1

Variational Approaches and Image Segmentation

Lecture #8Lecture #8Hossam Abdelmunim1 & Aly A. Farag2

1Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt

2Electerical and Computer Engineering Department, University of Louisville, Louisville, KY, USA

ECE 643 – Fall 2010

Adaptive Multi-modal SegmentationAdaptive Multi-modal Segmentation

OutlineOutline

• Multiple region representation.Multiple region representation.

• Energy function formulation for bimodal and Energy function formulation for bimodal and multi modal cases.multi modal cases.

• Adaptive region model PDE’s.Adaptive region model PDE’s.

• Initialization.Initialization.

• Experimental resultsExperimental results

• Conclusion and criticism.Conclusion and criticism.

Related PapersRelated Papers

T. Brox and J. Weickert. ”Level Set Based Image Segmentation with Multiple Regions,” in Pattern Recognition., Springer LNCS 3175, pp. 415–423, Aug. 2004.

A. A. Farag and Hossam Hassan, “Adaptive Segmentation of Multi-modal 3D Data Using Robust Level Set Techniques“, in Proc International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI’04), Saint Malo,France, pp. 143-150, September, 2004.

Regions RepresentationRegions Representation

Assume that we have image I with K classes (regions).

K (i=1..K) level set functions are defined to represent the regions:

outsideifXD

boundarytheon

insideifXD

Xi

)(

0

)(

)(

D is the minimum Euclidean distance between the current point and the contour/surface.

The positive part of the level set function is dedicated for the associated region. It is adaptive because the contour changes with time.

Segmentation ObjectivesSegmentation Objectives

K contours are initialized.

They are required to evolve to hit the boundaries of their associated regions.

Level sets change to minimize a given energy function.

The steady state solution will represent segmented regions in the positive part of each function.

Image and FeatureImage and Feature

Color intensityTexture tensor

Adaptive Region ParametersAdaptive Region Parameters

Regions statistics are described by Gaussian models.

The parameters are estimated by M.L.E as follows:

The prior probability is estimated as the region area:

dxH

IdxH

i

i

i))((

))((

dxH

dxIxIxH

i

Tiii

i))((

))()()())(((

K

ii

i

i

dxH

dxH

1

))((

))((

Automatic Seed InitializationAutomatic Seed Initialization

Results (Natural Image)Results (Natural Image)

Image Size: 200 X 276

Window Size: 15 X 15

Two Classes

Results (MRI-T1 image)Results (MRI-T1 image)

Image Size: 256 X 256

Window Size: 5 X 5

Two Classes

Results (MRI-PD Image)Results (MRI-PD Image)

Image Size: 375 X 373

Window Size: 5 X 5

Three Classes

Results (Synthetic)Results (Synthetic)

Image Size: 300 X 150

Window Size: 25 X 25

Three Classes

Results (Color Image)Results (Color Image)

Image Size: 342 X 450

Window Size: 35 X 35

Two Classes

Results (Continue)Results (Continue)

DiscussionsDiscussions

An adaptive multi region segmentation approach is proposed.

This method is very suitable for the homogeneous regions.

The regularization term in the PDE enable segmenting images with noise. In case of high noise levels, the convergence time increases and the boundaries are miss-classified by increasing the strength of the curvature component.

Synthetic, real, and medical examples are given.

Non parametric probability density functions may be investigated replacing the Gaussian models.

Thank You&

Questions

Thank You&

Questions