Concept of Distance in Affine Geometry and Its Applications in Theories of Vision

Abstract

In Euclidean spaces of an arbitrary number n of dimensions metrics are defined which are invariant with respect to affine transformations of the coordinates. These metrics are closely related to non-Euclidean distances in spaces of negative constant curvature. Special cases are discussed. The logarithmic scale results for n=1. The case n=2 occurs in the solution of a colorimetric problem. The most important case n=3 is connected to the color space and to Luneburg’s geometry of the space of binocular vision.