Diffusion-driven high-order matching of partial deformable shapes

This paper tackles the matching problem of partial deformable shapes with changing boundary and varying topology. We compute high-order graph matching directly on manifolds, without global/local surface parameterization. In particular, we articulate the heat kernel tensor (HKT), which is a high-order potential of geometric compatibility between feature tuples measured by heat kernels within bounded time. Inherited from the heat kernel, the HKT is multi-scale, invariant to isometric deformation, resilient to noise, and robust to topology changes. We also build up a two-level hierarchy via feature clustering, by which the searching space of HKT is greatly reduced. To evaluate the proposed method, we conduct experiments in various aspects, including scale, noise, deformation, comparison, and semantic matching.