Colour-to-Greyscale Image Conversion by Linear Anisotropic Diffusion of Perceptual Colour Metrics

We present an algorithm for conversion of colour images to greyscale. The underlying idea is that local perceptual colour differences in the colour image should translate into local differences in greylevel in the greyscale image. This is obtained by constructing a gradient for the greyscale image from the eigenvalues and eigenvectors of the structure tensor of the colour image, which, in turn, is computed by means of perceptual colour difference metrics. The greyscale image is then constructed from the gradient by means of linear anisotropic diffusion, where the diffusion tensor is constructed from the same structure tensor. By means of psychometric experiments, it is found that the algorithm gives the most accurate image reproduction when used with the $\triangle E_{99}$ colour metric, and that it performs at the level of, or better than, other state-of-the-art spatial algorithms. Surprisingly, the only algorithm that can compete in terms of accuracy is a simple luminance map computed as the $L^{*}$ channel of the image represented in the CIELAB colour space.