SIGMA: Scale-Invariant Global Sparse Shape Matching
This work addresses the problem of robust 3D shape matching for applications like computer graphics and vision, offering a method with optimality guarantees and invariance to transformations, though it is incremental in improving existing matching techniques.
The paper tackles the problem of generating precise sparse correspondences for highly non-rigid 3D shapes by proposing a novel mixed-integer programming formulation that is scale-invariant and initialization-free, achieving state-of-the-art results on challenging datasets with linear time scaling.
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.