DeepShapeMatchingKit: Accelerated Functional Map Solver and Shape Matching Pipelines Revisited
For researchers in 3D shape matching, this work provides practical speedups and clarifies implementation details, but the contributions are incremental.
The paper identifies a computational bottleneck in standard functional map solvers for non-rigid 3D shape matching and proposes a vectorized reformulation that achieves up to 33x speedup while preserving exact solutions. It also documents an implementation divergence in DiffusionNet's spatial gradient features and introduces balanced accuracy for partial-to-partial matching evaluation.
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