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matlabcolor-space

What range are L*a*b* values restricted to for a given reference white point?

I've got some images I want to do things in CIE L*a*b* with. What range can I expect the values to be in, given the initial sRGB values are in the range [0,1]?

I get my images like the following:

im_rgb = im2double(imread('/my/file/path/image.jpg'));

% ...do some muddling about with im_rgb, keeping range [0,1]

xform = makecform('srgb2lab');
im_lab = applycform(im_rgb, xform);

For starters, I'm reasonably sure that L* will be 0-100. However, I found this thread, which notes that "... a* and b* are not restricted to lie in the range [-100,100]."

Edit:

Matlab's default whitepoint is evaulated by whitepoint('ICC'), which returns 0.9642, 1, 0.8249. I'm using this value, as I'm not sure what else to use.

As I'm always using the same (default) transformation and the input colors are always real colors (as [0,1] for each of R, G, and B), Their equivalent L*a*b* representations are also real colors. Will these L*a*b* values also be bounded? If so, what are they bounded by, or how can I determine the boundaries?

Solution

  • You are basically asking how to find the boundary of the sRGB space in LAB, right?

    So starting with L*, yes it will be bound between 0 and 100. This is by definition. If you look at the formula for conversion from XYZ to LAB you'll see that L = 116*(Y/Ywhitepoint)-16. When you are at sRGB white that Y ratio turns to 1 which makes the equation 116-16 = 100. A similar thing happens as back where the formula basically collapses to 4/29 * 116 -16 = 0.

    Things are a little more complicated with the a and b. Since the XYZ -> LAB conversion is not linear the conversion doesn't make a easily described shape. But the outer surface of the sRGB cube will be become the outer boundary of the LAB space. What this means is you can take the extremes such as blue primary sRGB[0, 0, 1], convert to LAB and find what should be the furthest extent on the b axis: approximately -108. When you do that for all the corners of the sRGB cube you'll have a good idea about the extent of the sRGB space in LAB.

    Most applications (notably Photoshop), clamp the encoding of the a and b channels between -128 and 127. This works fine in practice, but some large RGB spaces like ProPhoto RGB actually extent beyond this. Generally this doesn't have much practical consequence because most of these colors are imaginary, i.e. they sit outside the spectral locus.