Cover

Half-title

Title

Copyright

Dedication

Contents

Preface

1 Introduction

1.1 Introductory remarks

1.2 Decision mechanism in image processing

1.2.1 Organization of the book

2 Statistical linear models

2.1 Introductory remarks

2.2 Linear models

2.2.1 Parameter estimation

2.2.2 Linear hypothesis testing

2.3 One-way designs

2.4 Two-way designs

2.5 Incomplete designs

2.5.1 Latin square design

2.5.2 Græco-Latin square design

2.5.3 Incomplete block design

2.6 Contrast functions

2.6.1 Multiple comparisons techniques

2.6.2 Selection of a comparison method

2.6.3 Estimable functions

2.6.4 Confidence ellipsoids and contrasts

2.7 Concluding remarks

3 Line detection

3.1 Introductory remarks

3.2 Unidirectional line detectors

3.3 Bidirectional line detectors

3.4 Multidirectional line detectors

3.5 Multidirectional contrast detectors

3.6 Multidirectional detectors in correlated noise

3.7 Trajectory detection

3.7.1 Unidirectional detectors

3.7.2 Bidirectional trajectory detectors

3.8 Multidirectional adaptive detectors

3.9 Concluding remarks

4 Edge detection

4.1 Introductory remarks

4.2 Edge detection methodology

4.3 Unidirectional edge detectors

4.4 Bidirectional edge detectors

4.5 Multidirectional edge detectors

4.5.1 Latin square-based detector

4.5.2 Græco-Latin square-based detector

4.6 Multidirectional detection in correlated noise

4.6.1 Sum of squares under Ω

4.6.2 Sum of squares under the hypotheses

4.7 Edge reconstruction

4.7.1 Methodology

4.7.2 Gradient method

4.8 Concluding remarks

5 Object detection

5.1 Introductory remarks

5.2 Detection methodology

5.3 Transformation-based object detector

5.3.1 Uncorrelated data case

5.3.2 Correlated data case

5.3.3 Sum of squares under Ω

5.3.4 Sum of squares under coa = Ha ∩ Ω

5.3.5 Sum of squares under co^ = Hb ∩ Ω

5.3.6 Determination of background and target correlation matrices

5.3.7 Background and target correlation matrices

5.3.8 Structure of the permutation matrices

5.3.9 A reduced algorithm

5.4 Partition-based object detector

5.4.1 Image representation

5.5 Basic regions and linear contrasts

5.5.1 Histogram approach

5.5.2 Linear contrasts

5.6 Detection procedure

5.6.1 Contrast estimate

5.6.2 Threshold selection

5.6.3 Contrast detection

5.7 Orthogonal contrasts—an extension

5.8 Form-invariant object detector

5.8.1 Invariant representation

5.9 Concluding remarks

A.1 Contrast calculation

A.2 Contrast variance

6 Image segmentation

6.1 Introduction

6.2 Segmentation strategy

6.3 Nested design model

6.3.1 Gray level images

6.4 Logical predicates

6.5 Adaptive class formation

6.5.1 Test outcomes

6.5.2 Merging strategies

6.6 Concluding remarks

7 Radial masks in line and edge detection

7.1 Introductory remarks

7.2 Radial masks in one-way ANOVA design

7.3 Boundary detection procedure

7.4 Contrast-based detectors using radial masks

7.5 Power calculation

7.6 Concluding remark

8 Performance analysis

8.1 Stochastic approximation in parameter estimation

8.1.1 Remarks

8.1.2 Stochastic approximation versus classical estimation

8.2 Stochastic approximation procedures

8.2.1 Deterministic case

8.2.2 Stochastic case

8.2.3 The scalar version of the Robbins-Monro procedure

8.2.4 The Kiefer-Wolfowitz procedure

8.3 Stochastic approximation in least square estimation

8.3.1 Scalar case

8.3.2 Vector case

8.3.3 Small sample theory

8.4 Robust recursive estimation

8.4.1 Rank statistic preprocessor

8.4.2 Huber's M-Estimator

8.4.3 Robust SAMVLS

8.5 An illustrative example

8.6 Power calculations

8.6.1 F-statistic based detectors

8.6.2 Contrast-based detectors

8.7 Concluding remarks

9 Some approaches to image restoration

9.1 Introductory remarks

9.2 Edge detection preprocessors

9.3 Image restoration using linear regressions

9.4 Suppression of salt and pepper noise

9.5 Some results

9.6 Concluding remarks

References

Index