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4fast because they can be implemented in the Fourier domain. More complicatedmodels usually include some sort of distributional assumptions about noise in theimage; for example, Bovik and Munson (1986) show that when both Gaussian andimpulse noise are present, an edge detector based on local median values is morerobust than a similar algorithm using mean values. A similar distributional assumptionis made by Kundu (1990), who develops a multi-stage approach to dealwith the different noise types.Pixel classification methods attempt to classify individual pixels using eitherthe pixel value or the pixel value and the values of adjacent or nearby pixels (alsoknown as a neighborhood). A simple pixel classification method is given in chapter3; this assumes that the pixel values follow a Gaussian mixture distribution andignores spatial information. The pixels are then classified into the component ofthe mixture from which they are most likely to have arisen. Methods which makeuse of neighborhood information include Markov random field models; an earlyexample of segmentation with Markov random field models is given by Hansenand Elliott (1982), who achieve good results, especially considering the limitedcomputing power available at the time.1.3 Other Methods for Image Segmentation with Choice of the Numberof SegmentsIn this dissertation I present an automatic and unsupervised method for image segmentationincluding the choice of K, based on mixture models and the BayesianInformation Criterion (BIC). Other methods which address the problem of choosingK can be divided into two categories: ad hoc procedures, and procedureswhich require tuning parameters. Although the ad hoc procedures may give goodresults for some applications, it is doubtful that they would be applicable in general.Similarly, methods which use an arbitrarily chosen tuning parameter may