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Mathematical Foundations of Image Processing and Analysis, Volume 1 by Jean-Charles Jean-Charles Pinoli Pinoli

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4

Binary Image Processing and Analysis

The purpose of this chapter is to provide a brief overview of the main fields and subfields of binary image processing and analysis. The main objective is to introduce, in a synthetic way, the key terms and notions that are necessary to understand the role and importance of the mathematical frameworks that will be discussed in parts 5–7 of Volume 2 of this book. The readers are advised to refer to the basic textbooks, mainly [PRA 07; Part 5] and [GON 08; Chapters 9, 11 and 12; 1st ed., 1992] for an introduction, and [SER 82] and [COS 86] for more fundamental treaties.

4.1. Binary image processing

Stricto sensu binary image processing [PAV 12; Original ed., 1982] [SER 82, BER 94] focuses on the transformation of a binary image or several binary images into one or more other binary images. Mathematically, this can be abstractly formalized by the following diagram:

 

[4.1] images

 

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

In very few cases, binary images can be acquired directly (e.g. the images of ‘silhouettes’ of objects), but they mostly result from gray-tone (or color or ...

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