ArticleSIAM journal on imaging sciences2020
Simplifying Transforms for General Elastic Metrics on the Space of Plane Curves.
Article in SIAM journal on imaging sciences, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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4 citing papers in PubMed.
- Fast and interpretable quantification of biological shape heterogeneity via stratified Wasserstein kernel.PLoS computational biology · 2026Article
- Geometric Learning of Canonical Parameterizations of 2Entropy (Basel, Switzerland) · 2025Article
- Elastic Statistical Shape Analysis of Biological Structures with Case Studies: A Tutorial.Bulletin of mathematical biology · 2019Article
- Analysis of shape data: From landmarks to elastic curves.Wiley interdisciplinary reviews. Computational statisticsArticle
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2 authors.
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Abstract
In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes and averaging of a collection of shapes. The performance of these algorithms depends heavily on the choice of the Riemannian metric. In the setting of plane curve shapes, attention has largely been focused on a two-parameter family of first order Sobolev metrics, referred to as elastic metrics. They are particularly useful due to the existence of simplifying coordinate transformations for particular parameter values, such as the well-known square-root velocity transform. In this paper, we extend the transformations appearing in the existing literature to a family of isometries, which take any elastic metric to the flat
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