Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction

Abstract

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 L1 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.

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Correspondence to Tom Goldstein.

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Dedicated to the memory of David Gottlieb.

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Goldstein, T., Bresson, X. & Osher, S. Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction. J Sci Comput 45, 272–293 (2010). https://doi.org/10.1007/s10915-009-9331-z

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  • Image segmentation
  • Split Bregman
  • Bregman iteration
  • Total variation