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.

• Content Type Journal Article
• DOI 10.1007/s10915-009-9331-z
• Authors
  
  
  • Tom Goldstein, UCLA Department of Mathematics Box 951555 Los Angeles CA 90095-1555 USA
  • Xavier Bresson, UCLA Department of Mathematics Box 951555 Los Angeles CA 90095-1555 USA
  • Stanley Osher, UCLA Department of Mathematics Box 951555 Los Angeles CA 90095-1555 USA
  
  

• Journal Journal of Scientific Computing
• Online ISSN 1573-7691
• Print ISSN 0885-7474

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Original source : http://www.springerlink.com/content/276433831109g4...