Image Processing Done Right

Abstract

A large part of “image processing” involves the computation of significant points, curves and areas (“features”). These can be defined as loci where absolute differential invariants of the image assume fiducial values, taking spatial scale and intensity (in a generic sense) scale into account. “Differential invariance” implies a group of “similarities” or “congruences”. These “motions” define the geometrical structure of image space. Classical Euclidian invariants don’t apply to images because image space is non-Euclidian. We analyze image structure from first principles and construct the fundamental group of image space motions. Image space is a Cayley-Klein geometry with one isotropic dimension. The analysis leads to a principled definition of “features” and the operators that define them.