Algebra and geometry of multichannel images. Part 1. Hypercomplex models of retinal images

Abstract

We present a new theoretical framework for multichannel image processing using hypercomplex commutative algebras. Hypercomplex algebras generalize the algebras of complex numbers. The main goal of the work is to show that hypercomplex algebras can be used to solve problems of multichannel (color, multicolor, and hyperspectral) image processing in a natural and effective manner. In this work we suppose that animal brain operates with hypercomplex numbers when processing and recognizing multichannel retinal images. In our approach, each multichannel pixel is considered not as an K–D vector, but as an K–D hypercomplex number, where K is the number of different optical channels. The aim of this part is to present algebraic models of subjective perceptual color, multicolor and multichannel spaces. Note, that the perceived color is the result of the human mind, not a physical property of an object. We also proposed a model of the MacAdam ellipses based on the triplet (color) geometry.