DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

To compute L* from optical
density D in the range 0 to 2,
use this relation:
-D/
3
L*
= 116 · 10 - 16
∆L* is pronounced delta
EL-star.
white. The quotient Y/Y n is relative luminance. (If you
normalize luminance to unity, then you need not
compute the quotient.)
A linear segment is defined near black: For Y/Y n values
0.008856 or less, L* is proportional to Y/Y n . The parameters
have been chosen such that the breakpoint occurs
at an L* value of 8. This value corresponds to less than
1% on the relative luminance scale! In a display system
having a contrast ratio of 100:1, the entire reproduced
image is confined to L* values between 8 and 100! The
linear segment is important in color specification;
however, Y/Y n values that small are rarely encountered
in video. (If you don’t use the linear segment, make
sure that you prevent L* from ranging below zero.)
The linear and power function segments are defined to
maintain function and tangent continuity at the breakpoint
between the two segments. The exponent of the
power function segment is 1 ⁄3, but the scale factor of
116 and the offset of -16 modify the pure power function
such that a 0.4-power function best approximates
the overall curve. Roughly speaking, lightness is 100
times the 0.4-power of relative luminance.
The difference between two L* values, denoted ∆L*, is
a measure of perceptual “distance.” A difference of less
than unity between two L* values is generally
imperceptible – that is, ∆L* of unity is taken to lie at
the threshold of discrimination. L* provides one component
of a uniform color space. The term perceptually
linear is not appropriate: Since we cannot directly
measure the quantity in question, we cannot assign to
it any strong properties of mathematical linearity.
In Chapter 8, Constant luminance, I described how
video systems encode a luma signal (Y’) that is an engineering
approximation to lightness. That signal is only
indirectly related to the relative luminance (Y) or the
lightness (L*) of color science.
CHAPTER 20 LUMINANCE AND LIGHTNESS 209