Contents -------- Chapter 1 Introduction --------- Section 1.1 Images and image representation Section 1.2 Regression curves and surfaces with jumps Section 1.3 Edge detection, image restoration and jump regression analysis Section 1.4 Statistical process control and some other related topics Section 1.5 Organization of the book Problems Chapter 2 Basic Statistical Concepts and Conventional Smoothing Techniques --------- Section 2.1 Introduction Section 2.2 Some basic statistical concepts and terminologies Subsection 2.2.1 Populations, samples and distributions Subsection 2.2.2 Point estimation of population parameters Subsection 2.2.3 Confidence intervals and hypothesis testing Subsection 2.2.4 Maximum likelihood estimation and least squares estimation Section 2.3 Nadaraya-Watson and other kernel smoothing techniques Subsection 2.3.1 Univariate kernel estimators Subsection 2.3.2 Some statistical properties of kernel estimators Subsection 2.3.3 Multivariate kernel estimators Section 2.4 Local Polynomial kernel smoothing techniques Subsection 2.4.1 Univariate local polynomial kernel estimators Subsection 2.4.2 Some statistical properties Subsection 2.4.3 Multivariate local polynomial kernel estimators Subsection 2.4.4 Bandwidths selection Section 2.5 Spline smoothing procedures Subsection 2.5.1 Univariate smoothing spline estimation Subsection 2.5.2 Selection of the smoothing parameter Subsection 2.5.3 Multivariate smoothing spline estimation Subsection 2.5.4 Regression spline estimation Section 2.6 Wavelet transformation methods Subsection 2.6.1 Function estimation based on Fourier transformation Subsection 2.6.2 Univariate wavelet transformations Subsection 2.6.3 Multivariate wavelet transformations Problems Chapter 3 Estimation of Jump Regression Curves --------- Section 3.1 Introduction Section 3.2 Jump detection when the number of jumps is known Subsection 3.2.1 Difference kernel estimation procedures Subsection 3.2.2 Jump detection based on local linear kernel smoothing Subsection 3.2.3 Estimation of jump regression functions based on semiparametric modeling Subsection 3.2.4 Estimation of jump regression functions by spline smoothing Subsection 3.2.5 Jump and cusp detection by wavelet transformations Section 3.3 Jump estimation when the number of jumps is unknown Subsection 3.3.1 Jump detection by comparing three local estimators Subsection 3.3.2 Estimation of the number of jumps by a sequence of hypothesis tests Subsection 3.3.3 Jump detection by DAKE Subsection 3.3.4 Jump detection by local polynomial regression Section 3.4 Jump-preserving curve estimation Subsection 3.4.1 Jump curve estimation by split linear smoothing Subsection 3.4.2 Jump-preserving curve fitting based on local piecewise-linear kernel estimation Subsection 3.4.3 Jump-preserving smoothers based on robust estimation Section 3.5 Some discussions Problems Chapter 4 Estimation of Jump Location Curves of Regression Surfaces --------- Section 4.1 Introduction Section 4.2 Jump detection when the number of jump location curves is known Subsection 4.2.1 Jump detection by RDKE Subsection 4.2.2 Minimax edge detection Subsection 4.2.3 Jump estimation based on a contrast statistic Subsection 4.2.4 Algorithms for tracking the JLCs Subsection 4.2.5 Estimation of JLCs by wavelet transformations Section 4.3 Detection of arbitrary jumps by local smoothing Subsection 4.3.1 Treat JLCs as a pointset in the design space Subsection 4.3.2 Jump detection by local linear estimation Subsection 4.3.3 Two modification procedures Section 4.4 Jump detection in two or more given directions Subsection 4.4.1 Jump detection in two given directions Subsection 4.4.2 Measuring the performance of jump detection procedures Subsection 4.4.3 Connection to the Sobel edge detector Subsection 4.4.4 Jump detection in more than two given directions Section 4.5 Some discussions Problems Chapter 5 Jump-Preserving Surface Estimation By Local Smoothing --------- Section 5.1 Introduction Section 5.2 A three-stage procedure Subsection 5.2.1 Jump detection Subsection 5.2.2 First-order approximation to the JLCs Subsection 5.2.3 Estimation of jump regression surfaces Section 5.3 Surface reconstruction with thresholding Subsection 5.3.1 Surface reconstruction by local piecewisely linear kernel smoothing Subsection 5.3.2 Selection of procedure parameters Section 5.4 Surface reconstruction with gradient estimation Subsection 5.4.1 Gradient estimation and three possible surface estimators Subsection 5.4.2 Choose one of the three estimators based on the WRMS values Subsection 5.4.3 Choose one of the three estimators based on their estimated variances Subsection 5.4.4 A two-step procedure Section 5.5 Surface reconstruction by adaptive weights smoothing Subsection 5.5.1 Adaptive weights smoothing Subsection 5.5.2 Selection of procedure parameters Section 5.6 Some discussions Problems Chapter 6 Edge Detection In Image Processing --------- Section 6.1 Introduction Section 6.2 Edge detection based on derivative estimation Subsection 6.2.1 Edge detection based on first-order derivatives Subsection 6.2.2 Edge detection based on second-order derivatives Subsection 6.2.3 Edge detection based on local surface estimation Section 6.3 Canny's edge detection criteria Subsection 6.3.1 Three criteria for measuring edge detection performance Subsection 6.3.2 Optimal edge detectors by the three criteria Subsection 6.3.3 Some modifications Section 6.4 Edge detection by multilevel masks Subsection 6.4.1 Step edge detection Subsection 6.4.2 Roof edge detection Section 6.5 Edge detection based on cost minimization Subsection 6.5.1 A mathematical description of edges Subsection 6.5.2 Five cost factors and the cost function Subsection 6.5.3 Minimization using simulated annealing Section 6.6 Edge linking techniques Subsection 6.6.1 Edge linking by curve estimation Subsection 6.6.2 Local edge linking based on image gradient estimation Subsection 6.6.3 Global edge linking by the Hough transform Section 6.7 Some discussions Problems Chapter 7 Edge-Preserving Image Restoration --------- Section 7.1 Introduction Section 7.2 Image restoration by Fourier transformations Subsection 7.2.1 An image restoration model Subsection 7.2.2 2-D Fourier transformations Subsection 7.2.3 Image restoration by Fourier transformation Subsection 7.2.4 Image restoration by algebraic approach Section 7.3 Image restoration by Markov random field modeling Subsection 7.3.1 Markov random field modeling and Bayesian estimation Subsection 7.3.2 Geman and Geman's MAP procedure Subsection 7.3.3 Besag's ICM procedure and some modifications Subsection 7.3.4 Image restoration by regularization Section 7.4 Image restoration by local smoothing filters Subsection 7.4.1 Robust local smoothing filters Subsection 7.4.2 Adaptive smoothing and bilateral filtering Subsection 7.4.3 Image restoration by surface estimation Section 7.5 Image restoration by nonlinear diffusion filtering Subsection 7.5.1 Diffusion filtering Subsection 7.5.2 Relationship with adaptive smoothing and bilateral filtering Subsection 7.5.3 Some generalizations and modifications Section 7.6 Some discussions Problems References ---------- Index -----