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DeepShapeMatchingKit: Accelerated Functional Map Solver and Shape Matching Pipelines Revisited

MCML Authors

Lennart Bastian

→ Group Nassir Navab
Computer Aided Medical Procedures & Augmented Reality

Maolin Gao

→ Group Daniel Cremers
Computer Vision & Artificial Intelligence

Daniel Cremers

Prof. Dr.

Director

Computer Vision & Artificial Intelligence

Abstract

Deep functional maps, leveraging learned feature extractors and spectral correspondence solvers, are fundamental to non-rigid 3D shape matching. Based on an analysis of opensource implementations, we find that standard functional map implementations solve k independent linear systems serially, which is a computational bottleneck at higher spectral resolution. We thus propose a vectorized reformulation that solves all systems in a single kernel call, achieving up to a 33$times$ speedup while preserving the exact solution. Furthermore, we identify and document a previously unnoticed implementation divergence in the spatial gradient features of the mainstay DiffusionNet: two variants that parameterize distinct families of tangent-plane transformations, and present experiments analyzing their respective behaviors across diverse benchmarks. We additionally revisit overlap prediction evaluation for partial-to-partial matching and show that balanced accuracy provides a useful complementary metric under varying overlap ratios. To share these advancements with the wider community, we present an opensource codebase, DeepShapeMatchingKit, that incorporates these improvements and standardizes training, evaluation, and data pipelines for common deep shape matching methods.

misc XBD+26