Multi-Label MRF Optimization via Least Squares s-t Cuts

TL;DR

This paper introduces a polynomial-time approximation method for multi-label graph partitioning in computer vision, reformulating the NP-hard problem as a minimal s-t cut problem using least squares and binary encoding.

Contribution

The authors propose a novel reformulation of k-way graph partitioning as an approximate s-t cut problem with a least squares solution, enabling efficient global optimization.

Findings

Provides a polynomial-time approximation for multi-label graph cuts

Achieves effective segmentation results in computer vision tasks

Introduces a binary encoding scheme for multi-label assignment

Abstract

There are many applications of graph cuts in computer vision, e.g. segmentation. We present a novel method to reformulate the NP-hard, k-way graph partitioning problem as an approximate minimal s-t graph cut problem, for which a globally optimal solution is found in polynomial time. Each non-terminal vertex in the original graph is replaced by a set of ceil(log_2(k)) new vertices. The original graph edges are replaced by new edges connecting the new vertices to each other and to only two, source s and sink t, terminal nodes. The weights of the new edges are obtained using a novel least squares solution approximating the constraints of the initial k-way setup. The minimal s-t cut labels each new vertex with a binary (s vs t) "Gray" encoding, which is then decoded into a decimal label number that assigns each of the original vertices to one of k classes. We analyze the properties of the approximation and present quantitative as well as qualitative segmentation results.