Hypercomplex Models of Multichannel Images
| Autor: | V. G. Labunets |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
IMAGE PROCESSING
Hypercomplex number Pixel Basis (linear algebra) HYPERCOMPLEX ALGEBRAS Computer science Image processing Invariant pattern recognition Mathematics (miscellaneous) Computer Science::Computer Vision and Pattern Recognition Algebra over a field Algorithm Commutative property Complex number MULTICHANNEL IMAGES |
| Zdroj: | Proceedings of the Steklov Institute of Mathematics |
| ISSN: | 1531-8605 0081-5438 |
| DOI: | 10.1134/s0081543821030160 |
| Popis: | We present a new theoretical approach to the processing of multidimensional and multicomponent images based on the theory of commutative hypercomplex algebras, which generalize the algebra of complex numbers. The main goal of the paper is to show that commutative hypercomplex numbers can be used in multichannel image processing in a natural and effective manner. We suppose that animal brains operate with hypercomplex numbers when processing multichannel retinal images. In our approach, each multichannel pixel is regarded as a $$K$$ -dimensional ( $$K$$ D) hypercomplex number rather than a $$K$$ D vector, where $$K$$ is the number of different optical channels. This creates an effective mathematical basis for various function–number transformations of multichannel images and invariant pattern recognition. |
| Databáze: | OpenAIRE |
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