New Statistical Methods for Shape

Abstract

In this chapter I propose statistical analyses of data which preserve the full rich information store of the outline as late as possible into the analysis. We can only deal ultimately, it is true, with a finite-dimensional space of parameters; but when shape is represented by a continuous function it is possible to sample from that function instead of discarding information earlier by sampling from the points of the outline. Distinctions between the methods I shall describe, and between them and the conventional approaches, can be summarized in the three schemes of Fig. IV-1. Sketch (a) indicates the conventional method of extracting shape variables from landmark locations alone, ignoring both the curving of the outline and the geometric order of the image. Sketch (b) corresponds to the tangent angle method, which follows the outline all the way around. Sketch (c) is a useful modification, the medial axis method, in which we pass up the “middle” of the form, in a sense to be defined objectively, and investigate the boundary on both sides simultaneously.