A fast algorithm for image segmentation based on fuzzy region competition
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A fast algorithm for image segmentation based on fuzzy region competition Fangfang Dong · Chunxiao Liu · De-Xing Kong
Received: 30 September 2009 / Accepted: 19 September 2010 / Published online: 23 September 2011 © Springer Science+Business Media, LLC 2011
Abstract Variational models for image segmentation are usually solved by the level set method, which is not only slow to compute but also dependent on initialization strongly. Recently, fuzzy region competition models or globally convex segmentation models have been introduced. They are insensitive to initialization, but contain TV-regularizers, making them difficult to compute. Goldstein, Bresson and Osher have applied the split Bregman iteration to globally convex segmentation models which avoided the regularization of TV norm and speeded up the computation. However, the split Bregman method needs to solve a partial differential equation (PDE) in each iteration. In this paper, we present a simple algorithm without solving the PDEs proposed originally by Jia et al. (2009) with application to image segmentation problems. The algorithm also avoids the regularization of TV norm and has a simpler form, which is in favor of implementing. Numerical experiments show that our algorithm works faster and more efficiently than other fast schemes, such as duality based methods and the split Bregman scheme.
Communicated by R. Q. Jia. This work was supported in part by the NNSF of China (Grant No. 10971190) and the Qiu-Shi Chair Professor Fellowship from Zhejiang University. F. Dong (B) School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China e-mail: [email protected] C. Liu Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China D.-X. Kong Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
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Keywords Image segmentation · Variational models · Level set method · Fuzzy region competition · Split Bregman method · Jia and Zhao’s algorithm Mathematics Subject Classifications (2010) 65K10 · 68U10 · 49M30
1 Introduction Image segmentation is an important research field in image processing and computer vision. The segmentation process is aimed to partition an image into several subregions with uniform characteristics like intensities, color and texture etc. Active contour methods have become very popular in recent years in image segmentation, one can see the literatures [3, 4, 8, 9, 14, 15, 20]. They include edge-based active contour models and region-based active contour models. Geodesic active contour (GAC)/snakes model, proposed originally in [14], identifies objects using an edge detector function and is an edgebased active contour model. One of the first region-based active contours is Mumford-Shah (MS) segmentation model [20]. In this model, an image is segmented by finding the best approximation of the image as a piecewise smooth function. One of the simplest and most successful formulations of this model is the “active contours without edges” (ACWE) model proposed by
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