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| Computational Photography |
Summary of Relative Noise in White Balanced and Color Corrected Signals.
QE Set SB TrSB L B SC Tr SC L C
397 000 000 1038 250 082
RGB 000 262 000 9.88 1.24 250 625 390 24.41 1.60
000 000 329 082 390 778
397 000 000 1822 1470 724
RPB 000 100 000 8.26 0.84 1470 2168 1394 53.22 2.51
000 000 329 724 1394 1332
202 000 000 2505 643 471
CMY 000 189 000 5.67 1.03 643 1045 828 51.34 1.90
000 000 175 471 828 1584
In the case where 2 P G G , where i 123, this simplifies to
C E i
g
G1 0 0
K 0 G2 0 G P (1.8)
B E C
0 0 G3
To focus on the relative sensitivity, the matrix S is defined by leaving out the factor of P :
B C
G1 0 0
SB 0 G2 0 GE (1.9)
0 0 G3
The values on the diagonal of SB show the relative noise levels in white balanced images
before color correction, accounting for the differences in photometric sensitivity. To finish
the comparison, the matrix S is defined as MS MT . The values on the diagonal of S in-
C B C
dicate the relative noise levels in color corrected images. The values L B and L C indicate
the estimated relative standard deviation for a luminance channel based on Equation 1.4.
As shown in Table 1.2, the TrSB and L B are smaller for CMY and for RPB than for
RGB, reflecting the sensitivity advantage of the broader spectral sensitivities. However,
TrSC and L C are greater for RPB and CMY than for RGB, reflecting the noise ampli-
fication from the color correction matrix. In summary, while optimal selection of spectral
sensitivity is important for limiting noise, a well-selected relatively narrow set of RGB
spectral sensitivies is close to optimum, as found in References [65] and [66]. Given these
results, it is tempting to consider narrower spectral bands for each color channel, reduc-
ing the need for color correction. This would help to a limited extent, but eventually the
signal loss from narrower bands would take over. Further, narrower spectral sensitivities
would produce substantially larger color errors, leading to lower overall image quality. The
fundamental problem is that providing acceptable color reproduction constrains the three
channel system, precluding substantial improvement in sensitivity.
Reference [65] considers the possibility of reducing the color saturation of the image,
lowering the noise level at the expense of larger color errors. However, the concept of
lowering the color saturation can be applied with RGB quantum efficiencies as well. Ref-
erence [66] shows that by allowing larger color errors at higher exposure index values, the
optimum set of quantum efficiencies changes with exposure index. In particular, at a high
exposure index, the optimum red quantum efficiency peaks at a longer wavelength and has
less overlap with the green channel. This is another way to accept larger color errors to
reduce the noise in the color corrected image.
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