We present a new theoretical framework for multichannel image processing using hypercomplexcommutative algebras. Hypercomplex algebras generalize the algebras of complexnumbers. The main goal of the work is to show that hypercomplex algebras can be usedto solve problems of multichannel (color, multicolor, and hyperspectral) image processing ina natural and effective manner. In this work we suppose that animal brain operates with hypercomplexnumbers when processing and recognizing multichannel retinal images. In ourapproach, each multichannel pixel is considered not as an K–D vector, but as an K–D hypercomplexnumber, where K is the number of different optical channels. The aim of this part isto 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 ofan object. We also proposed a model of the MacAdam ellipses based on the triplet (color) geometry.
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