Statistical Shape Analysis

Statistical Shape Analysis involves methods for the geometrical study of random objects where location, rotation and scale information can be removed. The book lays the foundations of the subject discussing key ideas and the very latest developments, as well as offering practical guidance and comparisons of techniques. There is a vast range of applications of shape analysis and the authors introduce the field to statisticians and applied researchers through important examples and data analysis in Biology, Medicine and Image Analysis. The text primarily concentrates on landmark data key points of correspondence located on each object. Careful consideration of the similarity invariances requires methods appropriate for non-Euclidean data analysis. In particular, multivariate statistical procedures cannot be applied directly, but can be adapted in certain instances. The book begins with introductory material on shape, size and coordinate systems. Planar Procrustes analysis is then discussed to highlight the main components of shape analysis. The shape space and general Procrustes methods are introduced, probability distributions for shape are described and statistical inference is discussed. Some deformation methods for shape change are also given and a special chapter is devoted to shape in image analysis. Finally, various alternative procedures including landmark-free methods are critically discussed and compared. Definitions and important results are highlighted throughout to assist the reader in learning about this new, exciting and important area. An introduction to the methods for the geometrical study of the random objects where location, rotation, and scale information can be removed. Primarily concentrating on landmark data (i.e. key points of correspondence located on each object), the authors discuss the field through applied examples and data analysis from biology, medicine, and image analysis. Planar Procrustes analysis is discussed and alternative methods are explored. This text deals primarily with the analysis of point set data to describe an object's shape. It discusses the theory behind the statistical analysis of shape and examines how it can be applied to a broad variety of subjects Thos book involves methods for the geometrical study of random objects where location, rotation and scale information