Effects of curvature on the analysis of landmark shape manifolds

Shape spaces can be endowed with the structure of Riemannian manifolds; this allows one to compute, for example, Euler-Lagrange equations and geodesic distance for such spaces. Until very recently little was known about the actual geometry of shape manifolds; in this paper we summarize results contained in [1], which deals with the computation of curvature for landmark shape spaces. Implications on both the qualitative dynamics of geodesics and the statistical analysis on shape manifolds are also discussed.

• Type: Conference
• Year: 2008
• Where: ICIP
• Authors: Mario Micheli
• Keywords: ICIP 2008, Image Processing, Landmark Shape Spaces, Shape Manifolds, Shape Spaces