Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps
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CVPR21_Fast_Sinkhorn_filters.pdf
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Accepted manuscript
Type
Conference PaperKAUST Department
Computer Science ProgramComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Visual Computing Center (VCC)
Date
2021-11-02Online Publication Date
2021-11-02Print Publication Date
2021-06Permanent link to this record
http://hdl.handle.net/10754/673099
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In this paper, we provide a theoretical foundation for pointwise map recovery from functional maps and highlight its relation to a range of shape correspondence methods based on spectral alignment. With this analysis in hand, we develop a novel spectral registration technique: Fast Sinkhorn Filters, which allows for the recovery of accurate and bijective pointwise correspondences with a superior time and memory complexity in comparison to existing approaches. Our method combines the simple and concise representation of correspondence using functional maps with the matrix scaling schemes from computational optimal transport. By exploiting the sparse structure of the kernel matrices involved in the transport map computation, we provide an efficient trade-off between acceptable accuracy and complexity for the problem of dense shape correspondence, while promoting bijectivity.Citation
Pai, G., Ren, J., Melzi, S., Wonka, P., & Ovsjanikov, M. (2021). Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps. 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). doi:10.1109/cvpr46437.2021.00045Publisher
IEEEConference/Event name
2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)ISBN
978-1-6654-4510-8Additional Links
https://ieeexplore.ieee.org/document/9577605/https://ieeexplore.ieee.org/document/9577605/
https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9577605
ae974a485f413a2113503eed53cd6c53
10.1109/CVPR46437.2021.00045