Maximum Perceptual Difference Qualitative Colormap Generator

Generates a qualitative palette with maximum color differences (CIE 1931 or CIEDE 2000). TSP 2-opt algorithm for 'max/min' contrast sorting.

Description

[COL,DMIN,~] = truecol(N,INI,LAB,IMAX,ORD): Returns the 'N'-color sample 'COL' that achieves maximum perceptual differences between entries and the minimum color distance 'DMIN', as per the inputs:

N: Color sample size if scalar, or initial color matrix to optimize (N-by-3). Negative 'N' for colorblind schemes (-12<=N<=-1). Pre-stored cases for 1<=N<=23 and specific 'INI' values.

INI: Initial sample of colors (to exclude): Empty, a M-by-3 matrix, or 'b'/'k', 'w' and 'bw'/'kw' for black/white. If NaN, the search settings are override, and only distances and plots are calculated.

LAB: By default, CIE 1931 color space. If set to 0 or false, CIEDE 2000 standard.

IMAX: Maximum iterations (scalar), cycles/iterations (2-element vector), or cycles/iterations/refinement iterations (NaN or 3-element vector, exploratory mode)

ORD: Sorting order: 1 (maximum contrast, set as default), -1 (minimum contrast), 0 (random), NaN (unsorted). If not NaN, the color array starts with the bluest color, evolving in the reddest direction.

Passing NO OUTPUT arguments queries the generation of MULTIPLE PLOTS. If THREE OUTPUT parameters are queried, a SMALL FIGURE containing the final color palette is produced. A database with optimized CIEDE 2000 and CIE 1931 colors is provided for 0<'N'<24, for 'black', 'white' or both 'black' and 'white' initial colors. Also, 12 distinct colorblind palettes are included if the function is called for -12<='N'<=-1. The parameter 'IMAX' passes the sorting order 'ORD' if the queried sample is stored in 'COLORBASE' for 4 input arguments. Therefore, quick ways to run the function for these cases are:

[x,d,~] = truecol(8,'bw',0);      % CIEDE 2000 -bw palette (8)
[x,d,~] = truecol(6,[0,0,0]);     % CIELAB 1931 -b palette (6)
[x,d,~] = truecol(9,'',0,-1);     % CIEDE2000 low contrast (9)
[x,d,~] = truecol(-2);            % Okabe-Ito (-b) palette (7)

The algorithm uses a MINIMAX routine to optimize the color space, and a TSP with 2-Opt to sort the final color matrix. The iteration of the color sample between colorblind, CIELAB and CIEDE standards is highly encouraged, as there is no unique method for optimal color selection. The user is kindly referred to the description of the function inputs or to the comments of the code for further assistance. A standard way of running this function for new samples is, for example:

% Exploratory mode to find a new CIEDE color palette
[x,d,~] = truecol(8,[0,0,0;1,1,1;1,1,0],0,[1e2,1e2,1e4],-1);

% Visualise a given sample (i.e, Tol's High Contrast)
col = [255,255,255;221,170,51;187,85,102;0,68,136;0,0,0]/255;
truecol(col,NaN);

% Sort an existing sample for minimum contrast
[x,d,~] = truecol(truecol(-3),NaN,0,0,-1);      % R-Default

Examples

Enjoy!

Miguel Moreno, July 2024