I have been trying to understand the normalisation of the a and b components of the CIE Lab implementation within PixInsight. For anyone wanting to look at colour spaces in general, I can highly recommend Bruce Lindbloom's site.
I have used sRGB with a D50 reference white. I have also used the true sRGB gamma function, not the 2.2 approximation.
As far as I can tell PI normalises both the a and the b channels using the following equation (subject to possible rounding errors): nv = 0.004639 * v + 0.54287, where v is the a or b component as calculated using the principles set out on Bruce Lindbloom's site, and nv is the normalised value as used in PI (eg in the CIEa and CIEb PixelMath functions).
As far as I can see the actual range of possible values (sRGB/D50) for "a" range from -79.29 to 93.55, and for "b" they range from -112.03 to 93.39.
The normalisation formula implies a normalised range from 0 to 1 would correspond to a range from -117.03 to 98.55. Comparing this to the ranges in the previous paragraph suggests a "buffer" of 5 at each end of the range has been added. My question is whether the PI normalisation is a standard approach, in which case is anyone able to point me to a reference, or is it a PI approach, in which case is this documented somewhere so I can understand better?
I have used sRGB with a D50 reference white. I have also used the true sRGB gamma function, not the 2.2 approximation.
As far as I can tell PI normalises both the a and the b channels using the following equation (subject to possible rounding errors): nv = 0.004639 * v + 0.54287, where v is the a or b component as calculated using the principles set out on Bruce Lindbloom's site, and nv is the normalised value as used in PI (eg in the CIEa and CIEb PixelMath functions).
As far as I can see the actual range of possible values (sRGB/D50) for "a" range from -79.29 to 93.55, and for "b" they range from -112.03 to 93.39.
The normalisation formula implies a normalised range from 0 to 1 would correspond to a range from -117.03 to 98.55. Comparing this to the ranges in the previous paragraph suggests a "buffer" of 5 at each end of the range has been added. My question is whether the PI normalisation is a standard approach, in which case is anyone able to point me to a reference, or is it a PI approach, in which case is this documented somewhere so I can understand better?