Correspondence-Free Region Localization for Partial Shape Similarity via Hamiltonian Spectrum Alignment

Arianna Rampini, Irene Tallini, Maks Ovsjanikov, Alex M. Bronstein, Emanuele Rodola

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations

Abstract

We consider the problem of localizing relevant subsets of non-rigid geometric shapes given only a partial 3D query as the input. Such problems arise in several challenging tasks in 3D vision and graphics, including partial shape similarity, retrieval, and non-rigid correspondence. We phrase the problem as one of alignment between short sequences of eigenvalues of basic differential operators, which are constructed upon a scalar function defined on the 3D surfaces. Our method therefore seeks for a scalar function that entails this alignment. Differently from existing approaches, we do not require solving for a correspondence between the query and the target, therefore greatly simplifying the optimization process; our core technique is also descriptor-free, as it is driven by the geometry of the two objects as encoded in their operator spectra. We further show that our spectral alignment algorithm provides a remarkably simple alternative to the recent shape-from-spectrum reconstruction approaches. For both applications, we demonstrate improvement over the state-of-the-art either in terms of accuracy or computational cost.
Original languageEnglish (US)
Title of host publication2019 International Conference on 3D Vision (3DV)
PublisherIEEE COMPUTER SOC
Pages37-46
Number of pages10
ISBN (Print)9781728131313
DOIs
StatePublished - Oct 31 2019
Externally publishedYes

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