Graph-cut optimization of the ratio of functions and its application to image segmentation

Optimizing the ratio of two functions of binary variables is a common task in many image analysis applications. In general, such a ratio is not amenable to graph-cut based optimization. In this paper, we show that if the numerator and the denominator of a ratio are individually graphrepresentable functions, then their ratio can be optimized via graph-cut based technique. As an example of such a ratio function we choose Yezzi et al.’s energy function [2], minimization of which produces a binary labeling of an image. Through examples, we illustrate that the advantage of working with graph-cut-based optimization for the aforementioned ratio in finding a global solution as opposed to local solutions found by level set methods proposed in [2].

• Type: Conference
• Year: 2008
• Where: ICIP
• Authors: Hui Wang, Nilanjan Ray, Hong Zhang
• Keywords: Aforementioned Ratio, Graph-cut Based Optimization, ICIP 2008, Image Processing, Ratio Function