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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