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Shape analysis of surfaces using general elastic metrics

Su, Z., Bauer, M., Preston, S.C., Laga, H.ORCID: 0000-0002-4758-7510 and Klassen, E. (2020) Shape analysis of surfaces using general elastic metrics. Journal of Mathematical Imaging and Vision .

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In this article, we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector-valued one-forms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence, it induces a metric on the “shape space” of surfaces. This new class of metrics generalizes a previously studied family of elastic metrics and includes in particular the Square Root Normal Field (SRNF) metric, which has been proven successful in various applications. We demonstrate our framework by showing several examples of geodesics and compare our results with earlier results obtained from the SRNF framework.

Item Type: Journal Article
Murdoch Affiliation(s): Information Technology, Mathematics and Statistics
Publisher: Kluwer Academic Publishers
Copyright: © 2020 Springer Nature Switzerland AG.
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