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.

Fast and Exact Primal-Dual Iterations for Variational Problems in Computer Vision

“…The authors use a similar method, but require iterative projections at each step. The basic Douglas-Rachford iteration [6,7] applied to the dual problem can be shown to be equivalent to the Alternating Direction Method of Multipliers [8] and the recently proposed Alternating Split Bregman method [9,20], hence our results equally apply in these formulations.…”

“…In terms of graph-based approaches, this can be thought of as the potentials on the edges of the graph. The formulation (9) carries over this principle to the continuous domain Ω. By discretizing u, v and s on a rectangular grid and choosing a forward finite differences discretization L of the gradient operator D, the above variational formulation can be posed in the saddle point form (3) without introducing grid bias (cf.…”

“…Regarding optimization, our work extends the approach proposed in [9] for two-, and in [14] for multiclass labeling. The authors use a similar method, but require iterative projections at each step.…”

Convex Image Segmentation Model Based on Local and Global Intensity Fitting Energy and Split Bregman Method

“…The efficiency of the split Bregman method for image segmentation has been demonstrated in 21,22 . We now apply the split Bregman method to solve the proposed minimization problem in a more efficient way.…”

Active Contour Model Based on Nonlocal Means Method For Color Texture Segmentation

“…At last, based on the nonlocal means method and the traditional active contour model, the model for color textures segmentation is proposed. What's more, we design the Split-Bregman algorithm [7]. At last, we make some numerical experiments.…”