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172A.3 Splus codehpcc - Hierarchical clustering on open principal curves is performed on point processdata; some plotting capability is also provided.clust.var.spline - This function is called by hpcc and is not intended for direct use.plot.pclust - This function is called by hpcc and is not intended for direct use.penalty - This function is called by hpcc and is not intended for direct use.vdist - This function is called by hpcc and is not intended for direct use.cempcc - This function refines a clustering on open principal curves by using theCEM algorithm; some plotting capability is also provided.calc.likelihood - This function is called by cempcc and is not intended for directuse.autoseg8 - This function fits greyscale image segmentation models for 1-8 segments.It calls segment.marginal, estimate.icm.phi0, and pseudol.unorder. It returns theinitial segmentation (by Ward’s method), the EM segmentation, and the ICMsegmentation, as well as all parameter estimates.segment.marginal - This function finds an initial segmentation by using Ward’smethod (calling ward.initclass) and then refines this marginal segmentation withthe EM algorithm (calling emfast.alg).ward.initclass - This function begins takes a matrix and a specified number of segmentsas input and returns a classification with the requisite number of segmentsbased on Ward’s method.emfast.alg - This function uses the EM algorithm to fit a Gaussian mixture. Aninitial classification of the data is required. The run time is linear in the number of
173unique data values, so it can handle large images in reasonable time as long as thenumber of unique data values is not large (as is the case with 256-level greyscaleimages).estimate.icm.phi0 - This function refines a segmentation by using ICM with parameterestimation. The phi parameter is constrained to be non-negative. Thisfunction calls the icm function.estimate.icm - The same as estimate.icm.phi0 but without the constraint on phi.icm - This function performs ICM without parameter estimation.pseudol.unorder - This function computes a pseudolikelihood for the unorderedcolors model conditional on parameter estimates.linehist - This function produces a histogram using vertical lines, which is usefulfor image data.mixplot - This function plots a Gaussian mixture density.flip - This function flips a matrix (not transpose) for plotting.morphit - This function performs a greyscale opening and closing on an integermatrix using a hard-coded 3x3 structuring element.
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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
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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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Page 150 and 151: 1305.3.4 Dog LungFigure 5.17 presen
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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
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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 194: VITA1993 B.S. Mathematics, Harvey M
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