Colour image filters based on hypercomplex convolution

Abstract
There are very few examples of true vector filters known for colour images. The authors introduce a new class of filter based on convolution with hypercomplex masks, and present three colour edge detecting filters inspired by the Prewitt, Sobel and Kirsch filters. These filters, when applied to a colour image, produce an almost greyscale image with colour edges where the original image had a sharp change of colour. They rely on a three-space rotation about the grey line of RGB space, implemented with the rotation operator R[ ]R−1 where R is a quaternion and R−1 is its inverse. Pixels of similar colour corresponding to opposing positions in the filter masks cancel to give a grey or monochromatic result, while pixels of different colour are differenced in a vector sense to give coloured edge pixels. The linearity of the new filters is discussed and the paper concludes with a discussion of the impulse response of a hypercomplex filter.

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