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2.3 The digital camera 77

Y’ Y
visible
Y’ = Y 1/Ȗ noise

Y = Y’ Ȗ

Y quantization Y’
noise

Figure 2.31 Gamma compression: (a) The relationship between the input signal luminance Y and the transmitted
ˆ
γ
signal Y is given by Y = Y 1/γ . (b) At the receiver, the signal Y is exponentiated by the factor γ, Y = Y .

Noise introduced during transmission is squashed in the dark regions, which corresponds to the more noise-
sensitive region of the visual system.
complicated transforms, which are sometimes the result of mapping to XYZ space and back,
actually perform a color twist, i.e., they use a general 3 × 3 color transform matrix. 21 Exer-
cise 2.9 has you explore some of these issues.

Gamma
In the early days of black and white television, the phosphors in the CRT used to display
the TV signal responded non-linearly to their input voltage. The relationship between the
voltage and the resulting brightness was characterized by a number called gamma (γ), since
the formula was roughly
γ
B = V , (2.110)
with a γ of about 2.2. To compensate for this effect, the electronics in the TV camera would
pre-map the sensed luminance Y through an inverse gamma,

1

Y = Y , (2.111)
γ
with a typical value of 1 =0.45.
γ
The mapping of the signal through this non-linearity before transmission had a beneficial
side effect: noise added during transmission (remember, these were analog days!) would be
reduced (after applying the gamma at the receiver) in the darker regions of the signal where
it was more visible (Figure 2.31). 22 (Remember that our visual system is roughly sensitive to
relative differences in luminance.)
When color television was invented, it was decided to separately pass the red, green, and
blue signals through the same gamma non-linearity before combining them for encoding.
Today, even though we no longer have analog noise in our transmission systems, signals are
still quantized during compression (see Section 2.3.3), so applying inverse gamma to sensed
values is still useful.
21
Those of you old enough to remember the early days of color television will naturally think of the hue adjustment
knob on the television set, which could produce truly bizarre results.
22 A related technique called companding was the basis of the Dolby noise reduction systems used with audio
tapes.