In this paper, we aim to provide a statistical theory for object matching
based on the Gromov-Wasserstein distance. To this end, we model general objects
as metric measure spaces. Based on this, we propose a simple and efficiently
computable asymptotic statistical test for pose invariant object
discrimination. This is based on an empirical version of a Ī²-trimmed
lower bound of the Gromov-Wasserstein distance. We derive for Ī²ā[0,1/2)
distributional limits of this test statistic. To this end, we introduce a novel
U-type process indexed in Ī² and show its weak convergence. Finally, the
theory developed is investigated in Monte Carlo simulations and applied to
structural protein comparisons.Comment: For a version with the complete supplement see [v2