8. Final discussion

The aim of this article was to provide as concise a presentation as possible of the main concepts, notions and mathematical frameworks involved in gray-scale image processing and analysis. The author hopes to have achieved several objectives despite the small size of the document:

• enable readers interested in imaging to better situate, in the world of mathematics, the methods and techniques for processing and analyzing grayscale images that they use, or wish or could use;

• show the more mathematically-inclined reader just how interesting mathematics can be, revealing some of its strengths as well as its weaknesses.

What is most surprising at first glance, not only for engineers and technicians, but also for a wider readership, is the leading role played by algebra and topology,...