Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
复制标题
DOI：
10.1007/s10915-009-9331-z
复制
发表时间：
2010-10-01
影响因子：
2.5
通讯作者：
Osher, Stanley
中科院分区：
文献类型：
--
作者：
Goldstein, Tom;Bresson, Xavier;Osher, Stanley
变分模型在图像分割中有很多应用，但是计算速度很慢。近年来，人们引入了全局凸分割模型，该模型具有很高的可靠性，但由于包含tv正则化算子，使得其难以计算。先前介绍的Split Bregman方法是一种快速最小化L1正则化函数的技术，并已应用于去噪和压缩感知问题。通过将Split Bregman概念应用于图像分割问题，我们构建了快速求解器，可以胜过传统的方案，如基于对偶性的方法和图切割。凸分割方案也大大优于传统的水平集方法，如基于Chan-Vese水平集的分割算法。我们还考虑了从无组织数据点重建表面的相关问题，该问题用于构造三维水平集表示。本文的主要目的是检验“分裂Bregman”技术解决这些问题的有效性，并将该方案与更传统的方法进行比较。
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.