There are many conflicting definitions of the Hue, Saturation and Brightness colour space. In the following documents, we attempt to clear up some of the confusion related to this subject:

• The latest version is this 2008 Pattern Recognition Letters Paper (© Springer-Verlag).
• A slightly older version of the work is presented in this SCIA 2003 paper (© Springer-Verlag).
• A much more detailed description is available in this PRIP technical report (with Jean Serra), which expands the material in chapter 4 of my thesis. A summary of this work is given in this paper presented at the DAGM 2003 (© Springer-Verlag). Note that there is an error in equation (6) of the printed version of the latter paper, which is corrected in the online version.
• For those of you wondering what the colour gamuts of the proposed spaces look like, the following animations are available (in AVI format). They present a slice through the achromatic axis of the spaces, which rotates through 360°. The achromatic axis is in the middle of the image, and the hue values (in degrees) to the left and right of it are indicated.
  • L1 norm space: Brightness is the mean of R, G and B, L1 chroma and (non-trigonometric) hue are used. View
  • max-min semi-norm space: Brightness is the mean of R, G and B, saturation is the max-min semi-norm and hue is the exact trigonometric version. View
  • max-min semi-norm space: The luminance weightings are used for brightness, while the other two coordinates are the same used in the previous animation. View

• Two Matlab functions which perform the forward and backward conversions between the RGB space and the suggested 3D polar coordinate IHLS (Improved Hue, Luminance and Saturation) colour space are here: hsy_rgb.zip (Thanks to Thomas Knudsen for the code optimisations).
• A Python version of the above functions, written by Alexander Schindler: hsy.zip.