Mathematical Foundations of Image Processing and Analysis, Volume 1

6

Mathematical Imaging Frameworks

The purpose of this chapter is to describe how and why mathematical imaging frameworks will be presented in this book. Section 6.1 focuses on the mathematical imaging framework notion and the key underlying concepts. Section 6.2 deals with the meaning of image representation and image modeling, which is more familiar to the image processing and analysis specialists, and their relations and overlaps with the mathematical imaging framework’s formalism. Section 6.3 briefly presents a methodology to implement a typical image processing and image analysis problem. Finally, a few books and articles are referred to and commented in section 6.4.

6.1. Mathematical imaging frameworks

In this book, a mathematical framework for Image Processing and Analysis (IPA) purposes will be systematically presented in a separate chapter, typically composed of the following four sections entitled: (1) paradigms, (2) mathematical notions and structures, (3) main approaches for IPA and (4) main applications to IPA.

In Epistemology (i.e. the theory of knowledge), a paradigm is a prerequisite distinct concept [KUH 96].

A mathematical imaging framework is based on some prerequisite paradigms and consists of different mathematical notions and structures, allowing us to build various approaches for image processing and analysis, in order to effectively address in fine real application issues.

In this book, the presentation of the mathematical imaging frameworks will be sequential, ...