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1065.3 Image Segmentation Examples5.3.1 Simulated Two Segment ImageThis simulation illustrates the use of spatial information by BIC P L compared tothe use of only marginal information by BIC IND , where BIC IND denotes the usualBIC value: twice the loglikelihood (assuming spatial independence) minus thepenalty term, which is the number of degrees of freedom in the model multipliedby the log of the number of data points. A more complete description of thesegmentation algorithm is given in section 5.3.2.The simulated two-segment image shown in figure 5.1 is comprised of two solidbands, with mean greyscale values of 120 and 140. Independent Gaussian noise(mean = 0, variance = 100) is added to each pixel, and then the values are roundedto integers. Compare this to the scrambled image in figure 5.2, which is a randomreordering of the pixels from figure 5.1. Since these two images contain exactlythe same pixels (just in a different order), their marginal information will be thesame. For instance, a histogram of the values in one image will be the same as theother. Such a histogram is shown in figure 5.3.Although it is clear visually that there are two segments in figure 5.1, thereis enough noise in the image that a histogram of the greyscale values, shown infigure 5.3, is unimodal. Since the marginal information of the histogram is thebasis of BIC IND , it is not surprising that it selects only one segment, as shownby the values in table 5.1. Note that the BIC IND results are identical for thetwo-segment image and the scrambled image, since they have the same marginalinformation. However, the BIC P L values favor two segments for the two-segmentimage and one segment for the scrambled image. The estimated φ values used incomputing BIC P L are also shown in the table. The large φ for the two segmentfit of the two-segment image indicates that a large degree of spatial homogeneity