Statistical Shape Analysis, 2nd Edition

Preface to the first edition

Whence and what art thou, execrable shape? John Milton (1667) Paradise Lost II, 681

In a wide variety of disciplines it is of great practical importance to measure, describe and compare the shapes of objects. The field of shape analysis involves methods for the study of the shape of objects where location, rotation and scale information can be removed. In particular, we focus on the situation where the objects are summarized by key points called landmarks. A geometrical approach is favoured throughout and so rather than selecting a few angles or lengths we work with the full geometry of the objects (up to similarity transformations of each object). Statistical shape analysis is concerned with methodology for analysing shapes in the presence of randomness. The objects under study could be sampled at random from a population and the main aims of statistical shape analysis are to estimate population average shapes, to estimate the structure of population shape variability and to carry out inference on population quantities.

Interest in shape analysis at Leeds began with an application in Central Place Theory in Geography. Mardia (1977) investigated the distribution of the shapes of triangles generated by certain point processes, and in particular considered whether towns in a plain are spread regularly with equal distances between neighbouring towns. Our joint interest in statistical shape analysis began in 1986, with an approach from Paul O’Higgins ...