Fast algorithms of hypercomplex Fourier transforms
Geometric computing with Clifford algebras
Multi-Dimensional Signal Processin Using an Algebraically Extended Signal Representation
AFPAC '97 Proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle
Optimized Fast Algorithms for the Quaternionic Fourier Transform
CAIP '99 Proceedings of the 8th International Conference on Computer Analysis of Images and Patterns
Some FFT-like algorithms for RGB-spectra calculation
Machine Graphics & Vision International Journal - Special issue on latest results in colour image processing and applications
Local quaternion Fourier transform and color image texture analysis
Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Fast Complexified Quaternion Fourier Transform
IEEE Transactions on Signal Processing
Hypercomplex Fourier Transforms of Color Images
IEEE Transactions on Image Processing
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Any color may be represented in terms of three components (RGB or HSL) or four components (CMYK). For the four component color representation the use of quaternions, with one real and three imaginary components, is natural. By setting one component to zero, quaternions have been used in RGB or HSL representation of colors and color images. In this paper a new quantity, trinion, with one real and two imaginary components, is introduced and its use in color image representation is examined. The goal is to see if significant efficiencies in representation, analysis and computation involving three component color images accrue with the use of trinions. Two versions of the trinion Fourier transform (TFT) are introduced and it is shown that using TFT is preferable for combined analysis of three component color images rather than separate monochromatic analysis of each component and use of quaternions. Joint space-wavenumber localized trinion S (TS) transform with a two-dimensional Gaussian window function that scales with wavenumbers is also presented. Invertibility, rotation invariance, and computational aspects of the TS transform are discussed.