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114Table 5.3: EM-based parameter estimates for the simulated image.8 segments.Means: 211.59 196.48 157.62 223.93 138.95 125.97 62.24 79.02SDs : 8.39 8.68 11.49 10.62 11.73 14.91 12.38 10.73Probs: 0.119 0.106 0.069 0.104 0.201 0.073 0.187 0.147 segments.Means: 215.42 197.42 157.37 138.89 125.95 62.25 79.02SDs : 12.83 9.84 11.05 11.69 14.89 12.38 10.73Probs: 0.24 0.091 0.068 0.201 0.073 0.187 0.146 segments.Means: 215.4 197.61 141.13 125.15 62.13 78.69SDs : 12.87 10.12 14.89 24 12.33 10.43Probs: 0.239 0.092 0.302 0.045 0.187 0.1355 segments.Means: 215.42 197.58 142.77 128.43 69.95SDs : 12.85 9.98 14.88 11.34 14.86Probs: 0.239 0.092 0.283 0.053 0.3334 segments.Means: 210.17 142.77 127.3 69.97SDs : 14.86 14.38 11.18 14.87Probs: 0.333 0.28 0.054 0.3333 segments.Means: 210.2 140.14 69.85SDs : 14.85 15.26 14.78Probs: 0.333 0.335 0.3322 segments.Means: 212.02 110SDs : 13.58 42.57Probs: 0.296 0.7041 segments.Means: 140.17SDs : 59.15Probs: 1
115Percent0.0 0.002 0.004 0.006 0.008 0.0100 50 100 150 200 250GreyscaleFigure 5.5: Marginal histogram <strong>of</strong> the simulated image, with the estimated 3 component mixturedensity.
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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
Page 84 and 85: 64and then computing a mean-correct
Page 86 and 87: 66regression, which can be written
Page 88 and 89: 68resulting R 2 values are 0.93 for
Page 90 and 91: 700 5 10 15 200 5 10 15 20Figure 4.
Page 92 and 93: 72negative value would mean that ne
Page 94 and 95: 74Once each pixel has been updated,
Page 96 and 97: 76The basic idea of this psuedolike
Page 98 and 99: 78The consistency result presented
Page 100 and 101: 80⎛∑ ⎞Kj=1f(Yg i (Y i ) = log
Page 102 and 103: 82| log(f(Y i |X i = S, θ 1 ))|
Page 104 and 105: 84⇒ (L ˆX (Y |K)) exp(−(D K
Page 106 and 107: 86the object of the expectation is
Page 108 and 109: 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
Page 124 and 125: 1045.2.6 Morphological Smoothing (O
Page 126 and 127: 1065.3 Image Segmentation Examples5
Page 128 and 129: 1080 10 20 30 400 10 20 30 40Figure
Page 130 and 131: 1100.0 0.005 0.010 0.015 0.020 0.02
Page 132 and 133: 112three pixels remain incorrectly
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Page 140 and 141: 1205.3.3 Ice FloesFigure 5.10 shows
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Page 144 and 145: 124Percent0.0 0.005 0.010 0.015 0.0
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Page 150 and 151: 1305.3.4 Dog LungFigure 5.17 presen
Page 152 and 153: 132Table 5.6: Logpseudolikelihood a
Page 154 and 155: 134Percent0.0 0.05 0.10 0.15 0.200
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Page 160 and 161: 140interior to the land which had i
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
Page 170 and 171: 150Table 5.10: Logpseudolikelihood
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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
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16494, 555-568.Fraley, C., and Raft
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166Maps,” Biological Cybernetics,
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168Zahn, C. (1971), “Graph-Theore
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170structuring element file.Segment
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172A.3 Splus codehpcc - Hierarchica
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VITA1993 B.S. Mathematics, Harvey M
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