Higher-Order Multicuts for Geometric Model Fitting and Motion Segmentation

Minimum cost lifted multicut problem is a generalization of the multicut problem and is a means to optimizing a decomposition of a graph w.r.t. both positive and negative edge costs. Its main advantage is that multicut-based formulations do not require the number of components given a priori; instead, it is deduced from the solution. However, the standard multicut cost function is limited to pairwise relationships between nodes, while several important applications either require or can benefit from a higher-order cost function, i.e. hyper-edges. In this paper, we propose a pseudo-boolean formulation for a multiple model fitting problem. It is based on a formulation of any-order minimum cost lifted multicuts, which allows to partition an undirected graph with pairwise connectivity such as to minimize costs defined over any set of hyper-edges. As the proposed formulation is NP-hard and the branch-and-bound algorithm is too slow in practice, we propose an efficient local search algorithm for inference into resulting problems. We demonstrate versatility and effectiveness of our approach in several applications: geometric multiple model fitting, homography and motion estimation, motion segmentation.