MKPJ - perceptually improved Jet colormap 1.0

function map=mkpj(n,scheme)% MKPJ Returns a perceptually improved Jet colormap% MKPJ (N,SCHEME) returns an Nx3 colormap.% usage: map=mkpj(n,scheme);%% JUSTIFICATION: rainbow, or spectrum color schemes are considered a poor% choice for scientific data display by many in the scientific community% (see for example reference 1 and 3) in that they introduce artifacts% that mislead the viewer. "The rainbow color map appears as if itd-deOaos separated% into bands of almost constant hue, with sharp transitions between hues.% Viewers perceive these sharp transitions as sharp transitions in the data,% even when this is not the casein how regularly spaced (interval) data are% displayed (quoted from reference 1). The default Matlab Jet is no exception.% Please see examples in my previous FEX submission "Perceptually improved% colormaps".% This submission is intended to share the results of my work to create a% more perceptually balanced, Jet colormap. Please see output arguments section% for more details.% A full series of posts on improved colormaps will appear on my blog at% http://mycarta.wordpress.com/%%% arguments: (input)% scheme - can be one of the following strings:% 'JetI'% The new, more perceptually balanced, Jet color map.% This explanation should be read in conjunction with the submitted figure% "JET_idea_after_scaling_final_L_plt.png"% The idea to improve the default jet came to me after seeing the human% wavelenght discrimination curve from Gregory (1964) in the paper by% Welland et al. (2006).% The top display in the figure is the standard Matlab Jet. Below it,% second display, is the Luminance versus wavelenght profile. This is% essentially the same as plot you would find in the left plot of% figure 3 in Rogowitz and Kalvin (2001). In the third display I reproduced% Gregory's curve. It's considering these two together that brought the% Eureka moment (though it took me a few experiments and some calculations% to line them up properly). The idea was: "can I use this curve to% dynamically stretch the rainbow where transitions are too sharp% (basically around the cyan and yellow), compared to everywhere else?".% The answer is yes, it can be done. In practice this amounted to calculate% the "inverted" function in the fourth display. Assuming a distance of 1% between each of the 256 samples on the x axis in the original Jet colormap,% the function was used to resample it at non-integer distances (up% to 1.5 where the yellow is, unmodified at 1 where the cyan is, less% than 1 everywhere else) resulting in a greater number of samples in% the yellow area in the display compared to all the blue areas, with% the total number of samples staying at 256. The next step was to force% all these new samples back to a distance of 1, achieving a% continuously dynamic stretch. The resulting colormap is shown in% the fifth display and accompanied by its Luminance versus wavelenght% in the last display. This profile is noticeably more perceptually% balnced with gentler transitions and a compressive character.% To me this is a very good result, even though it's not perfect.% In an ideal world I would have paired one of the several human wavelenght% discrimination curves found in Wyszecki and Stiles (2000)% with in conjunction with the corresponding spectrum color functions% (many are referenced in the FEX submission "Spectral and XYZ Color% Functions"), but the problem I had was to identify a matching pair;% a problem that in the end proved insurmountable.%% 'J'% This is the original default Jet which I clipped to lign up with Gregory's curve.%% n - scalar specifying number of points in the colorbar. Maximum n=256% If n is not specified, the size of the colormap is determined by the% current figure. If no figure exists, MATLAB creates one.%%% arguments: (output)% map - the output colormap i%%% Example: compare cape topography using the improved Jet vs. default Jet(clipped)% % load cape;% % imagesc(X); colormap(mkpj(128,'JetI')); colorbar;% % figure;% % imagesc(X); colormap(mkpj(128,'J')); colorbar; See also: JET, HSV, GRAY, HOT, COOL, BONE, COPPER, PINK, FLAG, PRISM, COLORMAP, RGBPLOT

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Areas,  Distance,  Distances,  Greater,  Noninteger,  Number,  Original,  Resulting,  Samples,  Unmodified
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