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Digital Geometry by Azriel Rosenfeld, Reinhard Klette

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CHAPTER 14

Transformations

Subfields of geometry are sometimes defined by systems of axioms and sometimes by groups of transformations under which certain geometric properties remain invariant. This chapter describes the transformation-based approach and presents a set of axioms for digital geometry. It discusses transformation groups and symmetries, neighborhood-preserving transformations, applying transformations to pictures, magnification and demagnification, and digital tomography.

14.1 Geometries

A wide variety of geometries have been developed, motivated by a wide variety of applications: Euclidean (Thales of Miletus, Hippocrates of Chios, the secret society of the Pythagoreans, Euclid, Archimedes); analytic (Descartes, also known as ...

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