Image processing and jump regression analysis / Peihua Qiu.

Format:

Book

Author/Creator:

Qiu, Peihua, 1965-

Series:

Wiley series in probability and statistics.

Wiley series in probability and statistics

Language:

English

Subjects (All):

Image processing.

Regression analysis.

Physical Description:

1 online resource (340 p.)

Edition:

1st ed.

Place of Publication:

Hoboken, N.J. : John Wiley, c2005.

Language Note:

English

Summary:

The first text to bridge the gap between image processing and jump regression analysis Recent statistical tools developed to estimate jump curves and surfaces have broad applications, specifically in the area of image processing. Often, significant differences in technical terminologies make communication between the disciplines of image processing and jump regression analysis difficult. In easy-to-understand language, Image Processing and Jump Regression Analysis builds a bridge between the worlds of computer graphics and statistics by addressing both the connections and the d

Contents:

Image Processing and Jump Regression Analysis; Contents; List of Figures; List of Tables; Preface; 1 Introduction; 1.1 Images and image representation; 1.1 A conventional coordinate system for expressing an image in industry.; 1.2 Regression curves and sugaces with jumps; 1.2 A log-transformed C-band, HH-polarization, synthetic aperture radar image of an area near Thetford forest, England.; 1.3 December sea-level pressures observed by a Bombay weather station in India during 1921-1992.; 1.3 Edge detection, image restoration, and jump regression analysis

1.4 Statistical process control and some other related topics1.5 Organization of the book; Problems; 2 Basic Statistical Concepts and Conventional Smoothing Techniques; 2.1 Introduction; 2.2 Some basic statistical concepts and terminologies; 2.2.1 Populations, samples, and distributions; 2.1 Probability density curve of the standard normal distribution.; 2.2.2 Point estimation of population parameters; 2.2.3 Confidence intervals and hypothesis testing; 2.2.4 Maximum likelihood estimation and least squares estimation; 2.3 Nadaraya- Watson and other kernel smoothing techniques

2.3.1 Univariate kernel estimators2.3.2 Some statistical properties of kernel estimators; 2.3.3 Multivariate kernel estimators; 2.4 Local polynomial kernel smoothing techniques; 2.4.1 Univariate local polynomial kernel estimators; 2.4.2 Some statistical properties; 2.2 The Nadaraya-Watson (NW) kernel estimator and the local linear kernel (LK) estimator.; 2.3 Behavior of the Nadaraya-Watson (NW) kernel estimator [plot (a)] and the local linear (LK) kernel estimator [plot (b)] of; 2.4.3 Multivariate local polynomial kernel estimators

2.4 Behavior of the Nadaraya- Watson (NW) kernel estimator [plot (a)] and the local linear kernel (LK) estimator [plot (b)] o2.4.4 Bandwidth selection; 2.5 Spline smoothing procedures; 2.5.1 Univariate smoothing spline estimation; 2.5.2 Selection of the smoothing parameter; 2.5.3 Multivariate smoothing spline estimation; 2.5.4 Regression spline estimation; 2.5 Four B-splines when ti, tj+1,tj+2, tj+3, and tj+4 are 0, 0.25, 0.5, 0.75, and 1.0.; 2.6 Wavelet transformation methods; 2.6.1 Function estimation based on Fourier transformation; 2.6.2 Univariate wavelet transformations

2.6 The Haar father wavelet, the Haar mother wavelet, the Haar wavelet function y1,0, and the Haar wavelet function y1,1.2.6.3 Bivariate wavelet transformations; Problems; 2.7 When f(x) and y(x) are the Haar father and mother wavelets, the two-dimensional wavelet functions F(x, y), Y(1)(x, y), Y(2)(x, y), and Y(3)(x, y) are displayed.; 3 Estimation of Jump Regression Curves; 3.1 Introduction; 3.2 Jump detection when the number of jumps is known; 3.2.1 Difference kernel estimation procedures

3.1 The true regression function f and the jump detection criterion MDKE dejined by expression (3.2) when c = 0,n = 100, and hn = 0.1.

Notes:

"Wiley-Interscience."

Includes bibliographical references (p. 281-300) and index.

ISBN:

9786610276851

9781280276859

1280276851

9780470356869

0470356863

9780471733157

0471733156

9780471733164

0471733164

OCLC:

475936401