Introduction

Abstract

In 1977, David Kendall published a brief note [87] in which he introduced a new representation of shapes as elements of complex projective spaces. The result stated in the paper was unusual: under an appropriate random clock, the shape of a set of independent particles diffusing according to a Brownian motion law could be regarded as a Brownian motion on complex projective space. Many statisticians, who knew little about complex projective spaces and who did not work on diffusion processes, did not see immediate applications to their own work. However, in a sequence of talks at conferences around the world, David Kendall continued to expound on his theory, with some applications to problems in archeology. Presented with great clarity and with excellent graphics, these talks gradually generated wider interest. It was not until 1984 that the full details of the theory were published [90]. At that point it became clear that Kendall’s theory of shape was of great elegance and contained some interesting areas of research for both the probabilist and the statistician.