SIGMA: Scale-Invariant Global Sparse Shape Matching

TL;DR

SIGMA introduces a globally optimal, scale-invariant method for sparse non-rigid shape matching using a novel MIP formulation and a new geometric operator, achieving state-of-the-art results.

Contribution

The paper presents a new MIP-based approach with a scale-invariant operator and optimality guarantees for non-rigid shape matching.

Findings

Achieves state-of-the-art accuracy on challenging datasets.

Proves invariance to rigid transformations and scaling.

Scales linearly with mesh resolution.

Abstract

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.