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140interior to the land which had initially been classified into the water segment havenow been properly classifed into one of the land segments. Figure 5.27 gives theICM refinement of the segmentation; we can see that much of the noise in theland interior has been smoothed out, while the tideline is still quite clear. Themorphological smoothing step, shown in figure 5.28, smooths the land further, butthe tideline becomes more obscure.In both the ICM classification (figure 5.27) and the post-morphology classification(figure 5.28), the water is well-characterized by the darkest segment. Thesecond-darkest segment corresponds to shallow tidewater near the bright beach, aswell as combining with the third-darkest segment to characterize most of the dryland. Although the second-darkest segment comprises both dry land and shallowtidewater, these two land types are spatially separated by the beach. The twobrightest segments correspond to the beach, which is quite reflective. The thirdbrightestsegment is transitional; it fills in between dry land and water in regionswhere the beach is not evident, as well as capturing the small hill in the upperright hand corner of the image.Comparison of the classifications in figures 5.27 and 5.28 provides a good exampleof the fact that one needs to know the goals of the analysis in order to knowhow much smoothing is reasonable. Figure 5.27 yields good spatial separation ofthe water and land, along with detail in the tidal area; however, the interior of theland and the water near the tideline are both a bit cluttered. Figure 5.28 smoothsout much of the clutter in the image while preserving the location of the tideline,but detail in the tideline is lost.
141Table 5.8: Logpseudolikelihood and BIC P L results for the Washington coast image. Missingvalues, noted with †, are discussed in the text.Segments ˆφ Logpseudolikelihood BICP L BIC IND1 – -64521.78 -129072.20 -133475.02 1.23 -56721.70 -113500.70 -125273.03 0.74 -45882.79 -91851.53 -117607.84 0.58 -45303.55 -90721.70 -117528.65 0.45 -42517.74 -85178.71 -117564.96 0.39 -42312.05 -84795.99 -117537.57 0.34 -55201.01 -110602.56 †8 0.30 -51279.68 -102788.55 †0 20 40 60 80 100 1200 20 40 60 80 100 120Figure 5.23: Satellite image of Washington coast, before processing.
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Fast Automatic Unsupervised Image S
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In presenting this dissertation in
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TABLE OF CONTENTSList of FiguresLis
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4.1.2 Penalty Adjustment . . . . .
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Appendix A: Software Discussion 169
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4.1 (a) Signal generated by an AR(1
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5.29 Aerial image of a buoy, before
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DEDICATIONThis work is dedicated to
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20 10 20 30 40 50 600 10 20 30 40 5
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4fast because they can be implement
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6multidimensional observations at e
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••••8Figure 2.1(a) is a sim
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10Principal Curve•••••Dat
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12based on the estimates of the par
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14first of these can be done by a h
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162.4 Examples2.4.1 A Simulated Two
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18Figure 2.5: HPCC applied to the t
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21Table 2.2: BIC results for simula
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232.4.3 New Madrid Seismic RegionDa
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25Table 2.3: BIC results for New Ma
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27Latitude35.5 36.0 36.5 37.0 37.5
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29set, so we want to avoid assumpti
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31The examples we have presented in
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Chapter 3MARGINAL SEGMENTATIONIn th
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35about ˜θ; this is a good approx
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373.2 Mixture ModelsThe mixture den
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39for estimating the model paramete
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41The ith pixel of X or C is denote
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43In componentwise classification,
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45ponent. This classification proce
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Chapter 4ADJUSTING FOR AUTOREGRESSI
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49Dependence CaseWhen |β| < 1, the
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52For practical purposes, equation
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54g ′′ (θ) ≈⎛⎜⎝∑ Ni=
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564.1.3 Computing BIC with the AR(1
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58upper, left, and right borders of
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60L(Y −B |M, B) = L IND (Y −B |
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62We now return to equation 4.56 an
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64and then computing a mean-correct
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66regression, which can be written
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68resulting R 2 values are 0.93 for
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700 5 10 15 200 5 10 15 20Figure 4.
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72negative value would mean that ne
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74Once each pixel has been updated,
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76The basic idea of this psuedolike
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78The consistency result presented
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80⎛∑ ⎞Kj=1f(Yg i (Y i ) = log
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82| log(f(Y i |X i = S, θ 1 ))|
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84⇒ (L ˆX (Y |K)) exp(−(D K
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86the object of the expectation is
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88Thus, equation 5.42 holds, so BIC
Page 110 and 111: 90the inequality in equation 5.55 h
Page 112 and 113: 92N log(σ K ) − N log(σ 1 ) −
Page 114 and 115: 94final number of clusters. The cho
Page 116 and 117: 96ization to initialize (see sectio
Page 118 and 119: 98ˆσ 2 j =∑ Ni=1 ˆQ ij (Y i
Page 120 and 121: 100one particular data value, which
Page 122 and 123: 102classification they are not. Eac
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Page 126 and 127: 1065.3 Image Segmentation Examples5
Page 128 and 129: 1080 10 20 30 400 10 20 30 40Figure
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Page 132 and 133: 112three pixels remain incorrectly
Page 134 and 135: 114Table 5.3: EM-based parameter es
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Page 140 and 141: 1205.3.3 Ice FloesFigure 5.10 shows
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Page 150 and 151: 1305.3.4 Dog LungFigure 5.17 presen
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Page 162 and 163: 142Table 5.9: EM-based parameter es
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Page 168 and 169: 1485.3.6 BuoyFigure 5.29 is an aeri
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Page 178 and 179: Chapter 6CONCLUSIONSThis dissertati
Page 180 and 181: 160of subsampling would have to be
Page 182 and 183: REFERENCESAllard, D., and Fraley, C
Page 184 and 185: 16494, 555-568.Fraley, C., and Raft
Page 186 and 187: 166Maps,” Biological Cybernetics,
Page 188 and 189: 168Zahn, C. (1971), “Graph-Theore
Page 190 and 191: 170structuring element file.Segment
Page 192 and 193: 172A.3 Splus codehpcc - Hierarchica
Page 194: VITA1993 B.S. Mathematics, Harvey M
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