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Qiu P. — Image processing and jump regression analysis
Qiu P. — Image processing and jump regression analysis

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Название: Image processing and jump regression analysis

Автор: Qiu P.

Аннотация:

Image Processing and Jump Regression Analysis builds a bridge between the worlds of computer graphics and statistics by addressing both the connections and the differences between these two disciplines. The author provides a systematic breakdown of the methodology behind nonparametric jump regression analysis by outlining procedures that are easy to use, simple to compute, and have proven statistical theory behind them. Key topics include conventional smoothing procedures, estimation of jump regression curves, edge detection in image processing, and edge-preserving image restoration, to name a few. With mathematical proofs kept to a minimum, this book is uniquely accessible as a primary text in nonparametric jump regression analysis and image processing as well as a reference on image processing or curve/surface estimation.


Язык: en

Рубрика: Computer science/Обработка изображений/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 313

Добавлена в каталог: 20.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$D_{4}$ distance      207
AIC criterion      69
B-splines      42 269
Basis functions      36—37 41 46 67 112 200
Basis functions, directional basis functions      201
Bayesian estimation      246
Bayesian estimation, Bayes estimator      250
Bayesian estimation, Bayes Theorem      250
Bayesian estimation, loss function      250
Bayesian estimation, posterior distribution      250 252
Bayesian estimation, prior distribution      249 251
BIC criterion      69
Block-circulant matrix      238 245
Bonferroni correction      142
Bootstrap techniques      61 181
Boundary curve      107 222
Cartesian coordinate system      224
Change-point estimation      8
Chebyshev’s polynomials      36 199
City-block distance      207
CLIQUE      246
Clique potentials      248
Conditional probability      246
Conditional probability density function      249
Convolution      191 196 202 237 239 252 269
Convolution, discrete version      237
Cost factors      216
Cost factors, point cost      218
Cost factors, total cost      218
Cubic splines      42
Curvature      37 89 141 218
Cusps      70 115
Data compression      7
Data smoothing      14
Delia function      236
Difference operator      190—191
Diffusion equation      270
Diffusion equation, anisotropic diffusion equation      270
Diffusion equation, isotropic diffusion equation      270
Diffusion equation, nonlinear diffusion equation      270
Diffusion equation, nonlinear diffusion equation, discrete version      271
Diffusivity      270
Divergence operator      270
Edge detection      1 7 187
Edge detection, Canny’s edge detection criteria      201
Edge detection, correction terms      210
Edge detection, cost minimization      216
Edge detection, deletion of deceptive edge pixels      222
Edge detection, derivative estimation      189
Edge detection, derivative estimation, estimation of the first-order derivatives      189
Edge detection, derivative estimation, estimation of the second-order derivatives      189
Edge detection, derivative of Gaussian (DoG) operators      192 202
Edge detection, derivative of Gaussian (DoG) operators, discrete version      192
Edge detection, difference of Gaussian operator      197
Edge detection, directional first-order derivative      205 209 215
Edge detection, directional second-order derivative      199—201 205 215
Edge detection, dissimilarity measure      218
Edge detection, edge fragmentation      219
Edge detection, edge linking      221
Edge detection, edge location      196
Edge detection, edge thickness      219
Edge detection, edge thinning      222
Edge detection, Frei — Chen masks      191
Edge detection, gradient estiamtion      190 200 223
Edge detection, greedy search      221
Edge detection, hill climbing      221
Edge detection, Laplacian of Gaussian (LoG) operator      195 197
Edge detection, local surface estimation      199
Edge detection, localization      201 203
Edge detection, Maxican hat filter      196—197
Edge detection, multilevel masks      206
Edge detection, optimal edge detector      202—204
Edge detection, post-processing      222
Edge detection, Prewitt masks      191 193
Edge detection, Roberts operator      191 193
Edge detection, roof edge detection      213
Edge detection, rotationally invariant operators      199
Edge detection, Sobel operator      139—140 191 193 222
Edge detection, thresholding      193 210 224
Edge detection, truncated pyramid masks      192—193
Edge detection, variational approach      204
Edge detection, zero-crossing properties      189 197 201
Edges      187
Edges, components      217
Edges, edge configuration      216
Edges, edge pixel      217
Edges, line edges      189 262
Edges, mathematical description      216
Edges, nonedge pixel      217
Edges, path      217
Edges, ramp edges      188
Edges, roof edges      7 188
Edges, roof edges, 1-D profile      188 213
Edges, spike edges      189
Edges, step edges      7 187—189
Edges, step edges, 1-D profile      188
