Signal modeling for two-dimensional image structures
Journal of Visual Communication and Image Representation
Local quaternion Fourier transform and color image texture analysis
Signal Processing
The trinion Fourier transform of color images
Signal Processing
Color texture segmentation based on quaternion-gabor features
CIARP'06 Proceedings of the 11th Iberoamerican conference on Progress in Pattern Recognition, Image Analysis and Applications
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Digital signal and image processing using reduced biquaternions (RBs) are introduced in this paper. RBs are an extension of the complex numbers, following the doubling procedure. Two useful representations of RBs (e1-e2 form and matrix representation) are discussed in this paper. Besides, we propose a new representation of RBs (the polar form) to calculate the multiplication and conjugation of RBs easily. Furthermore, we define a unique and suitable RB norm and its conjugate. These definitions are similar and compatible with the complex numbers. The efficient algorithms of the discrete reduced biquaternion Fourier transform (DRBFT), convolution (DRBCV), correlation (DRBCR), and phase-only correlation are discussed in this paper. In addition, linear-time-invariant and symmetric multichannel complex systems can be easily analyzed by RBs. For color image processing, we define a simplified RB polar form to represent the color image. This representation is useful to process color images in the brightness-hue-saturation color space. Many different types of color template matching and color-sensitive edge detection (brightness, hue, saturation, and chromaticity matched edges) can be performed simultaneously by RBs.