Pseudo-Boolean Optimization: Theory and Applications in Vision

Many problems in computer vision, such as stereo, segmentation and denoising can be formulated as pseudo-boolean optimization problems. Over the last decade, graphs cuts have become a standard tool for solving such problems. The last couple of years have seen a great advancement in the methods used to minimize pseudoboolean functions of higher order than quadratic. In this paper, we give an overview of how one can optimize higherorder functions via generalized roof duality and how it can be applied to problems in image analysis and vision. I. PSEUDO-BOOLEAN OPTIMIZATION A pseudo-boolean function is a function from the set of boolean vectors of dimension n, denoted B = {0, 1}, to the reals. Any pseudo-boolean f can be uniquely represented by a multilinear polynomial of the form