Edges, texture edges      189
Edges, thick edge      217
Edges, thin edge      217
Edges, walk      217
Energy function      220 248 252 258 269
Equi-temperature surfaces      8 149
Fidelity      6 37 259
Fourier transformation      44 235 238 240
Fourier transformation, discrete Fourier transformation      239
Fourier transformation, discrete inverse Fourier transformation      240
Fourier transformation, fast Fourier transformation      239
Fourier transformation, Fourier coefficients      44
Fourier transformation, inverse fast Fourier transformation      239
Fourier transformation, inverse Fourier transformation      44 239
Fourier transformation, orthonormal basis      44
Fourier transformation, Parseval’s relation      45
Generalized inverse matrix      244
Gibbs distribution      248 251—252 255
Gibbs sampler      253
Global topographical elevation data      157
Graph      246
Hat matrix      35 39
Hausdorff distance      118 127 135 137—139
Hough transform      224
Hypothesis test      22
Hypothesis test, alternative hypothesis      22 113
Hypothesis test, critical value      23
Hypothesis test, null distribution      24
Hypothesis test, null hypothesis      22 113
Hypothesis test, p-value      23
Hypothesis test, power      24
Hypothesis test, significance level      23
Hypothesis test, test statistic      23
Hypothesis test, Type I error      23
Hypothesis test, Type II error      23
Ill-posed problem      259
Image addressing      222
Image enhancement      187
Image reconstruction      234
Image restoration      1 8 233—234 246
Image restoration, adaptive smoothing      265 272
Image restoration, bilateral filtering      265 272
Image restoration, bilateral filtering, discrete version      267
Image restoration, edge-preserving      8
Image restoration, inverse filtering      243
Image restoration, iterated conditional modes (ICM) algorithm      254
Image restoration, local smoothing filters      261
Image restoration, Markov random field modeling      246
Image restoration, maximum a posteriori (MAP) estimator      252
Image restoration, model      236
Image restoration, nonlinear diffusion filtering      269 272
Image restoration, regularization      258
Image restoration, scale-space filtering      270
Image restoration, weak membrane model      260
Image restoration, weak string model      260
Image segmentation      187 222
Images      2
Images, black-and-white images      8 255
Images, coordinate system      2 10
Images, deblurring      8 235
Images, degradations      233
Images, degradations, linear blur      242
Images, degradations, point degradations      233
Images, degradations, sources of degradation      233
Images, degradations, spatial degradations      233 240
Images, denoising      7 235
Images, digitization      2 119
Images, digitizer      2
Images, gray level      3
Images, gray level quantization      3
Images, image intensity function      2
Images, image representation      2
Images, monochrome digital images      2
Images, noise      3 235
Images, point source images      237
Images, resolution      3
Images, smoothed image      196
Images, uniform sampling      2 8
Impulse function      236
Independent      18 247
Intensity process      251
Jump curve estimation      60 87
Jump curve estimation, boundary regions      93
Jump curve estimation, information-sharing property      61
Jump curve estimation, jump-preserving      88
Jump curve estimation, M smoother      93
Jump curve estimation, piecewise-linear kernel estimation      90
Jump curve estimation, robust estimation      93
Jump curve estimation, sigma filter      93
Jump curve estimation, split linear smoothing algorithm      88
Jump curve estimation, trimmed spline estimator      68
Jump curve estimation, two approaches      60—61
Jump detection      8
Jump detection, 1-D jump detection      56
Jump detection, 1-D jump detection, a modification procedure      79 129
Jump detection, 1-D jump detection, bandwidth selection      61
Jump detection, 1-D jump detection, boundary problem      60 95
Jump detection, 1-D jump detection, confidence interval      61
Jump detection, 1-D jump detection, convergence rate      61 71 85
Jump detection, 1-D jump detection, difference apart kernel estimation (DAKE)      78
Jump detection, 1-D jump detection, difference kernel estimators (DKEs)      59
Jump detection, 1-D jump detection, hypothesis tests      76
Jump detection, 1-D jump detection, jumps in derivatives of f      64—65 75 80 85
Jump detection, 1-D jump detection, local linear estimators      73
Jump detection, 1-D jump detection, local linear kernel smoothing      61—62
Jump detection, 1-D jump detection, local LS estimation      81
Jump detection, 1-D jump detection, multiple jumps      60 64 72
Jump detection, 1-D jump detection, one-sided kernel estimators      57
Jump detection, 1-D jump detection, properties      58 62 85
Jump detection, 1-D jump detection, semiparametric modeling      65
Jump detection, 1-D jump detection, spline smoothing      67
Jump detection, 1-D jump detection, thresholding      84 87
Jump detection, 1-D jump detection, wavelet transformation      70
Jump detection, 2-D jump detection      101 151
Jump detection, 2-D jump detection, arbitrary JLCs      118
Jump detection, 2-D jump detection, assumption on the design points      106
