The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases.

Regularized pointwise map recovery from functional correspondence / Rodolà, E.; Moeller, M.; Cremers, D.. - In: COMPUTER GRAPHICS FORUM. - ISSN 0167-7055. - ELETTRONICO. - 36:8(2017), pp. 700-711. [10.1111/cgf.13160]

Regularized pointwise map recovery from functional correspondence

Rodolà, E.
;
2017

Abstract

The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases.
2017
3D shape matching; Computer Networks and Communications; Computer Graphics and Computer-Aided Design
01 Pubblicazione su rivista::01a Articolo in rivista
Regularized pointwise map recovery from functional correspondence / Rodolà, E.; Moeller, M.; Cremers, D.. - In: COMPUTER GRAPHICS FORUM. - ISSN 0167-7055. - ELETTRONICO. - 36:8(2017), pp. 700-711. [10.1111/cgf.13160]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1066115
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