Analyzing Shape Datasets

Abstract

We present in this chapter some “shape analysis” methods, among those that are mainly used in practice, where the goal is to provide a low-dimensional description and to perform statistical validations of hypotheses for datasets in which each object is a shape. Most recent applications of this framework have taken place in medical imaging, in which the shapes are provided by anatomical regions segmented by MRI or computer tomography scans. The analysis of the anatomy derived from such images is called computational anatomy and has generated a huge literature. Beside this important range of applications, shape analysis can also be used in computed vision, or in biology, which was, for example, the main focus of D’Arcy-Thompson’s seminal treatise on Growth and Form. We here focus on methods that derive from the analysis of diffeomorphisms developed in the previous chapters, leading to “morphometric”, or “diffeomorphometric” analyses.