Simplifying Tone Curves for Image Enhancement

A single tone curve which is used to globally remap the brightness of each pixel in an image is one of the simplest ways to enhance an image. Tone curves might be the result of individual user edits or from algorithmic processing including in-camera processing pipelines. The precise shape of the tone curve is not strongly constrained other than it is usually limited to increasing functions of brightness. In this paper we constrain the shape further and define a simple tone adjustment, mathematically, to be a tone curve that has either no or one inflexion point. It follows that a complex tone curve is one with more than one inflexion point, visually making the curve appear ‘wiggly’. Empirically, complex tone curves do not seem to be used very often. For any given tone curve we show how the closest simple approximation can be efficiently found. We apply our approximation method to the MIT-Adobe FiveK dataset which comprises 5000 images that are manually tone-edited by 5 experts. For all 25,000 edited images - where some of the tone adjustments are complex - we find that they are all well-approximated by simple tone curve adjustments.