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Unformatted text preview: IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. , NO. 1 A Variational Framework for Multi-Region Pairwise Similarity-based Image Segmentation Luca Bertelli, Student Member, IEEE , Baris Sumengen, Member, IEEE , B. S. Manjunath, Fellow, IEEE , Frederic Gibou Abstract Variational cost functions that are based on pairwise similarity between pixels can be minimized within level set framework resulting in a binary image segmentation. In this paper we extend such cost functions and address multi-region image segmentation problem by employing a multi-phase level set framework. For multi-modal images cost functions become more complicated and relatively difficult to minimize. We extend our previous work [1], proposed for background/foreground separation, to the segmentation of images into more than two regions. We also demonstrate an efficient implementation of the curve evolution, which reduces the computational time significantly. Finally, we validate the proposed method on the Berkeley Segmentation Data Set by comparing its performance with other segmentation techniques. Index Terms Region-based image segmentation, grouping, level sets, multi-phase motion, pairwise similarity measure. I. INTRODUCTION I N this paper we present a variational approach to multi-region segmentation that is based on pairwise pixel similarity. Pairwise similarity-based cost functions have been extensively used in the literature, primarily for back- ground/foreground segmentation [2], [3], [1]. Extensions to multiple regions is then obtained by recursively bi-partioning the regions, which may not lead to a good overall segmenta- tion. In contrast, the method that we propose explicitly starts with the goal of segmenting the image into more than two regions, and we derive the appropriate evolution equations that result in the desired partitioning. It combines the advantages of pairwise pixel similarity based cost functions their ability to embed heterogeneous information derived from different image cues with the flexibility of the variational methods to deal with multiple regions, into a single, well defined framework for image segmentation. A pairwise similarity based variational framework was first introduced in [1] for the case of two-region segmentation. However, as we will see in the following, extension of this to multi-region segmentation is not straightforward and requires a reformulation of the cost functions. Using the notation w ( p 1 ,p 2 ) to represent the pairwise dissimilarity between point p 1 and point p 2 (where p i is a 2D point in the image domain) Luca Bertelli and B.S. Manjunath are with the Department of Electrical and Computer Engineering at the University of California, Santa Barbara (emails { lbertelli,manj } @ece.ucsb.edu). Baris Sumengen is with Like.com (email sumengen@ece.ucsb.edu). Frederic Gibou is with the Department of Mechanical Engineering and the Department of Computer Science at the University of California, Santa Barbara (email fgibou@engineering.ucsb.edu).University of California, Santa Barbara (email fgibou@engineering....
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This note was uploaded on 12/28/2011 for the course BIO 100 taught by Professor Gomez during the Fall '11 term at UCSB.

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