Volumetric Mapping of Genus Zero Objects via Mass Preservation
This addresses shape analysis and mesh generation for applications like finite element methods and computer graphics, but appears incremental as it builds on existing volumetric mapping techniques.
The paper tackles the problem of mapping genus zero solid objects onto a hexahedral decomposition of a solid cube, with a volume-preserving constraint, and demonstrates the method on various 3D models.
In this work, we present a technique to map any genus zero solid object onto a hexahedral decomposition of a solid cube. This problem appears in many applications ranging from finite element methods to visual tracking. From this, one can then hopefully utilize the proposed technique for shape analysis, registration, as well as other related computer graphics tasks. More importantly, given that we seek to establish a one-to-one correspondence of an input volume to that of a solid cube, our algorithm can naturally generate a quality hexahedral mesh as an output. In addition, we constrain the mapping itself to be volume preserving allowing for the possibility of further mesh simplification. We demonstrate our method both qualitatively and quantitatively on various 3D solid models