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LIST OF FIGURES1.1 (a) Simulated image with 3 underlying segments and Gaussian noise.(b) Result of automatic segmentation. . . . . . . . . . . . . . . . . . 22.1 (a) Simulated minefield with noise. (b) Final result. . . . . . . . . . 82.2 Principal curve example. . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Two part curvilinear minefield after denoising using nearest neighborcleaning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Initial clustering of two part curvilinear minefield . . . . . . . . . . 172.5 HPCC applied to the two-part curvilinear minefield. . . . . . . . . . 182.6 Simulated curvilinear minefield. . . . . . . . . . . . . . . . . . . . . 202.7 Simulated curvilinear minefield after denoising using nearest neighborcleaning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.8 Initial clustering of denoised curvilinear minefield. . . . . . . . . . . 222.9 CEM-PCC applied to the curvilinear minefield. . . . . . . . . . . . 222.10 New Madrid earthquakes 1974-1992. . . . . . . . . . . . . . . . . . 242.11 New Madrid data after denoising. . . . . . . . . . . . . . . . . . . . 242.12 Initial clustering of denoised New Madrid earthquake data . . . . . 262.13 HPCC applied to the New Madrid data. . . . . . . . . . . . . . . . 262.14 CEM-PCC applied to the New Madrid data. . . . . . . . . . . . . . 27vi
4.1 (a) Signal generated by an AR(1) process (R 2 = 0.93). (b) Signalconsisting of two sequences of independent Gaussian noise (R 2 =0.92). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.2 Simulated two segment image. . . . . . . . . . . . . . . . . . . . . . 705.1 Simulated two-segment image. . . . . . . . . . . . . . . . . . . . . . 1085.2 Scrambled version of figure 5.1. . . . . . . . . . . . . . . . . . . . . 1095.3 Marginal histogram of the simulated image. . . . . . . . . . . . . . 1105.4 Simulation of a three segment image, before processing. . . . . . . . 1135.5 Marginal histogram of the simulated image, with the estimated 3component mixture density. . . . . . . . . . . . . . . . . . . . . . . 1155.6 Initial segmentation of the simulated image by Ward’s method, using3 segments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.7 Segmentation of the simulated image into 3 segments after EM. . . 1175.8 Segmentation of the simulated image into 3 segments after ICM. . . 1185.9 Segmentation of the simulated image into 3 segments after morphologicalsmoothing (opening and closing, conditional on the edgepixels). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.10 Aerial image of ice floes. . . . . . . . . . . . . . . . . . . . . . . . . 1225.11 Marginal histogram of the ice floe image, with the estimated 2 componentmixture density. . . . . . . . . . . . . . . . . . . . . . . . . 1245.12 Initial segmentation of the ice floe image by Ward’s method, using2 segments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255.13 Segmentation of the ice floe image into 2 segments after EM. . . . . 1265.14 Segmentation of the ice floe image into 2 segments after refinementby ICM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127vii
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: Appendix A: Software Discussion 169
Page 17 and 18: 5.29 Aerial image of a buoy, before
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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
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Page 32 and 33: 12based on the estimates of the par
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Page 41 and 42: 21Table 2.2: BIC results for simula
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Page 53 and 54: Chapter 3MARGINAL SEGMENTATIONIn th
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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
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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
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1205.3.3 Ice FloesFigure 5.10 shows
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124Percent0.0 0.005 0.010 0.015 0.0
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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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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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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
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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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