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94final number of clusters. The choice of which clusters to merge is based on minimizinga sum of squares criterion at each step. When this process is complete,we have divided the greyscale levels into K groups, and we use this as the initialsegmentation. Because of the sum of squares criterion used in Ward’s method, itis appropriate when one intends to fit a Gaussian mixture model.One disadvantage of Ward’s method is the amount of computing it requires; asan alternative to Ward’s method, the initial parameter estimates can be randomlygenerated. This is quite fast. Since the EM algorithm typically moves very quicklytoward good parameter values, it is reasonably robust to the initial parameterestimates. However, random estimates may sometimes lead EM into undesiredlocal maxima in the likelihood. This can be alleviated by starting from severaldifferent sets of random parameter values, though this solution has the drawbackthat it once again increases computation time. Also, the use of random values isintuitively somewhat unsatisfying.Histogram equalization provides the basis for a fast and robust method offinding an initial segmentation. Consider a histogram of the greyscale values in animage (without regard to spatial information). The idea of histogram equalizationis to divide the greyscale levels into K bins which contain roughly equal numbersof pixels. Graphically, this means that we adjust the bin sizes (bins are not allthe same size) until the histogram is flat. I compute the histogram equalizationwith an iterative algorithm. First, I divide the number of data points N by thedesired number of bins K; the result N/K is the number of data points we wouldlike to have in each bin. Let T 0 denote the threshold number of pixels to allocateto each bin, so we set T 0 = N/K. Beginning with greyscale level 0, I allocate allpixels with that greyscale level into the first bin. Continuing with greyscale levels1, 2, and so on, I allocate each into the first bin until I have at least T 0 pixels inthe bin. I then allocate the following greyscale levels into the second bin until it