Journal
2019 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR 2019)
Volume -, Issue -, Pages 7521-7530Publisher
IEEE
DOI: 10.1109/CVPR.2019.00771
Keywords
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Funding
- ERC [802554, 724228, 758800]
- Google Research Faculty awards
- Royal Society Wolfson Research Merit award
- Rudolf Diesel industrial fellowship at TU Munich
- Google Focused Research Award
- KAUST OSR Award [OSR-CRG2017-3426]
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The question whether one can recover the shape of a geometric object from its Laplacian spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this paper we introduce a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another We implement the isospectralization procedure using modern differentiable programming techniques and exemplify its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction,pose and style transfer and dense deformable correspondence.
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