Statistical and Geometrical Image Modelling

Prof. Bernard Buxton

Department of Computer Science, University College London,

Gower Street, London, WC1E 6BT, UK

B.Buxton@cs.ucl.ac.ukhttp://www.cs.ucl.ac.uk/staff/B.Buxton/ 

Abstract

In any scientific or engineering endeavour it is important, if not essential, to have a model of the system or process under investigation or development. Models guide our thoughts and bring structure to our planning and execution of the work required. Computer or machine vision and image processing, as a scientific or engineering activity is no exception to this, although there are difficulties peculiar to the field that have hampered the process. The main problem is one of complexity and difficulty in establishing an appropriate characterisation. Although there are many different kinds of images and imaging techniques are applied in a wide variety of different situations, there is sufficient in common across the domain, in particular the implicit nature of the information contained in images and the potential complexity of image data, that we can learn a great deal, both about the modelling procedure and about general principles by studying, for example, conventional digital camera or TV imagery. Such imagery will therefore be used in order illustrate a range of statistical and geometric modelling techniques that are becoming increasingly widespread and useful in the field and how such techniques may be developed within a common framework.

This framework will be built up, first by considering simple statistical models of image intensity and colour in order to establish a consistent notation and to cover methods of parameter estimation. Higher order statistics will be introduced via pair correlation functions, and the relationship of image models to random fractals and natural imagery discussed. Markov random fields will be introduced as a way of capturing the relationships between larger groups or cliques of pixels beyond pair-wise correlations and a model of a linear feature or line segment will be used to show how, via choice of an appropriate prior, geometric concepts may be built into statistical models. Finally, we shall describe how object models may be built in pixel space by methods such as PCA, why such a method is feasible for image data and explain how geometric information may be included so as to result in more powerful and more compact models.

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