Statistical Shape Models in Image Analysis

David Hogg
School of Computer Studies, University of Leeds, Leeds LS2 9JT, United Kingdom

Abstract
Automated image analysis has an important role to play in the study of geography. Probably the most developed and widely used applications of the technology have been for the analysis of remotely-sensed images obtained from aircraft and satellites. In general terms the aim has been to segment the ground into areas of different land-use, to recognise particular objects such as rivers, roads and urban areas, and to acquire quantitative measurements either from the spatial-temporal extent of objects or from spectral signatures. From an image analysis perspective, one of the main problems in undertaking such tasks with sufficient reliability is the enormous variability in the shape and surface properties of the objects of interest.

In this paper we review a promising new approach to the characterisation of objects within the context of automated image analysis. The approach is based on methods for shape modelling developed in the field of statistics, combined with 'model-based' interpretation strategies used in image analysis. There are close links with the methods of statistical pattern recognition and neural networks, albeit with a strong geometrical flavour.

The idea is first to model a class of objects as a composition of geometric primitives augmented with parameters controlling their relative location and dimensions. Although the number and interconnection of primitives is fixed, variability in the overall shape is accommodated by making different substitutions for the parameters. The set of all possible substitutions across all parameters defines a vector space. Now, for a given class of objects, we model the prior probability of coming across instances as a probability density function over this space. Typically, this density is zero through most of the space and non-zero within a 'small' connected subset. The distribution may be thought of as defining a feasible subset within which all model instances must lie. Because such characterisations of shape are precise in dealing with the natural variation within a class, they can be used to detect and recognise objects more reliably than has hitherto been possible. We examine the way in which this approach has been applied in different domains, ranging from face recognition and pedestrian tracking to medical image analysis - areas for which the target objects have a common 'topology' but vary widely in shape, both between individuals and for the same individual over time.

Several methods for modelling the probability density function will be examined, with emphasis on its estimation either by sampling or by hand-crafting. Recent work on automating the acquisition of samples from images will be presented. Finally, we review the techniques available for recognising objects in images using the range of models described.