  Most recent unsupervised non-rigid 3D shape matching methods are based on the
functional map framework due to its efficiency and superior performance.
Nevertheless, respective methods struggle to obtain spatially smooth pointwise
correspondences due to the lack of proper regularisation. In this work,
inspired by the success of message passing on graphs, we propose a synchronous
diffusion process which we use as regularisation to achieve smoothness in
non-rigid 3D shape matching problems. The intuition of synchronous diffusion is
that diffusing the same input function on two different shapes results in
consistent outputs. Using different challenging datasets, we demonstrate that
our novel regularisation can substantially improve the state-of-the-art in
shape matching, especially in the presence of topological noise.
