Colour correction calculus (CCC): engineering the maths behind colour grading

To date, the digital world of still and moving pictures for video is almost essentially based on the 3-channel additive colour model, i.e. a plethora of RGB colour spaces. When it comes to creative or technical colour manipulations done digitally (be it either as part of on-location workflows, or during a post-production pipeline in a colour-correction theatre) controls available to artists and engineers range from very intuitive up to extremely new and nonlinear tools. By employing a unified yet simple and novel vector-based formalism typical of mathematical and physical field theories, [1], the author starts from classic Colour Science equations ([2]–[5]) and shows how this formalism may help to “part-and-divide” typical problems in in motion picture colour management, with the aim of simplifying and more consciously apply specific colour-related operations to footage. Video and film colour correction, particularly the one that is accomplished in the Digital Intermediate (DI) workflow inside a properly colour-calibrated DI theatre, is traditionally divided into various ‘canonical’ phases; the first affecting the picture as a whole (i.e. the same colour mappings are applied the same to every pixel in the frame) and called primary colour correction (CC); then comes the phase where only selected regions of the image (either static or moving) are colour-processed, and called secondary CC; then other oadditional phases may jump in. Secondary CC is the most important one from the creative point of view, where mathematical tools are essential to deliver, effectively, precisely and as quickly as possible, the Author of Photography’s creative intent.