Title: 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.