Volumetric Functional Maps
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914403327148032 |
|---|---|
| author | Maggioli, Filippo Melzi, Simone Livesu, Marco |
| author_facet | Maggioli, Filippo Melzi, Simone Livesu, Marco |
| contents | Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps framework. We show that the eigenfunctions of the volumetric Laplace operator define a functional space that is suitable for high-quality signal transfer. We also experiment with various techniques that edit this functional space, porting them to volume domains. We validate our method on novel volumetric datasets and on tetrahedralizations of well established surface datasets, also showcasing practical applications involving both discrete and continuous signal mapping, for segmentation transfer, mesh connectivity transfer and solid texturing. Finally, we show that the volumetric spectrum greatly improves the accuracy for classical shape matching tasks among surfaces, consistently outperforming surface-only spectral methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Volumetric Functional Maps Maggioli, Filippo Melzi, Simone Livesu, Marco Graphics Computational Geometry 68U05 I.3 Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps framework. We show that the eigenfunctions of the volumetric Laplace operator define a functional space that is suitable for high-quality signal transfer. We also experiment with various techniques that edit this functional space, porting them to volume domains. We validate our method on novel volumetric datasets and on tetrahedralizations of well established surface datasets, also showcasing practical applications involving both discrete and continuous signal mapping, for segmentation transfer, mesh connectivity transfer and solid texturing. Finally, we show that the volumetric spectrum greatly improves the accuracy for classical shape matching tasks among surfaces, consistently outperforming surface-only spectral methods. |
| title | Volumetric Functional Maps |
| topic | Graphics Computational Geometry 68U05 I.3 |
| url | https://arxiv.org/abs/2506.13212 |