A Classification Method for TCA-Images · Introduction Introduction to Tooth Cementum Annulation (TCA) Method and Images The Statistical Model - HMRF Application A Classification

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

http://www.demogr.mpg.de

● Introduction

Introduction to Tooth Cementum

Annulation (TCA) Method and

Images

The Statistical Model - HMRF

Application


Introduction

■ Introduction to Tooth Cementum Annulation (TCA) Methodand Images

■ The Statistical Model - HMRF■ Application

● Introduction



Images


Application


Introduction


■ The Statistical Model - HMRF

■ Application

● Introduction



Images


Application


Introduction


■ The Statistical Model - HMRF■ Application

● Introduction



Images

● TCA Method and Images

● TCA Image

● TCA-Image Analysis


Application


Introduction to Tooth CementumAnnulation (TCA) Method and Images

● Introduction



Images


● TCA Image



Application


TCA Method and Images

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■ 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



Images


● TCA Image



Application



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● Introduction



Images


● TCA Image



Application



- -

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■ age estimation method

■ paleodemographers: want to reconstruct mortality profiles ofhistorical populations by counting tooth rings→ need of an objective and automatic evaluation (Diss)




● Introduction



Images


● TCA Image



Application



- --






● Introduction



Images


● TCA Image



Application



- --






● Introduction



Images


● TCA Image



Application



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● Introduction



Images


● TCA Image



Application


TCA Image

● Introduction



Images


● TCA Image



Application


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



Images


● TCA Image



Application


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



Images


● Hidden Markov Random Field

(HMRF) Model

● Markov Random Field (MRF)

Model● Markov Random Field (MRF)

Model - FRAME

Application



● Introduction



Images



(HMRF) Model



Model - FRAME

Application


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



Images



(HMRF) Model



Model - FRAME

Application



true, unknown label image

TCA-imageIobs





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs

unknown label imageItrue





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs


0 0 1 0 1 1 0





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs


0 0 1 0 1 1 0

P (Itrue)





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs


0 0 1 0 1 1 0

P (Itrue) ∼ MRF

´6contextualconstraints





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs


0 0 1 0 1 1 0

P (Itrue) ∼ MRF


independent noiseInoise





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs


0 0 1 0 1 1 0

P (Itrue) ∼ MRF



P (Inoise) ∼





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs


0 0 1 0 1 1 0

P (Itrue) ∼ MRF



P (Inoise) ∼∏

(x,y)

N(

0, σ2)





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs


0 0 1 0 1 1 0

P (Itrue) ∼ MRF



P (Inoise) ∼∏

(x,y)

N(

0, σ2)

= µ

+





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs

0 0 1 0 1 1 0

P (Itrue) ∼ MRF



P (Inoise) ∼∏

(x,y)

N(

0, σ2)

=

µ

+unknown label imageItrue

P (Inoise) ∼∏

(x,y)

N(

0, σ2)

µ





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs

0 0 1 0 1 1 0

P (Itrue) ∼ MRF



P (Inoise) ∼∏

(x,y)

N(

0, σ2)

=

µ


P (Inoise) ∼∏

(x,y)

N(

0, σ2)

µ





● Introduction



Images



(HMRF) Model



Model - FRAME

Application



TCA-imageIobs

0 0 1 0 1 1 0

P (Itrue) ∼ MRF



P (Inoise) ∼∏

(x,y)

N(

0, σ2)

=

µ


P (Inoise) ∼∏

(x,y)

N(

0, σ2)

µ

²±¯°



■ specify MRF ! (include prior knowledge about tooth rings)a[Zhang et al., 2001]

● Introduction



Images



(HMRF) Model



Model - FRAME

Application


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



Images



(HMRF) Model



Model - FRAME

Application




X

■ FRAMEa






● Introduction



Images



(HMRF) Model



Model - FRAME

Application




X

■ FRAMEa






● Introduction



Images



(HMRF) Model



Model - FRAME

Application




X

■ FRAMEa



(by convolution)

◆ use a bank of filterswith variable ring width T

◆ select best T during maximization


● Introduction



Images



(HMRF) Model



Model - FRAME

Application




X

■ FRAMEa




with variable ring width T

◆ select best T during maximization


● Introduction



Images



(HMRF) Model



Model - FRAME

Application




X

■ FRAMEa






● Introduction



Images



(HMRF) Model



Model - FRAME

Application


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



Images



(HMRF) Model



Model - FRAME

Application


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



Images


Application

● Application

● Bibliography


Application

● Introduction



Images


Application

● Application

● Bibliography


Application

■ theor. ] rings: 38recognized: ≈ 35

■ miss thin rings■ bifurcations:

where tooth ringshave differentorientation

■ → reconstructionheavily influencedby filter F

■ global property →select locationdependent filters

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Application

● Application

● Bibliography


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● Introduction



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● Introduction



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Application

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Application


■ miss thin rings

■ bifurcations:where tooth ringshave differentorientation



● Introduction



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● Application

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● Bibliography


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



Images


Application

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● Introduction



Images


Application

Fourier Transform

● Fourier Transform


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



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Application

Fourier Transform



Fourier Transform






● Introduction



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Application

Fourier Transform



Fourier Transform






Documents

A Classification Method for TCA-Images · Introduction Introduction to Tooth Cementum Annulation (TCA) Method and Images The Statistical Model - HMRF Application A Classification