Heat Kernel Approximation on Kendall Shape Space

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.