Fully Spectral Partial Shape Matching

• Published in: Computer graphics forum Vol. 36; no. 2; pp. 247 - 258
• Main Authors: Litany, O., Rodolà, E., Bronstein, A. M., Bronstein, M. M.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.05.2017
• Subjects: 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
• DOI: 10.1111/cgf.13123

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.