Images such as Figure 1 are stored as an array of numbers in a computer by assigning a value to the shade of grey at each pixel. This can be done, for example, by using a scale from 0 to 1, with 0 standing for black and 1 for white. Image analysis is a rapidly developing branch of mathematics that involves processing these numerical arrays in such a way that useful information can be extracted and helpful interpretations made. This processing may involve highlighting certain features such as a fracture in an X-ray picture, or identifying land use from a satellite image of an agricultural area corrupted by atmospheric blurring. An ultrasound machine is used to look at a baby in the womb.
Statisticians are one group of mathematicians who have much to offer the science of image analysis.
Their general experience in dealing with random events and processes carries over to the modelling of mechanisms that cause image degradation. Often statisticians adopt a Bayesian approach to image analysis. Bayes' theorem allows us to update our beliefs in the light of new information. Let us assume that the available data comprise a satellite image of an agricultural area and that the pixels of this image correspond to square regions on the ground. Let us also suppose that it is of interest to identify the cover type at each pixel as one of water, forest, building, cultivated ground and uncultivated ground and that in the image each cover type corresponds to a shade of grey and hence to a number.