What Energy Functions Can Be Minimized via Graph Cuts?

In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper we characterize the energy functions that can be minimized by graph cuts. Our results are restricted to energy functions with binary variables. However, our work generalizes many previous constructions, and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration and scene reconstruction. We present three main results: a necessary condition for any energy function that can be minimized by graph cuts; a sufficient condition for energy functions that can be written as a sum of functions of up to three variables ...

• Type: Conference
• Year: 2002
• Where: ECCV
• Authors: Vladimir Kolmogorov, Ramin Zabih
• Keywords: Appropriate Graph, Computer Vision, ECCV 2002, Energy Functions, Graph Constructions, Graph Cuts, Particular Energy Function