Title :
Effects of curvature on the analysis of landmark shape manifolds
Author_Institution :
Div. of Appl. Math., Brown Univ., Providence, RI
Abstract :
Shape spaces can be endowed with the structure of Rieman- nian 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 geodesies and the statistical analysis on shape manifolds are also discussed.
Keywords :
computational geometry; statistical analysis; Euler-Lagrange equations; Riemannian manifolds; curvature; geodesic distance; landmark shape spaces; statistical analysis; Bioinformatics; Biomedical imaging; Computational geometry; Equations; Geophysics computing; Magnetic resonance imaging; Mathematics; Pattern analysis; Shape; Statistical analysis; Curvature; Dynamics; Landmarks; Shape Spaces; Statistical Analysis;
Conference_Titel :
Image Processing, 2008. ICIP 2008. 15th IEEE International Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
978-1-4244-1765-0
Electronic_ISBN :
1522-4880
DOI :
10.1109/ICIP.2008.4711967
