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

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 TVregularizers, 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. We also consider the related problem of surface reconstruction from unorganized data points, which is used for constructing level set representations in 3 dimensions.

• Type: Journal
• Year: 2010
• Where: JSCIC
• Authors: Tom Goldstein, Xavier Bresson, Stanley Osher
• Keywords: Convex Segmentation Models, JSCIC 2010, Split Bregman, Split Bregman Method