20 May 2016 2D hexagonal quaternion Fourier transform in color image processing
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Abstract
In this paper, we present a novel concept of the quaternion discrete Fourier transform on the two-dimensional hexagonal lattice, which we call the two-dimensional hexagonal quaternion discrete Fourier transform (2-D HQDFT). The concept of the right-side 2D HQDFT is described and the left-side 2-D HQDFT is similarly considered. To calculate the transform, the image on the hexagonal lattice is described in the tensor representation when the image is presented by a set of 1-D signals, or splitting-signals which can be separately processed in the frequency domain. The 2-D HQDFT can be calculated by a set of 1-D quaternion discrete Fourier transforms (QDFT) of the splitting-signals.
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Artyom M. Grigoryan, Artyom M. Grigoryan, Sos S. Agaian, Sos S. Agaian, } "2D hexagonal quaternion Fourier transform in color image processing", Proc. SPIE 9869, Mobile Multimedia/Image Processing, Security, and Applications 2016, 98690N (20 May 2016); doi: 10.1117/12.2223115; https://doi.org/10.1117/12.2223115
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