Recently, I read the idea of Ichiro Kasajima and Rym Fekih (see in attachment). Is there a possible problem that chroma value is distorted from linearity when a* and b* values are calculated from XYZ color values?
Dear Jun Tang,
The first thing to understand is that CIE XYZ values define colour identity according to the CIE Standard Observer, as a linear projection of stimulus power values (see CIE publication 15/2004). CIE L*a*b*space on the other hand, is a distinct model of visual difference that is based entirely on a separate large set of experimental colour difference judgements.
Chroma value is a numeric displacement in L*a*b*space whose definition was derived by the CIE as a supplementary addition to the CIE Standard Observer model (again see CIE publication 15/2004). A proportionate 3X3matrix is first specified to quantify linear cross-dependence between the two co-ordinate sets; and the scalar relationship that relates the basis of the ‘a and b’ axes of L*a*b* space to X,Y and Z values is then quantified by clearly non-linear Cube-root functions.
Dear Jun Tang,
The first thing to understand is that CIE XYZ values define colour identity according to the CIE Standard Observer, as a linear projection of stimulus power values (see CIE publication 15/2004). CIE L*a*b*space on the other hand, is a distinct model of visual difference that is based entirely on a separate large set of experimental colour difference judgements.
Chroma value is a numeric displacement in L*a*b*space whose definition was derived by the CIE as a supplementary addition to the CIE Standard Observer model (again see CIE publication 15/2004). A proportionate 3X3matrix is first specified to quantify linear cross-dependence between the two co-ordinate sets; and the scalar relationship that relates the basis of the ‘a and b’ axes of L*a*b* space to X,Y and Z values is then quantified by clearly non-linear Cube-root functions.
Hi Jun,
Yes, CIELAB is nonlinear. The L* is perceptual lightness, approximating the human eye gamma of photopic vision.
CIEXYZ is a linear representation of light. Luminance (the Y in XYZ) varies linearly just as light does in the real world.
XYZ and LAB serve two very different purposes. If you are working with light values, such as with adding together multiple colors of light, then linear spaces such as XYZ or xyY are your ideal choice as the math to do so is simple addition. of values.
But if you are working with perceptual quantities, such as how would this apple look if it was perceived as half as bright, then L*a*b* will give you an easier answer, as L*a*b* allows you to use simple linear math to model non-linear human perception.
The usual example is middle grey. in CIELAB, the middle grey that most people identify as "half way" between black (0.0) and white (100.0) is a value of 50.0 in L*a*b*.
However in XYZ, with black (0.0) and white (100.0) , that same middle grey is 18.4
In XYZ, if you double the quantity of light, say making 18.4 * 2 = 36.8, the result in L*a*b* would be a mild increase from 50.0 to 67.1
Also, L*a*b* allows you to determine perceived color difference by the simple Euclidian distance between colors.
-A
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