SIGMA: Scale-Invariant Global Sparse Shape Matching
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916190247452672 |
|---|---|
| author | Gao, Maolin Roetzer, Paul Eisenberger, Marvin Lähner, Zorah Moeller, Michael Cremers, Daniel Bernard, Florian |
| author_facet | Gao, Maolin Roetzer, Paul Eisenberger, Marvin Lähner, Zorah Moeller, Michael Cremers, Daniel Bernard, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08393 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | SIGMA: Scale-Invariant Global Sparse Shape Matching Gao, Maolin Roetzer, Paul Eisenberger, Marvin Lähner, Zorah Moeller, Michael Cremers, Daniel Bernard, Florian Computer Vision and Pattern Recognition 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. |
| title | SIGMA: Scale-Invariant Global Sparse Shape Matching |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2308.08393 |