Feature-aligned harmonic volumetric mapping using MFS

We present an efficient adaptive method to compute the harmonic volumetric mapping, which establishes a smooth correspondence between two given solid objects of the same topology. We solve a sequence of charge systems based on the harmonic function theory and the method of fundamental solutions (MFS) for designing the map with boundary and feature constraints. Compared to the previous harmonic volumetric mapping computation using MFS, this new scheme is more efficient and accurate, and can support feature alignment and adaptive refinement. Our harmonic volumetric mapping paradigm is therefore more effective for practical shape modeling applications and can handle heterogeneous volumetric data. We demonstrate the efficacy of this new framework on handling volumetric data with heterogeneous structure and nontrivial topological types.