Hypercomplex Models of Multichannel Images

Abstract

We present a new theoretical approach to the processing ofmultidimensional and multicomponent images based on the theory of commutativehypercomplex algebras, which generalize the algebra of complex numbers.The main goal of the paper is to show that commutative hypercomplex numberscan be used in multichannel image processing in a natural and effective manner.We suppose that animal brains operate with hypercomplex numbers when processingmultichannel retinal images. In our approach, each multichannel pixel isregarded as a k-dimensional (kD) hypercomplex number rather than a kDvector, where k is the number of different optical channels. This createsan effective mathematical basis for various function–number transformationsof multichannel images and invariant pattern recognition. © 2021, Pleiades Publishing, Ltd.