Share Email Print
cover

Spie Press Book

Statistics for Imaging, Optics, and Photonics
Author(s): Peter Bajorski
Format Member Price Non-Member Price

Book Description

In the field of imaging science, there is a growing need for students and practitioners to be equipped with the necessary knowledge and tools to carry out quantitative analysis of data. Providing a self-contained approach that is not too heavily statistical in nature, Statistics for Imaging, Optics, and Photonics presents necessary analytical techniques in the context of real examples from various fields, including remote sensing, color science, printing, and astronomy.

Bridging the gap between imaging, optics, photonics, and statistical data analysis, the author uniquely concentrates on statistical inference, providing a wide range of relevant methods. Brief introductions to key probabilistic terms are provided at the beginning of the book in order to present the notation used, followed by discussions on multivariate techniques such as:

  • Linear regression models, vector and matrix algebra, and random vectors and matrices
  • Multivariate statistical inference, including inferences about both mean vectors and covariance matrices
  • Principal components analysis
  • Canonical correlation analysis
  • Discrimination and classification analysis for two or more populations and spatial smoothing
  • Cluster analysis, including similarity and dissimilarity measures and hierarchical and nonhierarchical clustering methods

Intuitive and geometric understanding of concepts is emphasized, and all examples are relatively simple and include background explanations. Computational results and graphs are presented using the freely available R software, and can be replicated by using a variety of software packages. Throughout the book, problem sets and solutions contain partial numerical results, allowing readers to confirm the accuracy of their approach; and a related website features additional resources including the book's datasets and figures.

Made available in partnership with Wiley.


Book Details

Date Published: 25 October 2011
Pages: 408
ISBN: 9780819490209
Volume: PM219

Table of Contents
SHOW Table of Contents | HIDE Table of Contents

Table of Contents

1 INTRODUCTION

2 FUNDAMENTALS OF STATISTICS
2.1. Statistical thinking
2.2. Data format
2.3. Descriptive Statistics
2.4. Data visualization
2.5. Probability and Probability Distributions
2.6. Rules of two and three sigma
2.7. Sampling distributions and the laws of large numbers
2.8. Skewness and kurtosis

3 STATISTICAL INFERENCE
3.1. Introduction
3.2. Point estimation of parameters
3.3. Interval estimation
3.4. Hypothesis testing
3.5. Samples from two populations
3.6. Probability plots and testing for population distributions
3.7. Outlier detection
3.8. Monte Carlo simulations
3.9. Bootstrap

4 STATISTICAL MODELS
4.1. Introduction
4.2. Regression models
4.3. Experimental design and analysis
Supplement 4A: Vector and matrix algebra
Supplement 4B: Random vectors and matrices

5 FUNDAMENTALS OF MULTIVARIATE STATISTICS
5.1. Introduction
5.2. The multivariate random sample
5.3. Multivariate data visualization
5.4. The geometry of the sample
5.5. The generalized variance
5.6. Distances in the p-dimensional space
5.7. The multivariate normal (Gaussian) distribution

6 MULTIVARIATE STATISTICAL INFERENCE
6.1. Introduction
6.2. Inferences about a mean vector
6.3. Comparing mean vectors from two populations
6.4. Inferences about a covariance matrix
6.5. How to check multivariate normality

7 PRINCIPAL COMPONENT ANALYSIS
7.1. Introduction
7.2. Definition and properties of principal components
7.3. Stopping rules for principal components analysis
7.4. Principal component scores
7.5. Residual analysis
7.6. Statistical inference in principal components analysis
7.7. Further reading

8 CANONICAL CORRELATION ANALYSIS
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 DISCRIMINATION AND CLASSIFICATION - SUPERVISED LEARNING
9.1. Introduction
9.2. Classification for two populations
9.3. Classification for several populations
9.4. Spatial smoothing for classification
9.5. Further reading

10 CLUSTERING - UNSUPERVISED LEARNING
10.1. Introduction
10.2. Similarity and dissimilarity measures
10.3. Hierarchical clustering methods
10.4. Non-hierarchical clustering methods
10.5. Clustering variables
10.6. Further reading

APPENDIX A-1

APPENDIX A-2

APPENDIX A-3



© SPIE. Terms of Use
Back to Top