用分裂Bregman法高效实现两相图像分割，自动区分前景背景。
An Implemention of Two-Phase Image Segmentation using the Split Bregman Method
- 基于分裂Bregman法优化Chan-Vese模型能量函数
- 通过平滑边界和双均值假设实现像素归属划分
- 适合图像分割初学者及算法实现参考
本文详细实现了Goldstein、Bresson、Osher提出的两相图像分割算法。该方法将二维图像区域划分为前景与背景，每个像素被分配至其中一类。模型假设输入图像的像素值可由两个不同平均值概括，且区域边界光滑。能量函数由区域内图像数据项与边界长度惩罚项组成，原由Chan和Vese提出。该文改进了其能量形式，使其能通过分裂Bregman法高效最小化，从而实现等效两相分割。文中提供了完整实现细节，并在多幅图像上测试了不同参数下的性能表现。
原文摘要 · Abstract (English)
In this paper, we describe an implementation of the two-phase image segmentation algorithm proposed by Goldstein, Bresson, Osher in \cite{gold:bre}. This algorithm partitions the domain of a given 2d image into foreground and background regions, and each pixel of the image is assigned membership to one of these two regions. The underlying assumption for the segmentation model is that the pixel values of the input image can be summarized by two distinct average values, and that the region boundaries are smooth. Accordingly, the model is defined as an energy in which the variable is a region membership function to assign pixels to either region, originally proposed by Chan and Vese in \cite{chan:vese}. This energy is the sum of image data terms in the regions and a length penalty for region boundaries. Goldstein, Bresson, Osher modify the energy of Chan-Vese in \cite{gold:bre} so that their new energy can be minimized efficiently using the split Bregman method to produce an equivalent two-phase segmentation. We provide a detailed implementation of this method \cite{gold:bre}, and document its performance with several images over a range of algorithm parameters.
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