1 Lecture #8 Variational Approaches and Image Segmentation Lecture #8 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department,

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1 Lecture #8 Variational Approaches and Image Segmentation Lecture #8 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical and Computer Engineering Department, University of Louisville, Louisville, KY, USA ECE 643 – Fall 2010

Adaptive Multi-modal Segmentation

Outline Multiple region representation.Multiple region representation. Energy function formulation for bimodal and multi modal cases.Energy function formulation for bimodal and 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 Papers T. Brox and J. Weickert. ”Level Set Based Image Segmentation with Multiple Regions,” in Pattern Recognition., Springer LNCS 3175, pp. 415–423, Aug 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 , September, 2004.

Regions Representation Assume that we have image I with K classes (regions). K (i=1..K) level set functions are defined to represent the regions: 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 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 Feature Color intensity Texture tensor

Adaptive 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:

Automatic Seed Initialization

Results (Natural Image) Image Size: 200 X 276 Window Size: 15 X 15 Two Classes

Results (MRI-T1 image) Image Size: 256 X 256 Window Size: 5 X 5 Two Classes

Results (MRI-PD Image) Image Size: 375 X 373 Window Size: 5 X 5 Three Classes

Results (Synthetic) Image Size: 300 X 150 Window Size: 25 X 25 Three Classes

Results (Color Image) Image Size: 342 X 450 Window Size: 35 X 35 Two Classes

Results (Continue)

Discussions 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