Divergence-Free Shape Interpolation and Correspondence

Code

• github.com/sprengvogel/DivergenceFreeCorrespondence
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Abstract

We present a novel method to model and calculate deformation fields between shapes embedded in 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-Lo\`eve 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.

Reproductions