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Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases. | LitMetric

Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases.

Comput Graph Forum

LIX, École Polytechnique, IP Paris Palaiseau France.

Published: September 2022

AI Article Synopsis

Article Abstract

We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional map framework, but rather than promoting isometries we focus on near-conformal maps that preserve landmarks exactly. We achieve this, first, by introducing a novel landmark-adapted basis using an intrinsic Dirichlet-Steklov eigenproblem. Second, we establish the functional decomposition of conformal maps expressed in this basis. Finally, we formulate a conformally-invariant energy that promotes high-quality landmark-preserving maps, and show how it can be optimized via a variant of the recently proposed ZoomOut method that we extend to our setting. Our method is descriptor-free, efficient and robust to significant mesh variability. We evaluate our approach on a range of benchmark datasets and demonstrate state-of-the-art performance on non-isometric benchmarks and near state-of-the-art performance on isometric ones.

Download full-text PDF

Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9804561PMC
http://dx.doi.org/10.1111/cgf.14579DOI Listing

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