An Implemention of Two-Phase Image Segmentation using the Split Bregman Method

TL;DR

This paper details an implementation of a two-phase image segmentation algorithm using the split Bregman method, improving efficiency in partitioning images into foreground and background regions based on pixel intensity.

Contribution

It provides a detailed implementation and performance analysis of the split Bregman method applied to the Chan-Vese segmentation model.

Findings

Efficient segmentation achieved with the split Bregman method.

Performance varies with algorithm parameters and image characteristics.

Method effectively separates foreground and background regions.

Abstract

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.