Continuous and orientation-preserving correspondences via functional maps
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Visual Computing Center (VCC)
KAUST Grant NumberOSR-CRG2017-3426
Online Publication Date2018-11-28
Print Publication Date2018-12-04
Permanent link to this recordhttp://hdl.handle.net/10754/644890
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AbstractWe propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated directly in the functional (spectral) domain without using landmark or region correspondences and without relying on external symmetry information. This allows us to obtain functional maps that promote orientation preservation, even when using descriptors, that are invariant to orientation changes. We then show how higher quality, approximately continuous and bijective pointwise correspondences can be obtained from initial functional maps by introducing a novel refinement technique that aims to simultaneously improve the maps both in the spectral and spatial domains. This leads to a general pipeline for computing correspondences between shapes that results in high-quality maps, while admitting an efficient optimization scheme. We show through extensive evaluation that our approach improves upon state-of-the-art results on challenging isometric and non-isometric correspondence benchmarks according to both measures of continuity and coverage as well as producing semantically meaningful correspondences as measured by the distance to ground truth maps.
CitationRen J, Poulenard A, Wonka P, Ovsjanikov M (2018) Continuous and orientation-preserving correspondences via functional maps. ACM Transactions on Graphics 37: 1–16. Available: http://dx.doi.org/10.1145/3272127.3275040.
SponsorsThe authors would like to thank the anonymous reviewers for their valuable comments and helpful suggestions. The authors would like to thank Zorah Lähner, Danielle Ezuz, Emanuele Rodolà, Dorian Nogneng, Dongming Yan, and Ruqi Huang for providing code and valuable discussions. This work was supported by the KAUST Office of Sponsored Research (OSR) under Award No. OSR-CRG2017-3426, the Jean Marjoulet chair from Ecole Polytechnique, a Google Research Award, and the ERC Starting Grant No. 758800 (EXPROTEA).
JournalACM Transactions on Graphics