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mp_cell_tracking/distinguishable_colors.m
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function colors = distinguishable_colors(n_colors,bg,func) | |
% DISTINGUISHABLE_COLORS: pick colors that are maximally perceptually distinct | |
% | |
% When plotting a set of lines, you may want to distinguish them by color. | |
% By default, Matlab chooses a small set of colors and cycles among them, | |
% and so if you have more than a few lines there will be confusion about | |
% which line is which. To fix this problem, one would want to be able to | |
% pick a much larger set of distinct colors, where the number of colors | |
% equals or exceeds the number of lines you want to plot. Because our | |
% ability to distinguish among colors has limits, one should choose these | |
% colors to be "maximally perceptually distinguishable." | |
% | |
% This function generates a set of colors which are distinguishable | |
% by reference to the "Lab" color space, which more closely matches | |
% human color perception than RGB. Given an initial large list of possible | |
% colors, it iteratively chooses the entry in the list that is farthest (in | |
% Lab space) from all previously-chosen entries. While this "greedy" | |
% algorithm does not yield a global maximum, it is simple and efficient. | |
% Moreover, the sequence of colors is consistent no matter how many you | |
% request, which facilitates the users' ability to learn the color order | |
% and avoids major changes in the appearance of plots when adding or | |
% removing lines. | |
% | |
% Syntax: | |
% colors = distinguishable_colors(n_colors) | |
% Specify the number of colors you want as a scalar, n_colors. This will | |
% generate an n_colors-by-3 matrix, each row representing an RGB | |
% color triple. If you don't precisely know how many you will need in | |
% advance, there is no harm (other than execution time) in specifying | |
% slightly more than you think you will need. | |
% | |
% colors = distinguishable_colors(n_colors,bg) | |
% This syntax allows you to specify the background color, to make sure that | |
% your colors are also distinguishable from the background. Default value | |
% is white. bg may be specified as an RGB triple or as one of the standard | |
% "ColorSpec" strings. You can even specify multiple colors: | |
% bg = {'w','k'} | |
% or | |
% bg = [1 1 1; 0 0 0] | |
% will only produce colors that are distinguishable from both white and | |
% black. | |
% | |
% colors = distinguishable_colors(n_colors,bg,rgb2labfunc) | |
% By default, distinguishable_colors uses the image processing toolbox's | |
% color conversion functions makecform and applycform. Alternatively, you | |
% can supply your own color conversion function. | |
% | |
% Example: | |
% c = distinguishable_colors(25); | |
% figure | |
% image(reshape(c,[1 size(c)])) | |
% | |
% Example using the file exchange's 'colorspace': | |
% func = @(x) colorspace('RGB->Lab',x); | |
% c = distinguishable_colors(25,'w',func); | |
% Copyright 2010-2011 by Timothy E. Holy | |
% Parse the inputs | |
if (nargin < 2) | |
bg = [1 1 1]; % default white background | |
else | |
if iscell(bg) | |
% User specified a list of colors as a cell aray | |
bgc = bg; | |
for i = 1:length(bgc) | |
bgc{i} = parsecolor(bgc{i}); | |
end | |
bg = cat(1,bgc{:}); | |
else | |
% User specified a numeric array of colors (n-by-3) | |
bg = parsecolor(bg); | |
end | |
end | |
% Generate a sizable number of RGB triples. This represents our space of | |
% possible choices. By starting in RGB space, we ensure that all of the | |
% colors can be generated by the monitor. | |
n_grid = 30; % number of grid divisions along each axis in RGB space | |
x = linspace(0,1,n_grid); | |
[R,G,B] = ndgrid(x,x,x); | |
rgb = [R(:) G(:) B(:)]; | |
if (n_colors > size(rgb,1)/3) | |
error('You can''t readily distinguish that many colors'); | |
end | |
% Convert to Lab color space, which more closely represents human | |
% perception | |
if (nargin > 2) | |
lab = func(rgb); | |
bglab = func(bg); | |
else | |
C = makecform('srgb2lab'); | |
lab = applycform(rgb,C); | |
bglab = applycform(bg,C); | |
end | |
% If the user specified multiple background colors, compute distances | |
% from the candidate colors to the background colors | |
mindist2 = inf(size(rgb,1),1); | |
for i = 1:size(bglab,1)-1 | |
dX = bsxfun(@minus,lab,bglab(i,:)); % displacement all colors from bg | |
dist2 = sum(dX.^2,2); % square distance | |
mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color | |
end | |
% Iteratively pick the color that maximizes the distance to the nearest | |
% already-picked color | |
colors = zeros(n_colors,3); | |
lastlab = bglab(end,:); % initialize by making the "previous" color equal to background | |
for i = 1:n_colors | |
dX = bsxfun(@minus,lab,lastlab); % displacement of last from all colors on list | |
dist2 = sum(dX.^2,2); % square distance | |
mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color | |
[~,index] = max(mindist2); % find the entry farthest from all previously-chosen colors | |
colors(i,:) = rgb(index,:); % save for output | |
lastlab = lab(index,:); % prepare for next iteration | |
end | |
end | |
function c = parsecolor(s) | |
if ischar(s) | |
c = colorstr2rgb(s); | |
elseif isnumeric(s) && size(s,2) == 3 | |
c = s; | |
else | |
error('MATLAB:InvalidColorSpec','Color specification cannot be parsed.'); | |
end | |
end | |
function c = colorstr2rgb(c) | |
% Convert a color string to an RGB value. | |
% This is cribbed from Matlab's whitebg function. | |
% Why don't they make this a stand-alone function? | |
rgbspec = [1 0 0;0 1 0;0 0 1;1 1 1;0 1 1;1 0 1;1 1 0;0 0 0]; | |
cspec = 'rgbwcmyk'; | |
k = find(cspec==c(1)); | |
if isempty(k) | |
error('MATLAB:InvalidColorString','Unknown color string.'); | |
end | |
if k~=3 || length(c)==1, | |
c = rgbspec(k,:); | |
elseif length(c)>2, | |
if strcmpi(c(1:3),'bla') | |
c = [0 0 0]; | |
elseif strcmpi(c(1:3),'blu') | |
c = [0 0 1]; | |
else | |
error('MATLAB:UnknownColorString', 'Unknown color string.'); | |
end | |
end | |
end |