (Itrue) ∼ MRF
´6contextualconstraints
independent noiseInoise
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
=
µ
+unknown label imageItrue
P (Inoise) ∼∏
(x,y)
N(
0, σ2)
µ
²±¯°
■ maximize posterior distribution (computationally expensive)
P (Itrue|Iobs) ∝ P (Itrue)P (Inoise)
■ specify MRF ! (include prior knowledge about tooth rings)a[Zhang et al., 2001]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 9/15
Markov Random Field (MRF) Model
■ Markov-property: Itrue
X
■ FRAMEa
◆ special kind of MRF◆ Filters, Random Fields and Maximum Entropy◆ uses filters to collect neighborhood information
■ Filter◆ at each pixel: measure similarity of neighborhood to filter
(by convolution)◆ use a bank of filters
with variable ring width T◆ select best T during maximization
a[Zhu and Mumford, 1997],[Zhu et al., 1997],[Zhu et al., 1998]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 9/15
Markov Random Field (MRF) Model
■ Markov-property: Itrue
X
■ FRAMEa
◆ special kind of MRF◆ Filters, Random Fields and Maximum Entropy◆ uses filters to collect neighborhood information
■ Filter◆ at each pixel: measure similarity of neighborhood to filter
(by convolution)◆ use a bank of filters
with variable ring width T◆ select best T during maximization
a[Zhu and Mumford, 1997],[Zhu et al., 1997],[Zhu et al., 1998]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 9/15
Markov Random Field (MRF) Model
■ Markov-property: Itrue
X
■ FRAMEa
◆ special kind of MRF◆ Filters, Random Fields and Maximum Entropy◆ uses filters to collect neighborhood information
■ Filter◆ at each pixel: measure similarity of neighborhood to filter
(by convolution)◆ use a bank of filters
with variable ring width T◆ select best T during maximization
a[Zhu and Mumford, 1997],[Zhu et al., 1997],[Zhu et al., 1998]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 9/15
Markov Random Field (MRF) Model
■ Markov-property: Itrue
X
■ FRAMEa
◆ special kind of MRF◆ Filters, Random Fields and Maximum Entropy◆ uses filters to collect neighborhood information
■ Filter◆ at each pixel: measure similarity of neighborhood to filter
(by convolution)
◆ use a bank of filterswith variable ring width T
◆ select best T during maximization
a[Zhu and Mumford, 1997],[Zhu et al., 1997],[Zhu et al., 1998]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 9/15
Markov Random Field (MRF) Model
■ Markov-property: Itrue
X
■ FRAMEa
◆ special kind of MRF◆ Filters, Random Fields and Maximum Entropy◆ uses filters to collect neighborhood information
■ Filter◆ at each pixel: measure similarity of neighborhood to filter
(by convolution)◆ use a bank of filters
with variable ring width T
◆ select best T during maximization
a[Zhu and Mumford, 1997],[Zhu et al., 1997],[Zhu et al., 1998]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 9/15
Markov Random Field (MRF) Model
■ Markov-property: Itrue
X
■ FRAMEa
◆ special kind of MRF◆ Filters, Random Fields and Maximum Entropy◆ uses filters to collect neighborhood information
■ Filter◆ at each pixel: measure similarity of neighborhood to filter
(by convolution)◆ use a bank of filters
with variable ring width T◆ select best T during maximization
a[Zhu and Mumford, 1997],[Zhu et al., 1997],[Zhu et al., 1998]
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 10/15
Markov Random Field (MRF) Model - FRAME
■ prior distribution (incorporates prior knowledge in filter F )
P (Itrue) =1
Ze∑
(x,y) |(F∗Itrue)(x,y)|
■ typical prior assumption about TCA-image (Gibbs simulation)
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
● Hidden Markov Random Field
(HMRF) Model
● Markov Random Field (MRF)
Model● Markov Random Field (MRF)
Model - FRAME
Application
A Classification Method for TCA-Images München September 15, 2005 - p. 10/15
Markov Random Field (MRF) Model - FRAME
■ prior distribution (incorporates prior knowledge in filter F )
P (Itrue) =1
Ze∑
(x,y) |(F∗Itrue)(x,y)|
■ typical prior assumption about TCA-image (Gibbs simulation)
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 11/15
Application
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 12/15
Application
■ theor. ] rings: 38recognized: ≈ 35
■ miss thin rings■ bifurcations:
where tooth ringshave differentorientation
■ → reconstructionheavily influencedby filter F
■ global property →select locationdependent filters
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 12/15
Application
■ theor. ] rings: 38recognized: ≈ 35
■ miss thin rings■ bifurcations:
where tooth ringshave differentorientation
■ → reconstructionheavily influencedby filter F
■ global property →select locationdependent filters
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 12/15
Application
■ theor. ] rings: 38recognized: ≈ 35
■ miss thin rings■ bifurcations:
where tooth ringshave differentorientation
■ → reconstructionheavily influencedby filter F
■ global property →select locationdependent filters
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 12/15
Application
■ theor. ] rings: 38recognized: ≈ 35
■ miss thin rings
■ bifurcations:where tooth ringshave differentorientation
■ → reconstructionheavily influencedby filter F
■ global property →select locationdependent filters
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 12/15
Application
■ theor. ] rings: 38recognized: ≈ 35
■ miss thin rings■ bifurcations:
where tooth ringshave differentorientation
■ → reconstructionheavily influencedby filter F
■ global property →select locationdependent filters
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 12/15
Application
■ theor. ] rings: 38recognized: ≈ 35
■ miss thin rings■ bifurcations:
where tooth ringshave differentorientation
■ → reconstructionheavily influencedby filter F
■ global property →select locationdependent filters
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 12/15
Application
■ theor. ] rings: 38recognized: ≈ 35
■ miss thin rings■ bifurcations:
where tooth ringshave differentorientation
■ → reconstructionheavily influencedby filter F
■ global property →select locationdependent filters
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
● Application
● Bibliography
A Classification Method for TCA-Images München September 15, 2005 - p. 13/15
Bibliography
[Hoppa and Vaupel, 2002] Hoppa, R. D. and Vaupel, J. W., editors (2002).Paleodemography: Age Distributions from Skeletal Samples. CambridgeUniversity Press, Cambridge.
