Over The Rainbow: The Science of Picking a Good Colourmap

Synopsis

Colourmaps are ubiquitous in the presentation of numerical data, given their ability to render otherwise cluttered figures readable and aesthetically pleasing. They pervade every science, and are essential for many important applications like the representation of MRI data. However, the choice of a colourmap is not totally subjective; there are colourmaps that are measurably worse than others in terms of their ability to communicate data without visual artifacts that may confuse the reader (which can have dire consequences in the more important applications). It is therefore problematic that the most widely used colourmaps — the default option in many softwares — are rainbow colourmaps, which are widely regarded by scientists as among the worst existing colourmaps for data visualisation. I aim to explain precisely why this is the case, and how to pick a colourmap that is more useful, by introducing the formalism that underlies colourmap design. This will first involve a brief discussion of Wright and Guild’s colour matching experiments, and the construction of the visible gamut (and other related gamuts). This will allow me to introduce colourspaces, which are different coordinate systems used to represent colour — in particular, CIELab, which has a number of useful properties that make it useful to professionals and researchers for colourmap design. This will allow me to build a formal mathematical definition of a colourmap, which I will then use to explain the categories of colourmaps, where they are useful, and how to assess where they can fail.