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Book Cover
Author Bajorski, Peter, 1958-

Title Statistics for imaging, optics, and photonics / Peter Bajorski.

Published Hoboken, N.J. : Wiley, 2012.


Location Call No. Status
 UniM ERC  621.36015195 BAJO    AVAILABLE
Physical description xiv, 379 pages : illustrations ; 25 cm.
Series Wiley series in probability and statistics ; 808.
Wiley series in probability and statistics ; 808.
Notes Formerly CIP. Uk.
Bibliography Includes bibliographical references (pages 365-369) and index.
Contents Machine generated contents note: 1.1.Who Should Read This Book, -- 1.2.How This Book is Organized, -- 1.3.How to Read This Book and Learn from It, -- 1.4.Note for Instructors, -- 1.5.Book Web Site, -- 2.1.Statistical Thinking, -- 2.2.Data Format, -- 2.3.Descriptive Statistics, -- 2.3.1.Measures of Location, -- 2.3.2.Measures of Variability, -- 2.4.Data Visualization, -- 2.4.1.Dot Plots, -- 2.4.2.Histograms, -- 2.4.3.Box Plots, -- 2.4.4.Scatter Plots, -- 2.5.Probability and Probability Distributions, -- 2.5.1.Probability and Its Properties, -- 2.5.2.Probability Distributions, -- 2.5.3.Expected Value and Moments, -- 2.5.4.Joint Distributions and Independence, -- 2.5.5.Covariance and Correlation, -- 2.6.Rules of Two and Three Sigma, -- 2.7.Sampling Distributions and the Laws of Large Numbers, -- 2.8.Skewness and Kurtosis, -- 3.1.Introduction, -- 3.2.Point Estimation of Parameters, -- 3.2.1.Definition and Properties of Estimators, --
Contents note continued: 3.2.2.The Method of the Moments and Plug-In Principle, -- 3.2.3.The Maximum Likelihood Estimation, -- 3.3.Interval Estimation, -- 3.4.Hypothesis Testing, -- 3.5.Samples From Two Populations, -- 3.6.Probability Plots and Testing for Population Distributions, -- 3.6.1.Probability Plots, -- 3.6.2.Kolmogorov-Smirnov Statistic, -- 3.6.3.Chi-Squared Test, -- 3.6.4.Ryan-Joiner Test for Normality, -- 3.7.Outlier Detection, -- 3.8.Monte Carlo Simulations, -- 3.9.Bootstrap, -- 4.1.Introduction, -- 4.2.Regression Models, -- 4.2.1.Simple Linear Regression Model, -- 4.2.2.Residual Analysis, -- 4.2.3.Multiple Linear Regression and Matrix Notation, -- 4.2.4.Geometric Interpretation in an n-Dimensional Space, -- 4.2.5.Statistical Inference in Multiple Linear Regression, -- 4.2.6.Prediction of the Response and Estimation of the Mean Response, -- 4.2.7.More on Checking the Model Assumptions, -- 4.2.8.Other Topics in Regression, -- 4.3.Experimental Design and Analysis, --
Contents note continued: 4.3.1.Analysis of Designs with Qualitative Factors, -- 4.3.2.Other Topics in Experimental Design, -- Supplement 4A. Vector and Matrix Algebra, -- Vectors, -- Matrices, -- Eigenvalues and Eigenvectors of Matrices, -- Spectral Decomposition of Matrices, -- Positive Definite Matrices, -- A Square Root Matrix, -- Supplement 4B. Random Vectors and Matrices, -- Sphering, -- 5.1.Introduction, -- 5.2.The Multivariate Random Sample, -- 5.3.Multivariate Data Visualization, -- 5.4.The Geometry of the Sample, -- 5.4.1.The Geometric Interpretation of the Sample Mean, -- 5.4.2.The Geometric Interpretation of the Sample Standard Deviation, -- 5.4.3.The Geometric Interpretation of the Sample Correlation Coefficient, -- 5.5.The Generalized Variance, -- 5.6.Distances in the p-Dimensional Space, -- 5.7.The Multivariate Normal (Gaussian) Distribution, -- 5.7.1.The Definition and Properties of the Multivariate Normal Distribution, --
