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.
Bibliographical noteKAUST Repository Item: Exported on 2022-06-27
Acknowledged KAUST grant number(s): CRG-2017-3426
Acknowledgements: AR and ER are supported by the ERC StG no. 802554 (SPECGEO). MO is supported by the KAUST OSR Award no. CRG-2017-3426, a gift from NVIDIA Corporation and the ERC StG no. 758800 (EXPROTEA).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.