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1115.3.2 Simulated Three Segment ImageThe simulated image shown in figure 5.4 is comprised of three solid bands, withgreyscale values of 70, 140, and 210. Independent Gaussian noise (mean = 0,variance = 225) is added to each pixel, and then the values are rounded to integers.This simulation is meant to provide a simple illustration of the algorithm. It isvisually clear that there are three segments; examination of the marginal histogram(figure 5.5) reinforces this.From table 5.2, we see that BIC P L correctly chooses three segments for thisimage. The BIC penalty term plays an important role in this example; the logpseudolikelihoodis maximized at four segments, but the penalty term changes thechoice to three segments. One reason that the logpseudolikelihood is so similarbetween the three and four segment cases is that the final segmentation with foursegments is extremely similar to the three segment one; it simply has the middlesegment subdivided.Values of BIC IND are also shown in table 5.2. BIC IND is computed from themarginal (without spatial information) greyscale values of the image, using theparameters estimated by EM. For this simulation, BIC IND chooses 3 segments.One entry in the table, denoted by †, is missing because the final EM segmentationconverges to a classification with only 4 segments present, which is not a valid 5segment result.The parameter estimates shown in table 5.3 show that the true parametervalues are estimated quite accurately in the three segment solution.The initial segmentation by Ward’s method is shown in figure 5.6; after EM,the marginal segmentation is shown in figure 5.7. It is clear from the marginalhistogram in figure 5.5 that it would be very difficult for any other marginal methodto improve on these results. Significant improvement can only be found by takingaccount of spatial information. After refining the segmentation with ICM, only