Exploration in quaternion colour

Quaternions have been a subject for research in mathematics, physics, and engineering for decades. Using quaternions to represent colours, however, has recently been proposed and studied. Colour sensitive filtering can be achieved using a quaternion-valued filter. There are two colour edge detection methods defined on quaternions. One is based on the chromaticity cancellation that generates a grey colour for non-boundary regions; the other is based on estimation of homogeneity of regions. Trilateral filtering is proposed by locally adapting colour and changing the shape of the filter to achieve the effect of smoothing colours yet preserving edges. Furthermore, quaternion Fourier analysis has been implemented efficiently by decomposition into complex Fourier equivalence, which allows convolution and cross-correlation on quaternion-valued images in the frequency domain. Finally, based on quaternion singular value decomposition, quaternion principle analysis is implemented and applied to several applications, such as segmentation of colour images.