Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases. (arXiv:2205.04800v2 [cs.CV] UPDATED)

Web: http://arxiv.org/abs/2205.04800

We propose a principled approach for non-isometric landmark-preserving
non-rigid shape matching. Our method is based on the functional maps framework,
but rather than promoting isometries we focus instead 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 …

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