Mathematical Foundations of Image Processing and Analysis, Volume 1

Contents

Preface

Introduction

Elements of Mathematical Terminology

PART 1: An Overview of Image Processing and Analysis (IPA)

1 Gray-Tone Images

1.1. Intensity images, pixels and gray tones

1.2. Scene, objects, context, foreground and background

1.3. Simple intensity image formation process models

1.4. The five main requirements for a relevant imaging approach

1.5. Additional comments

2 Gray-Tone Image Processing and Analysis

2.1. Image processing

2.2. Image analysis

2.3. Image comparison

2.4. Importance of Human Vision

2.5. Additional comments

3 Binary Images

3.1. Scene, objects and context

3.2. Binary and multinary images

3.3. Additional comments

4 Binary Image Processing and Analysis

4.1. Binary image processing

4.2. Binary image analysis

4.3. Binary image and object description

4.4. Object comparison

4.5. Object analysis, recognition and formation

4.6. Additional comments

5 Key Concepts and Notions for IPA

5.1. Dimensionality

5.2. Continuity and discreteness

5.3. Scale, resolution and definition

5.4. Domains

5.5. Ranges

5.6. Additional comments

6 Mathematical Imaging Frameworks

6.1. Mathematical imaging frameworks

6.2. Image representation and image modeling

6.3. A mathematical imaging methodology

6.4. Additional comments

PART 2: Basic Mathematical Reminders for Gray-Tone and Binary Image Processing and Analysis

7 Basic Reminders in Set Theory

7.1. Mathematical disciplines

7.2. Sets and elements

7.3. Order and equivalence relations on sets

7.4. Mappings between sets

7.5. Mapping ...