{"id":1311,"date":"2015-04-03T16:40:04","date_gmt":"2015-04-03T20:40:04","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/?p=1311"},"modified":"2019-11-01T11:39:56","modified_gmt":"2019-11-01T15:39:56","slug":"displaying-a-color-gamut-surface","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2015\/04\/03\/displaying-a-color-gamut-surface\/","title":{"rendered":"Displaying a color gamut surface"},"content":{"rendered":"

Today I'll show you one way to visualize the sRGB color gamut in L*a*b* space with assistance with a couple of new functions introduced last fall in the R2014b release. (I originally planned to post this a few months ago, but I got sidetracked writing about colormaps<\/a>.)<\/p>

The first new function is called boundary<\/tt><\/a>, and it is in MATLAB. Given a set of 2-D or 3-D points, boundary<\/tt> computes, well, the boundary.<\/p>

Here's an example to illustrate.<\/p>

x = gallery('uniformdata'<\/span>,30,1,1);\r\ny = gallery('uniformdata'<\/span>,30,1,10);\r\nplot(x,y,'.'<\/span>)\r\naxis([-0.2 1.2 -0.2 1.2])\r\naxis equal<\/span>\r\n<\/pre>\"\" 
Now compute and plot the boundary around the points.<\/p>
k = boundary(x,y);\r\nhold on<\/span>\r\nplot(x(k),y(k))\r\nhold off<\/span>\r\n<\/pre>\"\" 
\"But, Steve,\" some of you are saying, \"that's not the only possible boundary around these points, right?\"<\/p>
Right. The function boundary<\/tt> has an optional shrink factor that you can specify. A shrink factor of 0 corresponds to the convex hull. A shrink factor of 1 gives a compact boundary that envelops all the points.<\/p>
k0 = boundary(x,y,0);\r\nk1 = boundary(x,y,1);\r\nhold on<\/span>\r\nplot(x(k0),y(k0))\r\nplot(x(k1),y(k1))\r\nhold off<\/span>\r\nlegend('Original points'<\/span>,'Shrink factor: 0.5 (default)'<\/span>,...<\/span>\r\n    'Shrink factor: 0'<\/span>,'Shrink factor: 1'<\/span>)\r\n<\/pre>\"\" 
Here's a 3-D example using boundary<\/tt>. First, the points:<\/p>
P = gallery('uniformdata'<\/span>,30,3,5);\r\nplot3(P(:,1),P(:,2),P(:,3),'.'<\/span>,'MarkerSize'<\/span>,10)\r\ngrid on<\/span>\r\n<\/pre>\"\" 
k = boundary(P);\r\nhold on<\/span>\r\ntrisurf(k,P(:,1),P(:,2),P(:,3),'Facecolor'<\/span>,'red'<\/span>,'FaceAlpha'<\/span>,0.1)\r\nhold off<\/span>\r\n<\/pre>\"\" 
Just for grins, let's reverse the a* and b* color coordinates for an image.<\/p>
rgb = imread('peppers.png'<\/span>);\r\nimshow(rgb)\r\n<\/pre>\"\" 
lab = rgb2lab(rgb);\r\nlabp = lab(:,:,[1 3 2]);\r\nrgbp = lab2rgb(labp);\r\nimshow(rgbp)\r\n<\/pre>\"\" 
Now let's get to work on visualizing the sRGB gamut surface. The basic strategy is to make a grid of points in RGB space, transform them to L*a*b* space, and find the boundary. (We'll use the default shrink factor.)<\/p>
[r,g,b] = meshgrid(linspace(0,1,50));\r\nrgb = [r(:), g(:), b(:)];\r\nlab = rgb2lab(rgb);\r\na = lab(:,2);\r\nb = lab(:,3);\r\nL = lab(:,1);\r\nk = boundary(a,b,L);\r\ntrisurf(k,a,b,L,'FaceColor'<\/span>,'interp'<\/span>,...<\/span>\r\n    'FaceVertexCData'<\/span>,rgb,'EdgeColor'<\/span>,'none'<\/span>)\r\nxlabel('a*'<\/span>)\r\nylabel('b*'<\/span>)\r\nzlabel('L*'<\/span>)\r\naxis([-110 110 -110 110 0 100])\r\nview(-10,35)\r\naxis equal<\/span>\r\ntitle('sRGB gamut surface in L*a*b* space'<\/span>)\r\n<\/pre>\"\" 
Here are another couple of view angles.<\/p>
view(75,20)\r\n<\/pre>\"\" 
view(185,15)\r\n<\/pre>\"\" 
That's it for this week. Have fun with color-space surfaces!<\/p>
The second new function I wanted to mention is rgb2lab<\/tt><\/a>. This function is in the Image Processing Toolbox. The toolbox could convert from sRGB to L*a*b* before, but this function makes it a bit easier. (And, if you're interested, it supports not only sRGB but also Adobe RGB 1998).<\/p>
Now the boundary, plotted using trisurf<\/tt><\/a>:<\/p>