Ortho-unitary transforms, wavelets and splines / Ostheimer E., Labunets V., Artemov I. // Communications in Computer and Information Science. - 2017. - V. 661, l. . - P. 346-356.

ISSN:
18650929
Type:
Conference Paper
Abstract:
Here we present a new theoretical framework for multidimensional image processing using hypercomplex commutative algebras that codes color, multicolor and hypercolor. In this paper a family of discrete color–valued and multicolor–valued 2–D Fourier–like, wavelet– like transforms and splines has been presented (in the context of hypercomplex analysis). These transforms can be used in color, multicolor, and hyperspectral image processing. In our approach, each multichannel pixel is considered not as an K–D vector, but as an K–D hypercomplex number, where K is the number of different optical channels. Orthounitary transforms and splines are specific combination (Centaurus) of orthogonal and unitary transforms. We present several examples of possible Centuaruses (ortho–unitary transforms): Fourier+Walsh, ComplexWalsh+OrdinaryWalsh and so on.We collect basis functions of these transforms in the form of iconostas. These transforms are applicable to multichannel images with several components and are different from the classical Fourier transform in that they mix the channel components of the image. New multichannel transforms and splines generalize real– valued and complex–valued ones. They can be used for multichannel images compression, interpolation and edge detection from the point of view of hypercomplex commutative algebras. The main goal of the work is to show that hypercomplex algebras can be used to solve problems of multichannel (color, multicolor, and hyperspectral) image processing in a natural and effective manner. © Springer International Publishing AG 2017.
Author keywords:
Image processing; Multichannel image; Ortho–unitary transforms; Splines; Wavelets
Index keywords:
Algebra; Color; Complex networks; Discrete Fourier transforms; Discrete wavelet transforms; Edge detection; Fourier transforms; Image analysis; Image processing; Mathematical transformations; Optical
DOI:
10.1007/978-3-319-52920-2_32
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85014282477&doi=10.1007%2f978-3-319-52920-2_32&partnerID=40&md5=7a5907fb1b7aa8eb7c6e8978ef5e53b1
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Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-85014282477&doi=10.1007%2f978-3-319-52920-2_32&partnerID=40&md5=7a5907fb1b7aa8eb7c6e8978ef5e53b1
Affiliations Capricat LLC, Pompano Beach, FL, United States; Ural Federal University, Yekaterinburg, Russian Federation
Author Keywords Image processing; Multichannel image; Ortho–unitary transforms; Splines; Wavelets
References Greaves, C., On algebraic triplets Proc. Irisn Acad., 3, pp. 51-54. , 57–64, 80–84, 105–108; Ekaterina, L.-R., Nikitin, I., Labunets, V., Unified approach to fourier-cliffordprometheus sequences, transforms and filter banks (2003) Computational Noncommutative Algebra and Applications. NAII, 136, pp. 389-400. , Byrnes, J. (ed.), Springer, Dordrecht; Ekaterina, L.-R., Maidan, A., Novak, P., Color wavelet-haar-prometheus transforms for image processing (2003) Computational Noncommutative Algebra and Applications; Labunets, V., Rundblad, E., Astola, J., Is the brain a ‘clifford algebra quantum computer’? (2002) Applied Geometrical Algebras in Computer Science and Engineering, pp. 486-495. , Dorst, L., Doran, C., Lasenby, J. (eds.), Birkhäuser Boston, New York; Labunets-Rundblad, E., Labunets, V., Astola, J., Is the visual cortex a “fast clifford algebra quantum computer”? (2001) Clifford Analysis and Its Applications, NATO Science Series II: Mathematics, Physics and Chemistry, 25, pp. 173-183. , Brackx, F., Chisholm, J.S.R., Souˆcek, V. (eds.), Springer, Dordrecht; Labunets, V., Maidan, A., Rundblad-Labunets, E., Astola, J., Colour triplet-valued wavelets and splines (2001) Image and Signal Processing Ana Analysis, ISPA 2001, pp. 535-541; Labunets, V., Maidan, A., Rundblad-Labunets, E., Astola, J., Colour triplet-valued wavelets, splines and median filters (2001) Spectral Methods and Multirate Signal Processing, SMMSP 2001, pp. 61-70; Labunets-Rundblad, E., Fast fourier-clifford transforms design and application in invariant recognition (2000) Spectral Methods and Multirate Signal Processing, SMMSP 2001, p. 265
Correspondence Address Ostheimer, E.; Capricat LLCUnited States; email: katya@capricat.com
Editors Loukachevitch N.Panchenko A.Vorontsov K.Labunets V.G.Savchenko A.V.Ignatov D.I.Nikolenko S.I.Khachay M.Y.
Sponsors Exactpro;IT Centre;OK.Ru (Mail.Ru Group)
Publisher Springer Verlag
Conference name 5th International Conference on Analysis of Images, Social Networks and Texts, AIST 2016
Conference date 7 April 2016 through 9 April 2016
Conference code 189269
ISBN 9783319529196
Language of Original Document English
Abbreviated Source Title Commun. Comput. Info. Sci.
Source Scopus