REFERENCESAllard, D., and Fraley, C. (1997) “Nonparametric Maximum Likelihood Estimation<strong>of</strong> Features in Spatial Point Processes Using Voronoi Tesselation,”Journal <strong>of</strong> the American Statistical Association, vol. 92, pp. 1485-1493.Ambroise, C., Dang, M., and Govaert, G. (1996), ”Clustering <strong>of</strong> Spatial Data bythe EM Algorithm,” unpublished manuscript.Ambroise, C., and Govaert, G. (1996) “Constrained Clustering and KohonenSelf-Organizing Maps” Journal <strong>of</strong> Classification, vol. 13, pp. 299-313.Banfield, J.D., and Raftery, A.E. (1992), “Ice Floe Identification in SatelliteImages Using Mathematical Morphology and Clustering about PrincipalCurves,” Journal <strong>of</strong> the American Statistical Association, 87, 7-16.Banfield, J.D., and Raftery, A.E. (1993), “Model-Based Gaussian and Non-Gaussian Clustering,” Biometrics, 49, 803–821.Besag, J. (1974), ”Spatial Interaction and the Statistical Analysis <strong>of</strong> Lattice Systems,”Journal <strong>of</strong> the Royal Statistical Society, Series B, 6, 192-236.Besag, J. (1986), ”Statistical Analysis <strong>of</strong> Dirty Pictures,” Journal <strong>of</strong> the RoyalStatistical Society, Series B, 48, 259-302.Bovik, A.C., and Munson, D.C. (1986), “Edge Detection Using Median Comparisons,”Computer Vision, Graphics, and Image Processing, 33, 377-389.Burdick, H. (1997) Digital Imaging. McGraw-Hill: New York.Byers, S.D., and Raftery, A.E. (1998), “Nearest Neighbor Clutter Removal forEstimating Features in Spatial Point Processes,” Journal <strong>of</strong> the AmericanStatistical Association, 93, 577-584.
163Campbell, N.W., Mackeown, W.P.J., Thomas, B.T., Troscianko, T. (1997), “InterpretingImage Databases by Region Classification,” Pattern Recognition,30, 555-563.Canny, J. (1986) “A Computational Approach to Edge Detection,” IEEE Transactionson Pattern Analysis and Machine Intelligence, 8, 679-698.Carstensen, J. (1992) Description and Simulation <strong>of</strong> Visual Texture, PhD Thesis,Imsor: Denmark.Celeux, G., and Govaert, G. (1992), “A Classification EM Algorithm and TwoStochastic Versions,” Computational <strong>Statistics</strong> and Data Analysis, 14, 315-332.Chickering, D. M., and Heckerman, D. (1996), ”Efficient Approximations for theMarginal Likelihood <strong>of</strong> Bayesian Networks with Hidden Variables,” Proceedings<strong>of</strong> the 12th Conference on Uncertainty in Artificial Intelligence, 158-168.Cunningham, S., and MacKinnon, S. (1998) “Statistical Methods for Visual DefectMetrology” IEEE Transactions on Semiconductor Manufacturing, vol.11, pp. 48-53.Dasgupta, A., and Raftery, A.E. (1998), “Detecting Features in Spatial Point Processeswith Clutter via Model-Based Clustering,” Journal <strong>of</strong> the AmericanStatistical Association, 93, 294-302.Delicado, P. (1998) “Another Look at Principal Curves and Surfaces” WorkingPaper 309, Department d’Economia i Empresa, Universitat Pompeu Fabra.Dempster, A., Laird, N., and Rubin, D. (1977), “Maximum Likelihood fromIncomplete Data via the EM Algorithm (with Discussion),” Journal <strong>of</strong> theRoyal Statistical Society, Series B, 39, 1-38.Forbes, F., and Raftery, A. E., (1999) “Bayesian Morphology: Fast UnsupervisedBayesian Image Analysis, ” Journal <strong>of</strong> the American Statistical Association,
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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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4fast because they can be implement
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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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162.4 Examples2.4.1 A Simulated Two
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18Figure 2.5: HPCC applied to the t
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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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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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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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