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

By Tom Goldstein, Xavier Bresson, Stanley J. Osher. Journal of Scientific Computing, 2010

491 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/460fcac51d921b1e8ded3291ad6c885258da4f1a

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Citations in the corpus

Unwrapping ADMM: Efficient Distributed Computing via Transpose Reduction (2015, methodology): “Finally, by updating the Lagrange multipliers { λ i } , the solutions to each sub-problem are forced to be progressively more similar on each iteration.”
On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers (2016, background): “We refer to [2,4,8,12,20,22,27,31,34,36] for a few examples of applications.”
Bregman Alternating Direction Method of Multipliers (2013, methodology): “In recent years, the alternating direction method of multip liers (ADM or ADMM) [4] has been successfully applied in a broad spectrum of applications, r anging from image processing [11, 1, 13] to applied statistics and machine learning [23, 27, 20, 26].”
Fast Alternating Direction Optimization Methods (2014, methodology): “In the context of 1-regularized problems, this technique is commonly known as the split Bregman method [22] and is known to be an efficient solver for problems involving the total variation norm [21].”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, methodology): “and called Split Bregman Algorithm [73,74]; this method has received significant attention in image processing [67, 75–78].”