Maximum Persistency in Energy Minimization

TL;DR

This paper introduces a new polynomial-time verifiable sufficient condition for partial optimality in energy minimization problems, enabling identification of larger optimal variable assignments than existing methods.

Contribution

A novel sufficient condition for partial optimality that is invariant, comprehensive, and efficiently computable, extending and unifying previous approaches.

Findings

The new condition includes many existing conditions as special cases.

The proposed linear program guarantees larger partial assignments than previous methods.

Method is applicable to multi-label energy minimization problems.

Abstract

We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variables is an interesting possibility. Existing methods are based on different sufficient conditions. We propose a new sufficient condition for partial optimality which is: (1) verifiable in polynomial time (2) invariant to reparametrization of the problem and permutation of labels and (3) includes many existing sufficient conditions as special cases. We pose the problem of finding the maximum optimal partial assignment identifiable by the new sufficient condition. A polynomial method is proposed which is guaranteed to assign same or larger part of variables than several existing approaches. The core of the method is a specially constructed linear program that identifies persistent assignments in an arbitrary multi-label setting.