Fully Spectral Partial Shape Matching

We propose an efficient procedure for calculating partial dense intrinsic correspondence between deformable shapes performed entirely in the spectral domain. Our technique relies on the recently introduced partial functional maps formalism and on the joint approximate diagonalization (JAD) of the La...

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Vydáno v:Computer graphics forum Ročník 36; číslo 2; s. 247 - 258
Hlavní autoři: Litany, O., Rodolà, E., Bronstein, A. M., Bronstein, M. M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishing Ltd 01.05.2017
Témata:
Categories and Subject Descriptors (according to ACM CCS)
Computer graphics
Deformation
Formability
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Shape Analysis
Image processing systems
Matching
Mathematical analysis
Shape recognition
Spectra
Topological manifolds
ISSN:0167-7055, 1467-8659
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Shrnutí:We propose an efficient procedure for calculating partial dense intrinsic correspondence between deformable shapes performed entirely in the spectral domain. Our technique relies on the recently introduced partial functional maps formalism and on the joint approximate diagonalization (JAD) of the Laplace‐Beltrami operators previously introduced for matching non‐isometric shapes. We show that a variant of the JAD problem with an appropriately modified coupling term (surprisingly) allows to construct quasi‐harmonic bases localized on the latent corresponding parts. This circumvents the need to explicitly compute the unknown parts by means of the cumbersome alternating minimization used in the previous approaches, and allows performing all the calculations in the spectral domain with constant complexity independent of the number of shape vertices. We provide an extensive evaluation of the proposed technique on standard non‐rigid correspondence benchmarks and show state‐of‐the‐art performance in various settings, including partiality and the presence of topological noise.
Bibliografie:ObjectType-Article-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13123