Divergence-Free Shape Interpolation and Correspondence
This work addresses shape deformation and correspondence for computer graphics and geometry processing, with incremental improvements in efficiency and volume preservation.
The paper tackles the problem of modeling deformation fields between shapes in ℝᴰ by introducing a method that simultaneously interpolates shapes and calculates correspondences using a divergence-free, volume-preserving field represented with a coarse-to-fine basis, achieving results on TOSCA and FAUST datasets.
We present a novel method to model and calculate deformation fields between shapes embedded in $\mathbb{R}^D$. Our framework combines naturally interpolating the two input shapes and calculating correspondences at the same time. The key idea is to compute a divergence-free deformation field represented in a coarse-to-fine basis using the Karhunen-Loève expansion. The advantages are that there is no need to discretize the embedding space and the deformation is volume-preserving. Furthermore, the optimization is done on downsampled versions of the shapes but the morphing can be applied to any resolution without a heavy increase in complexity. We show results for shape correspondence, registration, inter- and extrapolation on the TOSCA and FAUST data sets.