Synchronisation of Partial Multi-Matchings via Non-negative Factorisations

Abstract

In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full matching case all compositions of pairwise matchings over cycles must be equal to the identity. Motivated by clustering and matrix factorisation perspectives of cycle-consistency, we derive an algorithm to tackle the permutation synchronisation problem based on non-negative factorisations. In order to deal with the inherent non-convexity of the permutation synchronisation problem, we use an initialisation procedure based on a novel rotation scheme applied to the solution of the spectral relaxation. Moreover, this rotation scheme facilitates a convenient Euclidean projection to obtain a binary solution after solving our relaxed problem. In contrast to state-of-the-art methods, our approach is guaranteed to produce cycle-consistent results. We experimentally demonstrate the efficacy of our method and show that it achieves better results compared to existing methods.

References in corpus (8)

• A General Multi-Graph Matching Approach via Graduated Consistency-regularized Boosting
• Near-Optimal Joint Object Matching via Convex Relaxation
• Spectral Motion Synchronization in SE(3)
• A Solution for Multi-Alignment by Transformation Synchronisation
• Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization
• Distributed methods for synchronization of orthogonal matrices over graphs
• Clustering by Low-Rank Doubly Stochastic Matrix Decomposition
• Convex Relaxations for Permutation Problems

Cited by in corpus (7)

• Probabilistic Permutation Synchronization using the Riemannian Structure of the Birkhoff Polytope
• Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching
• MIXER: Multiattribute, Multiway Fusion of Uncertain Pairwise Affinities
• Leveraging Cycle-Consistent Anchor Points for Self-Supervised RGB-D Registration
• Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation
• Non-Negative Spherical Relaxations for Universe-Free Multi-Matching and Clustering
• MIXER: A Principled Framework for Multimodal, Multiway Data Association