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132Table 5.6: Logpseudolikelihood and BIC P L results for the dog lung image.Segments ˆφ Logpseudolikelihood BICP L BIC IND1 – -80641.02 -161311.13 -166007.12 1.14 -61081.56 -122221.33 -137193.03 1.09 -59536.76 -119160.82 -137019.84 0.52 -42147.64 -84411.69 -128746.25 0.71 -48914.07 -97973.64 -135323.56 0.69 -48508.12 -97190.83 -135333.67 0.47 -36602.26 -73408.23 -128800.68 0.42 -36254.37 -72741.54 -128825.80 20 40 60 80 100 1200 20 40 60 80 100 120Figure 5.17: PET image <strong>of</strong> a dog lung, before processing.
133Table 5.7: EM-based parameter estimates for the dog lung image.8 segments.Means: 41 36.24 46.28 78.28 120.06 147.19 174.8 214.25SDs : 0.5 9.14 9.25 18.22 15.01 9.15 13.93 15.13Probs: 0.241 0.285 0.336 0.04 0.028 0.019 0.036 0.0167 segments.Means: 41 36.26 46.27 78.25 135.39 175.21 216.28SDs : 0.5 9.13 9.26 20.39 23.58 16.97 14.58Probs: 0.241 0.285 0.335 0.042 0.05 0.034 0.0146 segments.Means: 40.86 42.67 90.68 137.66 175.45 216.31SDs : 3.2 12.29 16.57 22.71 17.05 14.59Probs: 0.398 0.479 0.029 0.048 0.033 0.0135 segments.Means: 40.86 42.65 90.23 138.2 182.43SDs : 3.2 12.27 17.38 25.81 28.69Probs: 0.398 0.478 0.029 0.046 0.054 segments.Means: 41 41.88 104.15 177.47SDs : 0.5 10.56 38.01 29.58Probs: 0.24 0.622 0.079 0.0593 segments.Means: 41.3 67.95 166.35SDs : 7.99 30.79 32.89Probs: 0.816 0.098 0.0862 segments.Means: 41.49 127.11SDs : 8.47 54.57Probs: 0.846 0.1541 segments.Means: 54.64SDs : 38.35Probs: 1
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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
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
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 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
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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
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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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