Geodesics in the TPS space

Abstract: 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

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Mathematics. - 10, 9 (2022) , 1562, ISSN: 2227-7390

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2022
• Creator: Varano, Valerio ; Gabriele, Stefano ; Milicchio, Franco ; Schlager, Stefan ; Dryden, Ian ; Piras, Paolo

Further information

• DOI: 10.3390/math10091562
• URN: urn:nbn:de:bsz:25-freidok-2285533
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:20 AM CEST