Even Simpler Tone Curves

Abstractly, a tone curve can be thought of as an increasing function of input brightness which, when applied to an image, results in a rendered output that is ready for display and is preferred. However, the shape of the tone curve is not arbitrary. Curves that are too steep or too shallow (which concomitantly result in too much or too little contrast) are not preferred. Thus, tone curve generation algorithms often constrain the shape of the tone curves they generate. Recently, it was argued that tone curves should - as well as being limited in their slopes - only have one or zero inflexion points. In this paper, we propose that this inflexion-point requirement should be strengthened further. Indeed, the single inflexion point-only constraint still admits curves with sharp changes in slope (which are sometimes the culprits of banding artefacts in images). Thus, we develop a novel optimisation framework which additionally ensures sharp changes in the tone curves are smoothed out (technically, mollified). Our even simpler tone curves are shown to render most real images to be visually similar to those rendered without the constraints. Experiments validate our method.