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Zbl 1203.65044
Goldstein, Tom; Bresson, Xavier; Osher, Stanley
Geometric applications of the split Bregman method: segmentation and surface reconstruction. (English)
[J] J. Sci. Comput. 45, No. 1-3, 272-293 (2010). ISSN 0885-7474; ISSN 1573-7691/e

Summary: Variational models for image segmentation have many applications, but can be slow to compute. Recently, globally convex segmentation models have been introduced which are very reliable, but contain TV-regularizers, making them difficult to compute. The previously introduced split Bregman method is a technique for fast minimization of $L^1$ regularized functionals, and has been applied to denoising and compressed sensing problems. By applying the split Bregman concept to image segmentation problems, we build fast solvers which can out-perform more conventional schemes, such as duality based methods and graph-cuts. The convex segmentation schemes also substantially outperform conventional level set methods, such as the Chan-Vese level set-based segmentation algorithm. We also consider the related problem of surface reconstruction from unorganized data points, which is used for constructing level set representations in 3 dimensions. The primary purpose of this paper is to examine the effectiveness of ``split Bregman'' techniques for solving these problems, and to compare this scheme with more conventional methods.

MSC 2000:: *65D18 Computer graphics and computational geometry
65D19
68U10 Image processing

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