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21Table 2.2: BIC results for simulated sine wave minefield.DF 0 Features 1 Feature 2 Features 3 Features2 -1031 -1034 -1018 -9913 -1031 -1016 -938 -9414 -1031 -975 -889 -9085 -1031 -911 -883 -9046 -1031 -884 -887 -9017 -1031 -873 -894 -9018 -1031 -868 -901 -9079 -1031 -869 -908 -92110 -1031 -872 -913 -92911 -1031 -873 -919 -94012 -1031 -877 -926 -951Figure 2.7: Simulated curvilinear minefield after denoising using nearest neighbor cleaning.
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 42 and 43: 22Figure 2.8: Initial clustering of
Page 44 and 45: 24Latitude35.5 36.0 36.5 37.0 37.5
Page 46 and 47: 26Latitude35.5 36.0 36.5 37.0 37.5
Page 48 and 49: 282.5 DiscussionWe have introduced
Page 50 and 51: 30transform type of approach. The e
Page 52 and 53: 32curve. Extending the method to ac
Page 54 and 55: 34is to use a likelihood ratio test
Page 56 and 57: 36The error of the approximation in
Page 58 and 59: 38the image with this independence
Page 60 and 61: 403.4.1 Mixture versus Componentwis
Page 62 and 63: 42P (X i = m|Y i ) ∝ P (Y i |X i
Page 64 and 65: 44In finding argmax C g(C|X), we ca
Page 66 and 67: 46fine tuning of this. For instance
Page 68 and 69: 48is σ 2 Y .Independence CaseWhen
Page 70: 50L(Y −1 |M, Y 1 ) = − N − 12
Page 73 and 74: 53analysis. We now consider g ′
Page 75 and 76: 55g(θ) ≈ log(p(Y |θ, M)) (4.38)
Page 77 and 78: 574.2 Adjusting BIC for the Raster
Page 79 and 80: 59ˆσ 2 ɛ = 1N 0 − 1∑(Y i −
Page 81 and 82: 61E[(Y i − µ)(Y (i−j) − µ)]
Page 83 and 84: 63The dependence model uses additio
Page 85 and 86: 65(BIC(K) = 2 L IND (Y −B | θ ˆ
Page 87 and 88: 67number of pixels minus the number
Page 89 and 90: 69in figure 4.1B). This problem cau
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Chapter 5AUTOMATIC IMAGE SEGMENTATI
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73the Gaussian parameters ˆθ, whi
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75f( ˆX|Y, ˆφ, ˆθ) ∝ ∏ if(
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77After running ICM, we have an est
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79denoted by µ K and σK; 2 equati
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81∫ ∞−∞|g i (Y i )|f(Y i )d
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83Lemma 2: ErgodicityLet X = X i ,
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85both dimensions) we are asymptoti
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87⎛∑ Kj=1f(YE KT⎝i |X i = j,
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89⎛∑ ∑ KTlog ⎝ j=1 f(Y i |X
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91− ∑ (Y i − µ 2 ) 2i∈S 22
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935.2 An Automatic Unsupervised Seg
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95has at least T 0 pixels. The proc
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97is the number of components (this
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99ˆµ j =∑ Ci=1H i ˆR ij V i∑
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101However, experience with the EM
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103log L ˆX (Y |K) = ∑ ilog(f(Y
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105operation. Then erosion can be e
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107is found; this results in a much
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1090 10 20 30 400 10 20 30 40Figure
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1115.3.2 Simulated Three Segment Im
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1130 10 20 30 40 50 600 10 20 30 40
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115Percent0.0 0.002 0.004 0.006 0.0
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1170 10 20 30 40 50 600 10 20 30 40
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1190 10 20 30 40 50 600 10 20 30 40
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121only one possible melt pool is e
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123Table 5.5: EM-based parameter es
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1250 20 40 60 80 1000 20 40 60 80 1
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1270 20 40 60 80 1000 20 40 60 80 1
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1290 20 40 60 80 1000 20 40 60 80 1
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131artifacts as well.The ICM refine
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133Table 5.7: EM-based parameter es
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1350 20 40 60 80 100 1200 20 40 60
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1370 20 40 60 80 100 1200 20 40 60
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1395.3.5 Washington CoastFigure 5.2
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141Table 5.8: Logpseudolikelihood a
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143Percent0.0 0.02 0.04 0.06 0.080
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1450 20 40 60 80 100 1200 20 40 60
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1470 20 40 60 80 100 1200 20 40 60
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149visible, both in jagged horizont
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151Table 5.11: EM-based parameter e
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153Percent0.0 0.02 0.04 0.06 0.080
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1550 20 40 60 80 1000 20 40 60 80 1
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1570 20 40 60 80 1000 20 40 60 80 1
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159The image segmentation examples
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161to provide predictive inference
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163Campbell, N.W., Mackeown, W.P.J.
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165Hartigan, J. A. (1975). Clusteri
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167Prim, R. (1957), “Shortest Con
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Appendix ASOFTWARE DISCUSSIONA.1 XV
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171emoutput.txt, emimageout.pgm.emn
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173unique data values, so it can ha
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