Mathematical Foundations of Image Processing and Analysis 1

Image processing and image analysis are typically important fields in information science and technology. By “image processing”, we generally understand all kinds of operation performed on images (or sequences of images) in order to increase their quality, restore their original content, emphasize some particular aspect of the information or optimize their transmission, or to perform radiometric and/or spatial analysis. By “image analysis” we understand, however, all kinds of operation performed on images (or sequences of images) in order to extract qualitative or quantitative data, perform measurements and apply statistical analysis. Whereas there are nowadays many books dealing with image processing, only a small number deal with image analysis. The methods and techniques involved in these fields of course have a wide range of applications in our daily world: industrial vision, material imaging, medical imaging, biological imaging, multimedia applications, satellite imaging, quality control, traffic control, and so on

Part 1. An Overview of Image Processing and Analysis (IPA)

1. Gray-Tone Images.

2. Gray-Tone Image Processing and Analysis.

3. Binary Images.

4. Binary Image Processing and Analysis.

5. Key Concepts and Notions for IPA.

6. Mathematical Imaging Frameworks.

Part 2. Basic Mathematical Reminders for Gray-Tone and Binary Image Processing and Analysis

7. Basic Reminders in Set Theory.

8. Basic Reminders in Topology and Functional Analysis.

Part 3. The Main Mathematical Notions for the Spatial and Tonal Domains

9. The Spatial Domain.

10. The Tonal Domain.

Part 4. Ten Main Functional Frameworks for Gray Tone Images

11. The Algebraic and Order Functional Framework.

12. The Morphological Functional Framework.

13. The Integral Functional Framework.

14. The Convolutional Functional Framework.

15. The Differential Functional Framework.

16. The Generalized Functional Framework.

17. The Frequential Functional Framework.

18. The Multiscale Functional Framework.

19. The Variational Functional Framework.

20. The Probabilistic Functional Framework.

Jean-Charles Pinoli is Full Professor at Ecole Nationale Supérieure des Mines, Saint-Etienne, France.