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Title: Overview of the geometries of shape spaces and diffeomorphism groups
Authors: Bauer, M
Bruveris, M
Michor, PW
Issue Date: 2017
Citation: Journal of Mathematical Imaging and Vision, 2014, 50 (1), pp. 60 - 97
Abstract: © Springer Science+Business Media New York 2014. This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics that can be defined thereon, and what is known about the properties of these metrics.We put particular emphasis on the induced geodesic distance, the geodesic equation and its well-posedness, geodesic and metric completeness and properties of the curvature.
ISSN: 0924-9907
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