Ortho-Unitary Transforms, Wavelets and Splines / Ostheimer Ekaterina,Labunets Valery,Artemov Ivan // . - 2017. - V. 661, l. . - P. 346-356.

ISSN/EISSN:

1865-0929 / нет данных

Type:

Proceedings 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.

Author keywords:

Ortho-unitary transforms; Wavelets; Splines; Image processing; Multichannel image

DOI:

10.1007/978-3-319-52920-2\_32

Web of Science ID:

ISI:000407059600032

Соавторы в МНС:

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Другие поля

Поле	Значение
Editor	Ignatov, DI and Khachay, MY and Labunets, VG and Loukachevitch, N and Nikolenko, SI and Panchenko, A and Savchenko, AV and Vorontsov, K
Booktitle	ANALYSIS OF IMAGES, SOCIAL NETWORKS AND TEXTS, AIST 2016
Series	Communications in Computer and Information Science
Note	5th International Conference on Analysis of Images, Social Networks, and Texts (AIST), Yekaterinburg, RUSSIA, APR 07-09, 2016
Organization	Exactpro; OK Ru; Ctr Informat Technologies
Publisher	SPRINGER INTERNATIONAL PUBLISHING AG
Address	GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND
Language	English
ISBN	978-3-319-52920-2; 978-3-319-52919-6
Author-Email	katya@capricat.com vlabunets05@yahoo.com
Number-of-Cited-References	8
Doc-Delivery-Number	BI1XP