DeepShapeMatchingKit: Accelerated Functional Map Solver and Shape Matching Pipelines Revisited

TL;DR

This paper introduces a faster, more efficient functional map solver for 3D shape matching, analyzes implementation details of DiffusionNet, and provides an open-source toolkit for the community.

Contribution

It proposes a vectorized reformulation for solving linear systems in shape matching, uncovers differences in DiffusionNet features, and releases a standardized codebase.

Findings

Achieves up to 33x speedup in functional map computation

Identifies two variants of DiffusionNet with different behaviors

Provides a new evaluation metric for partial shape matching

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 open-source 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 33x 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 open-source codebase, DeepShapeMatchingKit, that incorporates these improvements and standardizes training, evaluation, and data pipelines for common deep shape matching methods. The codebase is available at: https://github.com/xieyizheng/DeepShapeMatchingKit