Contents note continued: 5.7.2.Properties of the Mahalanobis Distance, -- 6.1.Introduction, -- 6.2.Inferences About a Mean Vector, -- 6.2.1.Testing the Multivariate Population Mean, -- 6.2.2.Interval Estimation for the Multivariate Population Mean, -- 6.2.3.T2 Confidence Regions, -- 6.3.Comparing Mean Vectors from Two Populations, -- 6.3.1.Equal Covariance Matrices, -- 6.3.2.Unequal Covariance Matrices and Large Samples, -- 6.3.3.Unequal Covariance Matrices and Samples Sizes Not So Large, -- 6.4.Inferences About a Variance-Covariance Matrix, -- 6.5.How to Check Multivariate Normality, -- 7.1.Introduction, -- 7.2.Definition and Properties of Principal Components, -- 7.2.1.Definition of Principal Components, -- 7.2.2.Finding Principal Components, -- 7.2.3.Interpretation of Principal Component Loadings, -- 7.2.4.Scaling of Variables, -- 7.3.Stopping Rules for Principal Component Analysis, -- 7.3.1.Fair-Share Stopping Rules, -- 7.3.2.Large-Gap Stopping Rules, --
Contents note continued: 7.4.Principal Component Scores, -- 7.5.Residual Analysis, -- 7.6.Statistical Inference in Principal Component Analysis, -- 7.6.1.Independent and Identically Distributed Observations, -- 7.6.2.Imaging Related Sampling Schemes, -- 7.7.Further Reading, -- 8.1.Introduction, -- 8.2.Mathematical Formulation, -- 8.3.Practical Application, -- 8.4.Calculating Variability Explained by Canonical Variables, -- 8.5.Canonical Correlation Regression, -- 8.6.Further Reading, -- Supplement 8A. Cross-Validation, -- 9.1.Introduction, -- 9.2.Classification for Two Populations, -- 9.2.1.Classification Rules for Multivariate Normal Distributions, -- 9.2.2.Cross-Validation of Classification Rules, -- 9.2.3.Fisher's Discriminant Function, -- 9.3.Classification for Several Populations, -- 9.3.1.Gaussian Rules, -- 9.3.2.Fisher's Method, -- 9.4.Spatial Smoothing for Classification, -- 9.5.Further Reading, -- 10.1.Introduction, -- 10.2.Similarity and Dissimilarity Measures, --
Contents note continued: 10.2.1.Similarity and Dissimilarity Measures for Observations, -- 10.2.2.Similarity and Dissimilarity Measures for Variables and Other Objects, -- 10.3.Hierarchical Clustering Methods, -- 10.3.1.Single Linkage Algorithm, -- 10.3.2.Complete Linkage Algorithm, -- 10.3.3.Average Linkage Algorithm, -- 10.3.4.Ward Method, -- 10.4.Nonhierarchical Clustering Methods, -- 10.4.1.K-Means Method, -- 10.5.Clustering Variables, -- 10.6.Further Reading,.
Summary "This important resource bridges the gap between imaging, optics, and photonics, and statistics and data analysis. The text contains a wide range of relevant statistical methods including a review of the fundamentals of statistics and expanding into multivariate techniques. The techniques are explained in the context of real examples from remote sensing, multispectral and hyperspectral imaging, signal processing, color science, and other related disciplines. The book also emphasizes intuitive and geometric understanding of concepts. The topics that are most relevant to imaging, optics, and photonics applications are covered thoroughly. In addition, supplemental topics are discussed to provide an overview of when and how the methods can be used"--
Subject Optics -- Statistical methods.
Image processing -- Statistical methods.
Photonics -- Statistical methods.
ISBN 9780470509456 (hardback)