Mathematical Foundations of Image Processing and Analysis, Volume 1

2

Gray-Tone Image Processing and Analysis

In its broadest sense, the notion of processing or analyzing an image involves the transformation of an image from one form to another. The result can be another image or can take the form of an abstraction, a quantification or a decision.

The purpose of this chapter is to briefly overview the main fields and subfields of gray-tone image processing and analysis. The main objective is to introduce, in a synthetic way, the key terms and notions necessary to understand the role and importance of the mathematical frameworks that will be exposed in Parts 3 and 6 of this book. A short and easy-to-read, but good introductory, monograph on image processing and analysis was presented in [GLA 95]. Readers are advised to refer to the basic textbooks, mainly [RUS 11; 1st ed., 1992], for an introduction, [GON 08; 1st ed., 1992] for a complete analysis and [PRA 07; 1st ed., 1978] [JAI 89] for additional discussions on the subject.

2.1. Image processing

Stricto sensu Image Processing focuses on the transformation of an image or several images into one or more other images [STO 72]. Mathematically, this can be abstractly formalized by the following diagram:

 

[2.1]

 

where f denotes the input image(s), (f) denotes the output image(s) and denotes the transformation ...