Volumetric Mapping of Genus Zero Objects via Mass Preservation

Abstract

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.

Distortion measure of spectrograms for classification of respiratory diseases

“…Note that for a large collection {S 1 , ..., S m } of shapes it may be very expensive to compute optimal deformations f ij , for each 1 ≤ i < j ≤ m. Therefore, instead of matching all the pairs of shapes, a more practical approach would be to compute an optimal mapping f i of each shape S i into a simple target domain. Depending on the dimensionality of an object and its topology, a simple target domain could be the plane, a sphere [22], the unit circle [23], a cube [24], or a ball [25].…”