TY - CHAP

T1 - HYPERCOMPLEX ALGEBRAS AS UNIFIED LANGUAGE FOR IMAGE PROCESSING AND PATTERN RECOGNITION PART 1. CLIFFORDEAN MODELS OF MULTICHANNEL IMAGES

T2 - chapter in book

AU - Labunets, Valeriy G.

AU - Smetanin, Juriy G.

AU - Chasovskikh, Victor P.

AU - Ostheimer, Ekaterina

PY - 2020

Y1 - 2020

N2 - In this work, we assume that a brain in the visual cortex (VC) operates with Clifford numbers when it calculates hypercomplex-valued invariants of an image as it recognizes it. Clifford algebras generalize the algebras of complex numbers, quaternions and octonions. Of course, the algebraic nature of hypercomplex numbers must correspond to the spaces with respect to geometrically perceivable properties. For recognition of 2-D (bichromatic), 3-D (color), and n-D (multi-channel) images, we turn the perceptual spaces into corresponding Clifford algebras (and call them the VC-perceptual algebras). This approach gives full representation of how algebraic structures can possess image features and how algebraic structures can be used in different visual systems. It is our aim to show that the use of Clifford algebras fits more naturally to the tasks of recognition of multicolor patterns than does the use of color vector spaces. One can argue that nature has, through evolution, also learned to utilize properties of Cliffordean numbers.

AB - In this work, we assume that a brain in the visual cortex (VC) operates with Clifford numbers when it calculates hypercomplex-valued invariants of an image as it recognizes it. Clifford algebras generalize the algebras of complex numbers, quaternions and octonions. Of course, the algebraic nature of hypercomplex numbers must correspond to the spaces with respect to geometrically perceivable properties. For recognition of 2-D (bichromatic), 3-D (color), and n-D (multi-channel) images, we turn the perceptual spaces into corresponding Clifford algebras (and call them the VC-perceptual algebras). This approach gives full representation of how algebraic structures can possess image features and how algebraic structures can be used in different visual systems. It is our aim to show that the use of Clifford algebras fits more naturally to the tasks of recognition of multicolor patterns than does the use of color vector spaces. One can argue that nature has, through evolution, also learned to utilize properties of Cliffordean numbers.

UR - https://www.elibrary.ru/item.asp?id=44474240

U2 - 10.1007/978-3-030-37514-0_1

DO - 10.1007/978-3-030-37514-0_1

M3 - Chapter

SN - 978-3-030-37513-3

T3 - Сер. Innovation and Discovery in Russian Science and Engineering (IDRSE)

SP - 3

EP - 19

BT - ADVANCES IN INFORMATION TECHNOLOGIES, TELECOMMUNICATION, AND RADIOELECTRONICS

A2 - Kumkov, S.

A2 - Shabunin, S.

A2 - Singellakis, S.

PB - Springer

CY - Cham

ER -