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.
Colour image filters based on hypercomplex convolution
2000-04-01
5 pages
Article (Journal)
English
three-space rotation , convolution , hypercomplex masks , edge detection , filtering theory , quaternion , Sobel filters , colour edges , impulse response , hypercomplex convolution , image representation , RGB space , Kirsch filters , colour image filters , greyscale image , Prewitt filters , linear vector filters , edge detecting filters , coloured edge pixels , image colour analysis
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