Towards Discrete Solution: A Sparse Preserving Method for Correspondence Problem

TL;DR

This paper introduces a novel sparse constraint-based relaxation model called SPM for the feature correspondence problem, effectively preserving discrete one-to-one mappings and improving matching accuracy and efficiency.

Contribution

The paper proposes the SPM model that encodes permutation constraints via sparsity, providing a tighter relaxation for IQP matching problems compared to traditional methods.

Findings

SPM achieves higher matching accuracy on benchmark datasets.

The proposed algorithm demonstrates improved computational efficiency.

SPM effectively preserves discrete one-to-one correspondences.

Abstract

Many problems of interest in computer vision can be formulated as a problem of finding consistent correspondences between two feature sets. Feature correspondence (matching) problem with one-to-one mapping constraint is usually formulated as an Integral Quadratic Programming (IQP) problem with permutation (or orthogonal) constraint. Since it is NP-hard, relaxation models are required. One main challenge for optimizing IQP matching problem is how to incorporate the discrete one-to-one mapping (permutation) constraint in its quadratic objective optimization. In this paper, we present a new relaxation model, called Sparse Constraint Preserving Matching (SPM), for IQP matching problem. SPM is motivated by our observation that the discrete permutation constraint can be well encoded via a sparse constraint. Comparing with traditional relaxation models, SPM can incorporate the discrete one-to-one mapping constraint straightly via a sparse constraint and thus provides a tighter relaxation for original IQP matching problem. A simple yet effective update algorithm has been derived to solve the proposed SPM model. Experimental results on several feature matching tasks demonstrate the effectiveness and efficiency of SPM method.