Heat Kernel Approximation on Kendall Shape Space

  • Riadh Mtibaa Université de Tunis El Manar, Institut Supérieur d’Informatique El Manar, LR16ES06. Laboratoire de recherche en Informatique, Modélisation et Traitement de l’Information et de la Connaissance (LIMTIC), 2 Rue Abou Raihane Bayrouni, 2080, l’Ariana, Tunisie; Université de Sousse, ISSAT Sousse, Cité Taffala(Ibn Khaldoun) 4003 Sousse, Tunisie
  • Salam Khan Alabama A&M University, Department of Physics, Chemistry and Mathematics, USA
Keywords: Kendall shape space, heat kernel expansion, special orthogonal group, quotient space, shape recognition

Abstract

The heat kernel on Kendall shape subspaces is approximated by an expansion. The Kendall space is useful for representing the shapes associated to collections of landmarks’positions. The Minakshisundaram-Pleijel recursion formulas are used in order to calculate the closed-form approximations of the first and second coefficients of the heat kernel expansion. Prior to the exploitation of the recursion scheme, the expression of the Laplace-Beltrami operator is adapted to the targeted space using geodesic spherical and angular coordinates.

Published
2020-07-30
How to Cite
Mtibaa, R. and Khan, S. (2020) “Heat Kernel Approximation on Kendall Shape Space”, Contemporary Mathematics, 1(4). doi: 10.37256/cm.142020414.