Create a uniform colormap for plots in Matlab

This is just a quick one, and I know that there are plenty of other methods for doing this.  I figured that if I'm going to demonstrate that the symmetric normalized HuSLp and HSYp color models can be used for image editing, I might as well show other uses as well.

The symmetric models HuSLp (CIELUV and CIELAB) and HSYp (YPbPr)

Recall the nonuniformity addressed by the rotationally-symmetric normalization of HuSLp and HSYp.  While HuSL and HSY are attempts to bring the convenience of models like HSL and HSV to other, more uniform color spaces (e.g. CIELAB, CIELUV), their normalization method distorts the relationship between S and C.  A path of constant normalized saturation now has a radius dependent on hue.  To regain the uniformity of the parent space, HuSLp and HSYp are normalized to the maximal rotationally symmetric subset of the projected RGB space.  This means that HuSLp and HSYp retain visual uniformity, but at the expense of maximum chroma range.

Surfaces of maximum S: HSL (top); HuSLab, HSY (middle); HuSLpab, HSYp (bottom)

Comparing HuSL and HSY to HSL, we see the difficulty of naive color selection by simply varying hue alone.  The low resolution of these gradients makes the brightness variation much easier to notice.  The HuSLp and HSYp maps appear as a series of uniform rows.  Color selection in these maps is limited, but greatly simplified.  While care can be taken to make colormaps of higher chroma from discontinuous paths in CIELAB or YPbPr, these generic image conversion methods can be used quite easily with adequate results.

In this example, we create three colormaps corresponding to the hue angles of the primary and secondary colors.  Note the brightness variation in HSL; anyone who has spent any time making plots in Matlab has probably found themselves avoiding certain named line colors due to their poor visibility ('b' on black, 'y' on white).  While notably less saturated, the HSYp and HuSLp colormaps yield lines which are all equally visible.  Here, the HuSLp method uses CIELUV simply because the saturated corners of the RGB space are not 60 degrees apart in CIELAB. Also, take note that I'm inverting colors in the plot() call and in the imwrite() call because I'm operating with an inverted X display.

steps=6;

H=0:360/steps:(360-360/steps);
K=ones(size(H));

hslset=permute(colorspace('<hsl',cat(3,H,K,K*0.5)),[2 3 1]);
hsypset=permute(hsy2rgb(cat(3,H,K,K*0.6),'pastel'),[2 3 1]);
huslpset=permute(husl2rgb(cat(3,H,K*100,K*65),'luvp','aligned'),[2 3 1]);

lw=2;
x=0:0.01:1.4;
os=2;
d=9;
sl=1.2;
subplot_tight(1,1,1);
for n=1:1:steps;
    plot(x,     (atan(x/(n/d))-sl*x),'color',1-hslset(n,:),'linewidth',lw); hold on;
    plot(x,    -(atan(x/(n/d))-sl*x),'color',1-hslset(n,:),'linewidth',lw); hold on;
    plot(x,1*os+(atan(x/(n/d))-sl*x),'color',1-hsypset(n,:),'linewidth',lw); hold on;
    plot(x,1*os-(atan(x/(n/d))-sl*x),'color',1-hsypset(n,:),'linewidth',lw); hold on;
    plot(x,2*os+(atan(x/(n/d))-sl*x),'color',1-huslpset(n,:),'linewidth',lw); hold on;
    plot(x,2*os-(atan(x/(n/d))-sl*x),'color',1-huslpset(n,:),'linewidth',lw); hold on;
end
view(-90, 90);
set(gca,'ydir','reverse');

to=-0.45;
text(1,-to  ,'HSL','fontsize',16,'fontweight','bold');
text(1,-to+1*os,'HSYp','fontsize',16,'fontweight','bold');
text(1,-to+2*os,'HuSLpuv','fontsize',16,'fontweight','bold');

frame=getframe;
imwrite(255-frame.cdata,'blogshit/colormaps1.png','png');

Plots using colormaps generated in HSL, HSYp, HuSLp

Certainly one has to weigh uniformity against the ability to discriminate plot colors.  Strategic selection of colors based on adjacency of plot objects is often unavoidable, and at some point, one has to ask how many things should even be in a plot before a different approach to visualization is more appropriate.  Perhaps these HuSLp/HSYp palettes would be even more appropriate for creating color themes for your favorite terminal emulator.

Maybe I'll do more to extend these tools toward making discontinuous color sets at higher chroma, but I think there are plenty of people working on that already.  Then again, it's not like I'm unaccustomed to reinventing wheels.  It's not like I have anything better to do, either.