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Spectral approaches to partial deformable 3D shape correspondence

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VMVW03 - Flows, mappings and shapes

In this talk we will present our recent line of work on (deformable) partial 3D shape correspondence in the spectral domain. We will first introduce Partial Functional Maps (PFM), showing how to robustly formulate the shape correspondence problem under missing geometry with the language of functional maps. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. We will show further extensions to deal with the presence of clutter (deformable object-in-clutter) and multiple pieces (non-rigid puzzles). In the second part of the talk, we will introduce a novel approach to the same problem which operates completely in the spectral domain, avoiding the cumbersome alternating optimization used in the previous approaches. This allows matching shapes with constant complexity independent of the number of shape vertices, and yields state-of-the-art results on challenging correspondence benchmarks in the presence of partiality and topological noise. Authors: E. Rodola, L. Cosmo, O. Litany, J. Masci, A. Bronstein, M. Bronstein, A. Torsello, D. Cremers

This talk is part of the Isaac Newton Institute Seminar Series series.

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