Divergence-Free Shape Interpolation and Correspondence

2018/06/27 by Marvin Eisenberger, Eisenberger, Marvin, Zorah Lähner +3 · 2 citations
Engineering · Computer Science · #3D Shape Modeling and Analysis #Medical Image Segmentation Techniques #Advanced Vision and Imaging

paper · pdf · doi:10.48550/arxiv.1806.10417

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-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.

Citations

• Robust Estimation of a Location Parameter
• Efficient Deformable Shape Correspondence via Kernel Matching

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