I was working on my ‘colour balance by hue variance’ filter I stumbled on this and I thought it might be useful to add it to GMIC. This kind of technical paper is a little above my head but I thought it would be straight-forward for you.

A 3D-Polar Coordinate Colour Representation Suitable for Image Analysis

AbstractThe processing and analysis of colour images has become an important area of study and application. The representation of the RGB colour space in 3D-polar coordinates (hue, saturation and brightness) can sometimes simplify this task by revealing characteristics not visible in the rect- angular coordinate representation. The literature describes many such spaces (HLS, HSV, etc.), but many of them, having been developed for computer graphics applications, are unsuited to image processing and analysis tasks. We describe the flaws present in these colour spaces, and present three prerequisites for 3D-polar coordinate colour spaces well-suited to image processing and analysis. We then derive 3D-polar coordinate representations which satisfy the prerequisites, namely a space based on the norm which has efficient linear transform functions to and from the RGB space; and an improved HLS (IHLS) space. The most important property of this latter space is a “well-behaved” saturation coordinate which, in contrast to commonly used ones, always has a small numerical value for near-achromatic colours, and is completely independent of the brightness function. Three applications taking advantage of the good properties of the IHLS space are described: the calculation of a saturation-weighted hue mean and of saturation-weighted hue histograms, and feature extraction using mathematical morphology.