NEW LARGE SAMPLE AND BOOTSTRAP METHODS ON SHAPE SPACES IN HIGH LEVEL ANALYSIS OF NATURAL IMAGES

Abstract

This paper, dedicated to the 80th birthday of Professor C. R. Rao, deals with asymptotic distributions of Fréchet sample means and Fréchet total sample variance that are used in particular for data on projective shape spaces or on 3D shape spaces. One considers the intrinsic means associated with Riemannian metrics that are locally flat in a geodesically convex neighborhood around the support of a probability measure on a shape space or on a projective shape space. Such methods are needed to derive tests concerning variability of planar projective shapes in natural images or large sample and bootstrap confidence intervals for 3D mean shape coordinates of an ordered set of landmarks from laser images.

Keywords:

• Central limit theorem
• Bootstrap
• Shape spaces
• Projective shape spaces

5. ACKNOWLEDGMENT

I would like to thank Professor Rabi Bhattacharya from Indiana University, for his thorough review of the paper and for his many useful suggestions, to Professor Izu Vaisman from Haifa University for sharing with me his view on shape coordinates, and to my colleague Professor Raj Sunderraman, from our Department of Computer Science, for helping me create the .ps files from imaging files. I am also grateful to the reviewer of the paper who helped me improve the presentation.