Calculation of the CIELAB color coordinates and differences for map color legends
This MS Excel spreadsheet implements the procedure for calculating the CIELAB perceptually-uniform color attributes and color differences from the primary-defined RGB color coordinates, which are integer numbers between 0 (zero) and 255. It may be used by map designers to obtain specific color legends according to their requirements. The spreadsheet contains a starting list of colors (the Romanian color standard for soil type map legends), which is color-ordered (one color in a row; approximate spectral-order, including lightness/chroma degrees). The CIELAB color attributes, color attribute differences and overall color difference are those defined by the CIELAB color model/space (CIE, 2007). This model/space represents a color by using three abstract coordinates (orthogonal axes): L* has values between 0 (black) and 100 (white), indicating the color lightness; a* has positive values indicating amounts of red, negative values indicating the amounts of green and the value zero indicating neutral grey; b* has positive values indicating amounts of yellow, negative values indicating the amounts of blue and the value zero indicating neutral grey. From these three coordinates, other important perceptually-uniform color attributes are calculated: CIELAB chroma (C*ab), CIELAB hue angle/angle° (hab/hab°), CIELAB attribute differences (DL*, Da*, Db*, DC*ab, Dhab) and overall CIELAB color difference (DE*ab). The color differences calculated regarding a color are those between that color and the immediately-preceding color in the list. The list being color-ordered, the adjacent colors are normally the closest colors in the list, thus the color differences between them may be easily checked. Different other colors that appear as close in the list may be duplicated near others to see the color differences between them. The implemented calculation procedure consists of the following steps: (i) transformation of RGB coordinates to CIEXYZ coordinates (tristimulus values) (IEC, 1999), (ii) transformation of CIEXYZ coordinates to CIELAB (perceptually-uniform) coordinates and calculation of other CIELAB color attributes (CIE, 2007), and (iii) calculation of CIELAB colour differences (perceptually-uniform) (CIE, 2007). References: Brychtova, A., Coltekin, A., 2017. Calculating colour distance on choropleth maps with sequential colours – A case study with ColorBrewer 2.0. Kartographische Nachrichten 2, 53-60. CIE, 2007. CIE S 014-4:2007. Colorimetry - Part 4: CIE 1976 L*a*b* Colour space. Commission Internationale de l'Eclairage / International Commission on Illumination, CIE Tech. Committee 1-57, ISO 11664-4:2008. IEC, 1999. IEC 61966-2-1. Multimedia systems and equipment - Colour measurement and management. Part 2-1: Colour management – Default RGB colour space – sRGB. International Electrotechnical Commission, IEC Technical Committee 100.
Steps to reproduce
In order to obtain color lists (legends) appropriate for specific requirements, by using the “trial and error” method, the RGB coordinates of the list colors can be easily modified/adjusted to define other colors that are reliably-distinguishable from one another, and/or new colors can be inserted into the list in an appropriate place (order). Usually, a color difference threshold of 10 DE*ab units ensures acceptably-distinguishable colors (Brychtova and Coltekin, 2017), but, naturally, this threshold may be increased. The “Recolor” button refreshes the colors in the “Colours” column of the spreadsheet, after RGB coordinates have been modified.