Simple tone curves: theory and applications

A single tone curve that remaps the brightnesses of each image pixel is a simple and widely deployed way to enhance an image. Tone curves might be crafted by individual users or determined algorithmically in camera processing pipelines. The precise shape of the tone curve is not a priori strongly constrained, other than it is usually limited to increasing functions of brightness. In this paper, we constrain the shape further and define a tone curve to be simple if it has no or one inflexion point. With respect to our representation, wiggly tone curves have several inflexion points and are deemed to be complex. A key contribution of our work is to show how we can best approximate a complex curve with a simple counterpart. For the MIT-Adobe FiveK dataset, comprising thousands of images that are tone-adjusted by photographic experts, we calculate corresponding simple tone curve adjusted images. Using objective similarity metrics, we find that simple curves deliver equally good image enhancement. In terms of preference experiments, simple curves deliver slightly preferred images compared to complex counterparts. Similar results are reported for a second smaller underwater image dataset.