View - Statistics - University of Washington

1395.3.5 Washington CoastFigure 5.23 is a satellite image of a section of the Pacific coast of Washington state’sOlympic peninsula; this image, provided by the USGS as part of the NationalAerial Photography Program (NAPP), was obtained from the Terraserver webpage, terraserver.microsoft.com. The resolution is 8 meters per pixel, and it is a256-level greyscale image.Table 5.8 shows that the first maximum in BIC P L occurs at K = 6 segments,so we regard this as the optimal choice of K for this model. Parameter estimatesare given in table 5.9. The marginal histogram of this image is shown in figure5.24, along with the estimated mixture density for K = 6. The large spike is dueto the small variance in the greyscale value of the water.For comparison, BIC IND values are also shown in the table. The first localmaximum occurs at 4 segments. The BIC IND values are computed based onlyon marginal (without spatial information) greyscale data from the image. Twoof the table entries, denoted by †, are missing from the table. The entry for 7segments is missing because the EM algorithm converges to a classification whichcontains fewer segments than the number of components in the mixture. In otherwords, we do not obtain a valid segmentation into 7 segments from the final EMclassification. The entry for 8 segments is missing due to slow convergence, whichis not surprising in light of the result for 7 segments.Figures 5.25 to 5.28 illustrate the steps of the segmentation algorithm for thisimage. An initial segmentation is created by using Ward’s method to cluster themarginal greyscale values of the image; this is shown in figure 5.25. The wateris quite well classified as a single segment, while the land is mostly containedin two segments. The tideline accounts for most of the variability in the image.Starting from the initial segmentation, the EM algorithm is used to fit a Gaussianmixture; the resulting segmentation is displayed in figure 5.26. Most of the pixels