Structured Regularization of Functional Map Computations

We consider the problem of non‐rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace‐Beltrami operators on the source and tar...

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Veröffentlicht in:Computer graphics forum Jg. 38; H. 5; S. 39 - 53
Hauptverfasser: Ren, Jing, Panine, Mikhail, Wonka, Peter, Ovsjanikov, Maks
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Blackwell Publishing Ltd 01.08.2019
Wiley
Schlagworte:
CCS Concepts
Computer graphics
Computer Science
Computer Vision and Pattern Recognition
Computing methodologies → Shape analysis
Laplace transforms
Regularization
ISSN:0167-7055, 1467-8659
Online-Zugang:Volltext
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Zusammenfassung:We consider the problem of non‐rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace‐Beltrami operators on the source and target shapes. We show that this approach has certain undesirable fundamental theoretical limitations, and can be undefined even for trivial maps in the smooth setting. Instead we propose a novel, theoretically well‐justified approach for regularizing functional maps, by using the notion of the resolvent of the Laplacian operator. In addition, we provide a natural one‐parameter family of regularizers, that can be easily tuned depending on the expected approximate isometry of the input shape pair. We show on a wide range of shape correspondence scenarios that our novel regularization leads to an improvement in the quality of the estimated functional, and ultimately pointwise correspondences before and after commonly‐used refinement techniques.
Bibliographie:ObjectType-Article-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13788