Jump detection, 2-D jump detection, bandwidth selection      132
Jump detection, 2-D jump detection, boundary estimation      107
Jump detection, 2-D jump detection, continuity regions      102
Jump detection, 2-D jump detection, contrast statistic      110
Jump detection, 2-D jump detection, convergence rate      136
Jump detection, 2-D jump detection, deceptive jump candidates      128 136
Jump detection, 2-D jump detection, false jump detection rate      167
Jump detection, 2-D jump detection, gradient estimation      123 139
Jump detection, 2-D jump detection, jump location curves (JLCs)      102
Jump detection, 2-D jump detection, local linear estimation      119
Jump detection, 2-D jump detection, minimax estimator      107—108
Jump detection, 2-D jump detection, modification procedures      128 136 143
Jump detection, 2-D jump detection, multiple JLCs      106 115
Jump detection, 2-D jump detection, one-sided kernel estimators      105
Jump detection, 2-D jump detection, performance measurement      137—138
Jump detection, 2-D jump detection, pointset estimator      119 132
Jump detection, 2-D jump detection, properties      106 117 127 135
Jump detection, 2-D jump detection, rotational difference kernel estimators (RDKEs)      105
Jump detection, 2-D jump detection, rotational kernel functions      104
Jump detection, 2-D jump detection, singular point      119 134
Jump detection, 2-D jump detection, smooth, closed and simple curve      110 147
Jump detection, 2-D jump detection, thresholding      117 125 128 132 142
Jump detection, 2-D jump detection, tracking algorithm      112
Jump detection, 2-D jump detection, wavelet transformation      115
Jump regression analysis      7
Jump regression analysis, related statistical research areas      8
Jump surface estimation      149
Jump surface estimation, a three-stage procedure      150
Jump surface estimation, a three-stage procedure, first-order approximation to the JLCs      151
Jump surface estimation, adaptive weights smoothing (AWS)      177
Jump surface estimation, convergence rate      153 155
Jump surface estimation, explicit mathematical formula      159
Jump surface estimation, gradient estimation      169 184
Jump surface estimation, jump-preserved      149
Jump surface estimation, M smoother      150
Jump surface estimation, measuring jump preservation      183
Jump surface estimation, one-sided estimators      170
Jump surface estimation, parameter selection      166 180
Jump surface estimation, piecewise-linear kernel estimation      159
Jump surface estimation, properties      153—154 176
Jump surface estimation, sigma filter      150
Jump surface estimation, singular points      163 172
Jump surface estimation, symmetric “padding” method      155
Jump surface estimation, thresholding      157 163
Laplacian operator      194 270
Laplacian operator, eight-neighbor Laplacian mask      195 197
Laplacian operator, four-neighbor Laplacian mask      195
Least squares (LS) estimation      25 41 45 147 244
Least squares (LS) estimation, local LS estimation      81
Least squares (LS) estimation, local LS plane      121
Least squares (LS) estimation, residual sum of squares      25
Lena image      193 197
Line process      250 256
Manhattan distance      207 215
Marginal probability density function      250
Markov random field (MRF)      247
Markov random field (MRF), local characteristics      247
Maximum Likelihood Estimation      24 109
Maximum likelihood estimation, kernel-weighted likelihood function      113
Maximum likelihood estimation, likelihood function      24
Maximum likelihood estimation, likelihood ratio test      114
Maximum likelihood estimation, log-likelihood function      24 109
Median filtering      262
Median filtering, center weighted median filtering      265
Median filtering, weighted median filtering      265
Microarray image      146 222
Mountain image      233 257
Moving local least median squares (MLMS) approximation      267
Neighborhood averaging      261
Neighborhood system      246
Neighbors      246
Newton — Raphson algorithm      112
Nonparametric regression analysis      1
Nonparametric regression analysis, automatic boundary carpentry      32
Nonparametric regression analysis, bandwidth      25
Nonparametric regression analysis, bandwidth selection      34
Nonparametric regression analysis, bandwidth selection, cross-validation (CV)      34 39 167
Nonparametric regression analysis, bandwidth selection, Mallow’s Cp      34
Nonparametric regression analysis, bandwidth selection, plug-in algorithm      34
Nonparametric regression analysis, bias      27—28 32
Nonparametric regression analysis, boundary problem      25 28 32 64 157 223
Nonparametric regression analysis, conventional nonparametric regression analysis      6
Nonparametric regression analysis, global smoothing      26 38 45
Nonparametric regression analysis, kernel function      26
Nonparametric regression analysis, local constant kernel estimator      30
Nonparametric regression analysis, local linear kernel estimator      30 90 159 170 223
Nonparametric regression analysis, local polynomial kernel estimator      30
Nonparametric regression analysis, local smoothing      26
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