Riemannian Functional Map Synchronization for Probabilistic Partial Correspondence in Shape Networks
share
Functional maps are efficient representations of shape correspondences, that provide matching of real-valued functions between pairs of shapes. Functional maps can be modelled as elements of the Lie group SO(n) for nearly isometric shapes. Synchronization can subsequently be employed to enforce cycle consistency between functional maps computed on a set of shapes, hereby enhancing the accuracy of the individual maps. There is an interest in developing synchronization methods that respect the geometric structure of SO(n), while introducing a probabilistic framework to quantify the uncertainty associated with the synchronization results. This paper introduces a Bayesian probabilistic inference framework on SO(n) for Riemannian synchronization of functional maps, performs a maximum-a-posteriori estimation of functional maps through synchronization and further deploys a Riemannian Markov-Chain Monte Carlo sampler for uncertainty quantification. Our experiments demonstrate that constraining the synchronization on the Riemannian manifold SO(n) improves the estimation of the functional maps, while our Riemannian MCMC sampler provides for the first time an uncertainty quantification of the results.
READ FULL TEXT