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26Latitude35.5 36.0 36.5 37.0 37.5 38.0-91.0 -90.5 -90.0 -89.5 -89.0 -88.5LongitudeFigure 2.12: Initial clustering <strong>of</strong> denoised New Madrid earthquake data using MCLUST. Thereare four clusters.Latitude35.5 36.0 36.5 37.0 37.5 38.0-91.0 -90.5 -90.0 -89.5 -89.0 -88.5LongitudeFigure 2.13: HPCC applied to the New Madrid data.
27Latitude35.5 36.0 36.5 37.0 37.5 38.0-91.0 -90.5 -90.0 -89.5 -89.0 -88.5LongitudeFigure 2.14: CEM-PCC applied to the New Madrid data.
Page 1: Fast Automatic Unsupervised Image S
Page 5: In presenting this dissertation in
Page 9 and 10: TABLE OF CONTENTSList of FiguresLis
Page 11 and 12: 4.1.2 Penalty Adjustment . . . . .
Page 13 and 14: Appendix A: Software Discussion 169
Page 15 and 16: 4.1 (a) Signal generated by an AR(1
Page 17 and 18: 5.29 Aerial image of a buoy, before
Page 19: DEDICATIONThis work is dedicated to
Page 22 and 23: 20 10 20 30 40 50 600 10 20 30 40 5
Page 24 and 25: 4fast because they can be implement
Page 26 and 27: 6multidimensional observations at e
Page 28 and 29: ••••8Figure 2.1(a) is a sim
Page 30 and 31: 10Principal Curve•••••Dat
Page 32 and 33: 12based on the estimates of the par
Page 34 and 35: 14first of these can be done by a h
Page 36 and 37: 162.4 Examples2.4.1 A Simulated Two
Page 38 and 39: 18Figure 2.5: HPCC applied to the t
Page 41 and 42: 21Table 2.2: BIC results for simula
Page 43 and 44: 232.4.3 New Madrid Seismic RegionDa
Page 45: 25Table 2.3: BIC results for New Ma
Page 49 and 50: 29set, so we want to avoid assumpti
Page 51 and 52: 31The examples we have presented in
Page 53 and 54: Chapter 3MARGINAL SEGMENTATIONIn th
Page 55 and 56: 35about ˜θ; this is a good approx
Page 57 and 58: 373.2 Mixture ModelsThe mixture den
Page 59 and 60: 39for estimating the model paramete
Page 61 and 62: 41The ith pixel of X or C is denote
Page 63 and 64: 43In componentwise classification,
Page 65 and 66: 45ponent. This classification proce
Page 67 and 68: Chapter 4ADJUSTING FOR AUTOREGRESSI
Page 69 and 70: 49Dependence CaseWhen |β| < 1, the
Page 72 and 73: 52For practical purposes, equation
Page 74 and 75: 54g ′′ (θ) ≈⎛⎜⎝∑ Ni=
Page 76 and 77: 564.1.3 Computing BIC with the AR(1
Page 78 and 79: 58upper, left, and right borders of
Page 80 and 81: 60L(Y −B |M, B) = L IND (Y −B |
Page 82 and 83: 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,
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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
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90the inequality in equation 5.55 h
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92N log(σ K ) − N log(σ 1 ) −
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94final number of clusters. The cho
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96ization to initialize (see sectio
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98ˆσ 2 j =∑ Ni=1 ˆQ ij (Y i
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100one particular data value, which
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102classification they are not. Eac
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1045.2.6 Morphological Smoothing (O
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1065.3 Image Segmentation Examples5
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1080 10 20 30 400 10 20 30 40Figure
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1100.0 0.005 0.010 0.015 0.020 0.02
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112three pixels remain incorrectly
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114Table 5.3: EM-based parameter es
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1160 10 20 30 40 50 600 10 20 30 40
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1180 10 20 30 40 50 600 10 20 30 40
Page 140 and 141:
1205.3.3 Ice FloesFigure 5.10 shows
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1220 20 40 60 80 1000 20 40 60 80 1
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124Percent0.0 0.005 0.010 0.015 0.0
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1260 20 40 60 80 1000 20 40 60 80 1
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1280 20 40 60 80 1000 20 40 60 80 1
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1305.3.4 Dog LungFigure 5.17 presen
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132Table 5.6: Logpseudolikelihood a
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134Percent0.0 0.05 0.10 0.15 0.200
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1360 20 40 60 80 100 1200 20 40 60
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1380 20 40 60 80 100 1200 20 40 60
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140interior to the land which had i
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142Table 5.9: EM-based parameter es
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1440 20 40 60 80 100 1200 20 40 60
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1460 20 40 60 80 100 1200 20 40 60
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1485.3.6 BuoyFigure 5.29 is an aeri
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150Table 5.10: Logpseudolikelihood
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1520 20 40 60 80 1000 20 40 60 80 1
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1540 20 40 60 80 1000 20 40 60 80 1
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1560 20 40 60 80 1000 20 40 60 80 1
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Chapter 6CONCLUSIONSThis dissertati
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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
Page 194:
VITA1993 B.S. Mathematics, Harvey M
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