Abstract
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.
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References
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Acknowledgements
This work was supported by the RFBR grant number 19-29-09022/19 and by the Ural State Forest Engineering’s Center of Excellence in “Quantum and Classical Information Technologies for Remote Sensing Systems”
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Labunets, V.G., Smetanin, J.G., Chasovskikh, V.P., Ostheimer, E. (2020). Hypercomplex Algebras as Unified Language for Image Processing and Pattern Recognition Part 1. Cliffordean Models of Multichannel Images. In: Kumkov, S., Shabunin, S., Syngellakis, S. (eds) Advances in Information Technologies, Telecommunication, and Radioelectronics. Innovation and Discovery in Russian Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-37514-0_1
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