Statistical Shape Analysis in High-Level Vision
Wednesday, November 15, 2000 - 9:30am - 10:30am
Ian Dryden (University of Nottingham)
Shape is an essential ingredient of high-level image analysis. The geometrical description of an object can be separated into two parts: the registration information and the `shape' (which is invariant under registration transformations). A common choice of registration is the group of Euclidean similarity transformations and the geometrical prosperities that are invariant under this group of transformations are known as `similarity shape'. In a Bayesian approach to object recognition shape information is usually specified as part of the prior distribution. The prior is then combined with the likelihood, or image model, leading to posterior inference about the object. The statistical theory of shape began with the independent work of David Kendall, Fred Bookstein and Herbert Ziezold in the 1970s. Subsequent developments have led to a deep differential geometric theory of shape spaces, as well as practical statistical approaches to analysing objects using probability distributions of shape and likelihood based inference. A summary of the field is given by Dryden and Mardia (1998, Wiley), where the main emphasis is on the shapes of labeled point set configurations. In the image analysis literature there are numerous works on the notion of shape, many of which are directly related to the work in Kendall's shape spaces. A common feature of the approaches is some form of shape metric, and many of the shape representations and metrics in common use are related through approximate affine transformations of the particular shape coordinates being used. In the talk I shall discuss some of the main aspects of statistical shape analysis, making comparisons with alternative approaches, which are often based on collections of angles or ratios of distances. Some applications of shape analysis in image analysis will be described. Finally, one of the major advantages of using statistical shape analysis is that statistical inference can be carried out when the images consists a sample of objects, and we consider an example where it is of interest to test whether or not two populations have different mean shapes.