The eye's non-linear response to light vs XYZ_Y vs L*
The eye's non-linear response to light vs XYZ_Y vs L*
- Subject: The eye's non-linear response to light vs XYZ_Y vs L*
- From: Steve Kale <email@hidden>
- Date: Thu, 20 Oct 2005 15:25:17 +0100
- Thread-topic: The eye's non-linear response to light vs XYZ_Y vs L*
Title: The eye's non-linear response to light vs XYZ_Y vs L*
Hi
I am having trouble connecting the dots between a few statements I’ve read in Bruce Fraser’s “Real World Color Management” and would really appreciate some help. I understand the fact that our eye’s have a non-linear (logarithmic) reaction (perceived “brightness”) to light (covered by Bruce on pg 31, second edition). Increased light intensity produces progressively smaller increases in perceived brightness. When introducing on pg 41 the CIE colormetric system, under CIE XYZ Primary System Bruce jumps to the notion of luminance (I believe previously undefined) rather than brightness and says “the primary Y doubles as the average luminance function of the cones – so a color’s Y value is also its luminance.” Furthermore on pg 42 when mentioning the Uniform Color Spaces (LAB, LUV) he says “both compute the lightness value L* in exactly the same way – it’s approximately the cube root of the luminance value Y (which is a rough approximation of our logarithmic response to luminance).”
(I think I understand the change in reference from “brightness” (the perceived response to light intensity) on pg 31 to “lightness” (brightness relative to some absolute white reference) on pg 42 – the former is a generic discussion whereas the latter is a discussion of a colour space which assumes a standard or reference illuminant/white. I am not sure I understand the importance of the distinct use of the term “luminance” (luminous intensity per unit area of the light emitting surface) on pg 41 when discussing XYZ_Y.)
I am trying to relate these three things – perceived brightness, XYZ_Y and L* – to each other. From the statement on pg 41 I would have thought that XYZ_Y is intended to characterise or model the eye’s reaction to increasing light intensity (of a standard illuminant D50). But if I plot XYZ_Y versus normalised pixel values don’t I get a concave curve rather than a convex curve? Also my recollection of school maths is very rusty. Isn’t the cube root of x equal to x^(1/3) ? I don’t see how L* 50 is approximately the cube root of XYZ_Y 18.4. I am sure the answer to this last part is easy and obvious and the question simply reflects my rusty maths! So if the answer is mathematical take it slow please!
At any rate, any help in connecting the dots between these three concepts would be appreciated.
Regards
Steve
PS: The ultimate reason for my query is a better understanding of black point compensation and white point scaling for media colorimetry where the scaling of each of these is done with XYZ_Y, our perception of the affect of this scaling, and the reason why we linearize RIPs with respect L* (and not XYZ_Y).
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