Data analysis in Weitzenbock space

Marsland, Stephen; Twining, Carole J.

doi:10.1109/ijcnn.2017.7965874

2017 International Joint Conference on Neural Networks (IJCNN) 2017

DOI: 10.1109/ijcnn.2017.7965874

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Data analysis in Weitzenbock space

Stephen Marsland

Carole J. Twining

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2022

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Geodesics in the TPS Space

et al. 2022

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In shape analysis, the interpolation of shapes’ trajectories is often performed by means of geodesics in an appropriate Riemannian Shape Space. Over the past several decades, different metrics and shape spaces have been proposed, including Kendall shape space, LDDMM based approaches, and elastic contour, among others. Once a Riemannian space is chosen, geodesics and parallel transports can be used to build splines or piecewise geodesics paths. In a recent paper, we introduced a new Riemannian shape space named TPS Space based on the Thin Plate Spline interpolant and characterized by an appropriate metric and parallel transport rule. In the present paper, we further explore the geometry of the TPS Space by characterizing the properties of its geodesics. Several applications show the capability of the proposed formulation to conserve important physical properties of deformation, such as local strains and global elastic energy.

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Geodesics in the TPS Space

et al. 2022

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Data analysis in Weitzenbock space

Cited by 1 publication

References 13 publications

Geodesics in the TPS Space

Geodesics in the TPS Space

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