Efficient Deformable Shape Correspondence via Kernel Matching

Lähner, Zorah; Vestner, Matthias; Boyarski, Amit; Litany, Or; Slossberg, Ron; Remez, Tal; Rodolà, Emanuele; Bronstein, Alex; Bronstein, Michael M.; Kimmel, Ron; Cremers, Daniel

doi:10.48550/arxiv.1707.08991

Cited by 1 publication

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“…The results show the advantages of using medially driven spectral coordinates when compared to the best conformal model that we could find. We also achieve results that are comparable to those produced by the state of the art deep neural network based models, such as PMF [54]. We show qualitative results of correspondences obtained on four different models from the TOSCA dataset in Figure 5.…”

Section: Glasses Airplane Teddysupporting

confidence: 58%

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Medial Spectral Coordinates for 3D Shape Analysis

Rezanejad¹,

Khodadad²,

Pourreza³

et al. 2021

Preprint

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In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by the increased availability of RGBD cameras, and by applications of computer vision to autonomous driving, medical imaging, and robotics. In these settings, spectral coordinates have shown promise for shape representation due to their ability to incorporate both local and global shape properties in a manner that is qualitatively invariant to isometric transformations. Yet, surprisingly, such coordinates have thus far typically considered only local surface positional or derivative information. In the present article, we propose to equip spectral coordinates with medial (object width) information, so as to enrich them. The key idea is to couple surface points that share a medial ball, via the weights of the adjacency matrix. We develop a spectral feature using this idea, and the algorithms to compute it. The incorporation of object width and medial coupling has direct benefits, as illustrated by our experiments on object classification, object part segmentation, and surface point correspondence.

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Section: Glasses Airplane Teddysupporting

confidence: 58%

“…Figure 6: Correspondence accuracy on the TOSCA dataset [51] for different methods. The methods we have compared include PMF [54], SGMDS [55], FM [56], BIM [57], Mobius Voting [7], Conformal [57], and the use of our new MedialSpectral signature.…”

Section: % Correspondencementioning

confidence: 99%