Maximally Distinct Color Generator

Generate maximally-distinct colors in an RGB colormap.

MAXDISTCOLOR generates an RGB colormap of maximally-distinct colors.

MAXDISTCOLOR has two required input arguments:

1. the number of colors, specified as a positive number.
2. a function handle that converts from sRGB to some kind of uniform colorspace (e.g. CIELab, OKLab, DIN99, DIN99o, OSA-UCS, CAM02-LCD, CAM02-UCS, CAM16-LCD, CAM16-UCS, etc.).

Optional input arguments allow the user to:

• Limit the lightness range.
• Limit the chroma range.
• Provide a colormap of colors to be excluded (e.g. background colors, existing plot colors).
• Provide a colormap of colors to be included (e.g. company colorscheme).
• Specify the class (double/single) used for the RGB calculations.
• Specify the bit/color depth to control the number of samples of each color channel.
• Sort the colormap (e.g. by hue, chroma, lightness, farthest colors, etc.).

See the Examples tab (HTML documentation) for explanations of the required and optional input arguments.

Warning

Requesting many colors from a large gamut can require hours/days/... of processing. Some option combinations are not tractable.

Examples

>> N = 5;
>> fun = @sRGB_to_OKLab;
>> rgb = maxdistcolor(N,fun)
rgb =
         0         0    0.8095
    1.0000    0.3858         0
    0.8254         0    1.0000
    0.4286         0    0.0159
         0    0.8189         0
>> axes('ColorOrder',rgb, 'NextPlot','replacechildren')
>> X = linspace(0,pi*3,1000);
>> Y = bsxfun(@(x,n)n*sin(x+2*n*pi/N), X(:), 1:N);
>> plot(X,Y, 'linewidth',4)

>> maxdistcolor(5,fun, 'exc',[0,0,0]) % Exclude only black.
ans =
    1.0000    1.0000    1.0000
         0         0    1.0000
         0    0.6772         0
    1.0000    0.1969    1.0000
    0.5238         0    0.0635

>> maxdistcolor(5,fun, 'inc',[1,0,1]) % Include magenta.
ans =
    1.0000         0    1.0000        % <------ magenta!
         0    0.8583         0
    0.1111         0    1.0000
         0    0.2677         0
    0.8254    0.3858         0

>> [rgb,Lab] = maxdistcolor(6,@sRGB_to_CIELab, 'Lmin',0.5, 'Lmax',0.7)
rgb =
    0.7619         0    1.0000
    1.0000         0         0
         0    0.7795         0
         0    0.5591    1.0000
    0.8254    0.6457    0.0794
    0.8254    0.2835    0.5397
Lab =
   50.3665   89.7838  -77.4181
   53.2329   80.1146   67.2197
   69.9972  -71.4422   68.9560
   58.7262    9.8332  -64.4628
   69.8987    5.1753   70.3783
   52.1378   59.8804   -6.6667

Motivation

The development of MAXDISTCOLOR was prompted by:

1. Existing "distinct color" generators use inadequate colorspaces and/or algorithms, leading to suboptimal color distinctiveness.
2. The realization that 64 bit PCs with >8 GB of RAM can operate on the entire 16 million colors of 24 bit TrueColor, allowing for neat and simple vectorized MATLAB code.

These two motivations are closely linked to two non-trivial tasks that have to be solved in order to generate maximally-distinct colors:

1. An algorithm to find the best color combination requires finding the global optimum, a task which grows exponentially with the number of requested colors and with the color gamut size. In MAXDISTCOLOR I use repeated application of a simple greedy algorithm to find the maximally-distinct colors: the repeated greedy algorithm is not particularly fast and is not a general solution for finding a global optimum, but luckily it gives good results for the regularly sampled RGB cube. Note that this algorithm contains no random numbers: it is entirely deterministic and repeatable.
2. Defining a true uniform colorspace: the venerable CIELab (used by most existing tools I could find) is not really very uniform, particularly around the blues/greens. For MAXDISTCOLOR I recommend CAM02-LCD or CAM02-UCS or CAM16-LCD or CAM16-UCS or OKLab or OSA-UCS, all of which provide a more accurate measure of the color distance.