Is the brain a "Clifford algebra quantum computer"? / Labunets V.G., Labunets-Rundblad E.V., Astola J. // Proceedings of SPIE - The International Society for Optical Engineering. - 2001. - V. 4453, l. . - P. 134-145.

ISSN:
0277786X
Type:
Conference Paper
Abstract:
We propose a novel method to calculate invariants of colour and multicolour images. It employs an idea of classical and quantum hypercomplex numbers and combines it with the idea of classical and quantum number theoretical transforms over hypercomplex algebras, which reduce the computational complexity of the global recognition algorithm for nD k-multispectral images from O(knNn+1) to O(kNn log N) and to O(kn log N), respectively. Our hypotheses are 1) the brain of primates calculates hypercomplex-valued invariants of an image during recognizing, 2) visual systems of animals with different evolutionary history use different hypercomplex algebras. The main goal of the paper is to show that quantum Clifford algebras can be used to solve pattern recognition in multispectral environment in a natural and effective manner.
Author keywords:
Fast fourier transforms; Invariant pattern recognition; Multicolour images; Quantum Clifford algebras
Index keywords:
Algorithms; Color; Computational complexity; Fast Fourier transforms; Quantum theory; Relativity; Clifford algebra quantum computer; Erlangen program; Informatics; Lorenz transformations; Pattern reco
DOI:
10.1117/12.447643
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Affiliations Department of Automation Technology, Urals State Technical University, Ekaterinburg, Russian Federation
Author Keywords Fast fourier transforms; Invariant pattern recognition; Multicolour images; Quantum Clifford algebras
References Kienle, G., Experiments concerning the non-Euclidian structure of the visual space (1964) Bioastronautics, 4, pp. 386-400; Luneburg, R.K., Metric methods in binocular visual perception (1948) Studies and Essays. Courant Anniv, 1, pp. 215-239; Luneburg, R.K., The metric methods in binocular visual space (1950) J.Opt.Soc.Amer, 40 (10), pp. 627-642; Hestenes, D., Sobczyk, G., (1984) Clifford Algebra to Geometric Calculus, , D. Reidel Publishing; Lasenby, A.N., Doran, C.J.L., Gull, S.F., Lectures in geometric algebra (1996) Clifford (Geometric) Algebras with Applications to Physics, , In: W. E. Baylis, Ed; Mathematics and Engineering, Birkhuser, Boston; Doran, C.J.L., Geometric algebra and its application to mathematical physics (1994), Ph.D. thesis, University of Cambridge; Dorst, L., Geometric algebra: A practical tool for efficient geometrical representation http//carol.wins.uva.nl/leo/publications.html; Clifford, W.K., (1968) Mathematical Papers, , N.Y; Vela, M., Explicit solutions of Galois embedding problems by means of generalized Clifford algebras (2000) J. Symbolic Computation, 30, pp. 811-842; Labunets-Rundblad, E.V., Labunets, V.G., Astola, J., Fast calculation algorithms of invariants for colour and multispectral image recognition (2000) Algebraic Frames for the Perception-Action Cycle. Second Inter. Workshop, AFPAC 2000, Kiel, Germany, September 2000, pp. 78-103. , Lectures Notes in Computer Science, 1888, Berlin; Labunets, V.G., Labunets-Rundblad, E.V., Astola, J., Algebra and geometry of colour images (2000) Proc. of First International Workshop on Spectral Tecniques and Logic Design for Future Digital Systems, Tampere, Finland, June 2-3, pp. 231-361; Labunets-Rundblad, E.V., Labunets, V.G., Astola, J., Is the visual cortex a "Fast Clifford algebra quantum computer"? (2000) A NATO Advanced Research Workshop "Clifford Analysis and Its Applications", , 30 October, Prague; be published; Labunets-Rundblad, E.V., Labunets, V.G., Chapter 7. Spatial-Colour Clifford algebra for invariant image recognition (2001) Geometric Computing with Clifford Algebra, 452, pp. 155-185. , Edt. G. Sommer, Springer, Berlin Heideberg; Labunets, V.G., Fast spectral algorithms of invariant pattern recognition and image matching based on modular invariants (1990) 1st Int. Conf. on Informat. Techn. for Image Analysis and Pattern Recognition. Lviv, USSR, pp. 70-89; Labunets, E.V., Labunets, V.G., Hypercomplex moments using in pattern invariant recognition (1996) New Information Methods in Research of Discrete Structures, pp. 58-63. , (in Russian), IMM UD RAS, Ekaterinburg; Labunets, E.V., Labunets, V.G., Hypercomplex moments application in pattern invariant recognition. Part 1. Generalized complex moments and invariants (1995) The Century of Radio, pp. 125-148. , (in Russian), IMM UD RAS, Ekaterinburg; Labunets-Rundblad, E.V., (2000) Fast Fourier-Clifford Transforms Design and Application in Invariant Recognition, p. 262. , PhD thesis, Tampere University Technology, Tampere, Finland
Correspondence Address Labunets, V.G.; Department of Automation Technology, Urals State Technical University, Ekaterinburg, Russian Federation; email: lab@cs.tut.fi
Editors Armenise M.N.
Sponsors SPIE
Conference name Materials and Devices for Photonic Circuits II
Conference date 1 August 2001 through 2 August 2001
Conference location San Diego, CA
Conference code 59945
CODEN PSISD
Language of Original Document English
Abbreviated Source Title Proc SPIE Int Soc Opt Eng
Source Scopus