ZoomOut: spectral upsampling for efficient shape correspondence

Simone Melzi, Jing Ren, Emanuele Rodolà, Abhishek Sharma, Peter Wonka, Maks Ovsjanikov

Research output: Contribution to journalArticlepeer-review

100 Scopus citations


We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.
Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalACM Transactions on Graphics
Issue number6
StatePublished - Nov 8 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): CRG2017-3426
Acknowledgements: The authors wish to thank the anonymous reviewers for their valuable comments and helpful suggestions, and Danielle Ezuz and Riccardo Marin for providing source code for experimental comparisons. This work was supported by KAUST OSR Award No. CRG2017-3426, a gift from the NVIDIA Corporation, the ERC Starting Grant StG-2017-758800 (EXPROTEA) and StG-2018-802554 (SPECGEO).


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