This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Frechet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of...

Take an exhilarating journey through the modern revolution in statistics with two of the ringleaders.

The standard resource for statisticians and applied researchers. Accessible to the wide range of researchers who use statistical modelling techniques.