TY - GEN
T1 - Isospectralization, or how to hear shape, style, and correspondence
AU - Cosmo, Luca
AU - Panine, Mikhail
AU - Rampini, Arianna
AU - Ovsjanikov, Maks
AU - Bronstein, Michael M.
AU - Rodola, Rodola
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/6
Y1 - 2019/6
N2 - 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.
AB - 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.
KW - Grouping and Shape
KW - Physics-based Vision and Shape-from-X
KW - Segmentation
KW - Vision + Graphics
UR - http://www.scopus.com/inward/record.url?scp=85073188550&partnerID=8YFLogxK
U2 - 10.1109/CVPR.2019.00771
DO - 10.1109/CVPR.2019.00771
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AN - SCOPUS:85073188550
T3 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
SP - 7521
EP - 7530
BT - Proceedings - 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2019
PB - IEEE Computer Society
T2 - 32nd IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2019
Y2 - 16 June 2019 through 20 June 2019
ER -