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Geometric applications of the split Bregman method: segmentation and surface reconstruction. (English) Zbl 1203.65044
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.
65D18Computer graphics, image analysis, and computational geometry
65D19Computational issues in computer and robotic vision
68U10Image processing (computing aspects)
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