On completness in early vision from systems theory

Abstract

This paper shows the interaction among the algebraic-analytical data fields theory, the complete descriptions that may be truncated for practical visual tasks and the different level of processing in the early visual pathway, in order to establish a measure of the representation of similarity between images. Our work is based on the approach of modeling the representational capabilities of systems of receptive fields found in early mammalian vision. It is well known that a representation scheme with a metric in the space of representation induce, in a natural way, a similarity measure between images. We propose in this paper to compare different representation schemes, based in previous theorems about completnes on data fields, according to the induced similarity measure.