Shape analysis of surfaces using general elastic metrics
Date
2020
Authors
Su, Z.
Bauer, M.
Preston, S.C.
Laga, H.
Klassen, E.
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Journal article
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Journal of Mathematical Imaging and Vision, 2020; 62(8):1087-1106
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Abstract
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
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Link to a related website: http://arxiv.org/pdf/1910.02045, Open Access via Unpaywall
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Copyright 2020 Springer