ACM-SE 45 Proceedings of the 45th annual southeast regional conference
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Curve evolution implementations [3][23] [25] of the Mumford-Shah functional [16] are of broad interest in image segmentation. These implementations, however, have initialization problems [6] [25]. A mathematical analysis of the initialization problem for the Chan-Vese implementation [3] [25] is provided in this paper. The initialization problem is a result of the non-convexity of the Mumford- Shah functional and the top-down hierarchy of the model's use of global region information in the image. Based on the analysis, efficient implementation methods are proposed for the Chan-Vese models [3] [25]. The proposed methods do not have to solve PDEs and thus work fast. The advantages of level set methods, such as automatic handling of topological changes, are preserved. These methods work well for images without strong noise. Initialization problems, however, still exist. A bottom-up image segmentation method is proposed that alleviates the initialization problem, based on region competition and the Mumford Shah functional [16]. This algorithm extends the method in [15], and is able to automatically and efficiently segment objects in complicated images. Using a bottom-up hierarchy, the method avoids the initialization problem in the Chan-Vese model and works for images with multiple junctions and color images. It is then extended to textured images using Gabor filters and fractal methods. Experimental results show that the proposed method works well and is robust to the effects of noise.