1

Level Set Segmentation with Shape Priors

Jue Wang and Jiun-Hung Chen

CSE/EE 577 Spring 2004

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Notes on Level Set

Steps for implementation Define your own energy functional Initialize the curve and surface Evolve according to the numerical solution:

Continue until stopping criteria is reached

)0( )0,,( ji yx )(

),,(),,(),,(

),,()(),(

1 njinjinji

njinji

tyxFtyxtyx

tyxFttt

yx

3

Notes on Level Set

So the key is Defining a good energy function according to your

application

For basic image segmentation, the energy functional is usually defined as:

)(

))(1()()()()()(),,( 2

22

121 HcfHcfcc

2

22

1)( cfcfdivt

4

Notes on Level Set

Numerical Implementation Not easy to figure out but they’re in books, for example

Numerical stability should be also considered when you design your own energy function

2/322

22 2

yx

xyyxyyxyxxdiv

2

11 ,,2,,

h

yxyxyxyx jijijijixx

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Segmentation with Shape Prior

Reference shape

Input image Level set seg. w/o shap

e prior

Level set seg. w/ shape

prior

D. Cremers and S. Soatto. A pseudo-distance for shape priors in level set segmentation. IEEE Workshop on Variational, Geometric and Leve Set Methods in

Computer Vision, 2003.

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Segmentation with Shape Prior

Basic Idea Shape prior can be represented as another implicit

function The evolution of current is influenced by the

distance between and .

Problem: how to define the distance

r

r

rd ,

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Segmentation with Shape Prior

A Pseudo-distance

Shape energy:

Evolution function:

dx

hhd

2, 212

21212

)(),(,,, 2 xRxdE rs

dxhdxHt

originalt rr

22

2

8

Segmentation with Shape Prior

Pose parameters

Numerical solution help needed for this

),(

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Results

An image’s worth of thousands of words

An EXE is worth more

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Future Work

How to incorporate statistical shape models? Have a bunch of reference shapes instead of

one X.M. et al. Integrating prior shape models into

level-set approaches. Pattern Recognition Letters, April 2004.