[Zhang et al., 2001] Zhang, Y., Brady, M., and Smith, S. (2001). Segmenta-tion of Brain MR Images Through a Hidden Markov Random Field Modeland the Expectation-Maximization Algorithm. IEEE Transactions on Med-ical Imaging, 20(1):45–57.
[Zhu and Mumford, 1997] Zhu, S. C. and Mumford, D. B. (1997). PriorLearning and Gibbs Reaction-Diffusion. IEEE Transactions on PatternAnalysis and Machine Intelligence, 19(11):1236–1250.
[Zhu et al., 1998] Zhu, S. C., Wu, Y., and Mumford, D. B. (1998). Fil-ters, Random Fields and Maximum Entropy (FRAME): Towards a Uni£edTheory for Texture Modeling. International Journal of Computer VisionArchive, 27(2):107 – 126.
[Zhu et al., 1997] Zhu, S. C., Wu, Y. N., and Mumford, D. B. (1997). Min-imax Entropy Principle and Its Application to Texture Modeling. NeuralComputation, 9(8):1627–1660.
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
●
A Classification Method for TCA-Images München September 15, 2005 - p. 14/15
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
Fourier Transform
● Fourier Transform
A Classification Method for TCA-Images München September 15, 2005 - p. 15/15
Fourier Transform
■ is a directional and global methodThis could introduce a substantial error, if◆ direction of tooth rings is not horizontal (or vertical)◆ rings are changing directions too heavy across the image◆ there exists directional noise, not orthogonal to tooth rings
(noise can not be removed without over-smoothing)◆ image contains thin and thick rings (removing a frequency
removes rings of a certain size from the whole image)It is herewith also erroneous to smooth a whole TCAimage, including parts where no rings exist like the dentin.
■ Fourier frequencies can not be translated to a person’s age.Because of superposition of sine and cosine waves we cannot directly interpret one frequency of the Fourier transforminto one ring width or one ring count. Cutting out certainfrequencies therefore does not have an explicit meaning forTCA image analysis.
■ back to the presentation
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
Fourier Transform
● Fourier Transform
A Classification Method for TCA-Images München September 15, 2005 - p. 15/15
Fourier Transform
■ is a directional and global methodThis could introduce a substantial error, if◆ direction of tooth rings is not horizontal (or vertical)◆ rings are changing directions too heavy across the image◆ there exists directional noise, not orthogonal to tooth rings
(noise can not be removed without over-smoothing)◆ image contains thin and thick rings (removing a frequency
removes rings of a certain size from the whole image)It is herewith also erroneous to smooth a whole TCAimage, including parts where no rings exist like the dentin.
■ Fourier frequencies can not be translated to a person’s age.Because of superposition of sine and cosine waves we cannot directly interpret one frequency of the Fourier transforminto one ring width or one ring count. Cutting out certainfrequencies therefore does not have an explicit meaning forTCA image analysis.
■ back to the presentation
● Introduction
Introduction to Tooth Cementum
Annulation (TCA) Method and
Images
The Statistical Model - HMRF
Application
Fourier Transform
● Fourier Transform
A Classification Method for TCA-Images München September 15, 2005 - p. 15/15
Fourier Transform
■ is a directional and global methodThis could introduce a substantial error, if◆ direction of tooth rings is not horizontal (or vertical)◆ rings are changing directions too heavy across the image◆ there exists directional noise, not orthogonal to tooth rings
(noise can not be removed without over-smoothing)◆ image contains thin and thick rings (removing a frequency
removes rings of a certain size from the whole image)It is herewith also erroneous to smooth a whole TCAimage, including parts where no rings exist like the dentin.
■ Fourier frequencies can not be translated to a person’s age.Because of superposition of sine and cosine waves we cannot directly interpret one frequency of the Fourier transforminto one ring width or one ring count. Cutting out certainfrequencies therefore does not have an explicit meaning forTCA image analysis.
■ back to the presentation