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| Inside Canon |
to illustrate their limitations and show the motivation for a camera with four color channels.
Color correction from capture device spectral sensitivity to output device color will be
illustrated using an additive three-primary system, such as a video display.
The colors that can be reproduced with a three-color additive display are defined by the
tristimulus values of its three primaries [47]. The range of colors, or gamut, of the display
is a triangle in chromaticity space. The spectral locus traces the chromaticity of
monochromatic (narrow band) light of each wavelength in the visible spectrum, with sev-
eral wavelengths marked for illustration. All visible colors are contained in this horseshoe
region. The XYZ set of primaries is a hypothetical set of primaries that bound a triangle
including the entire spectral locus. The sRGB primaries are standard video primaries sim-
ilar to most television and computer displays, specifically ones based on CRT technology.
The Reference Input Medium Metric (RIMM) RGB [57] primaries are used in applications
where a gamut larger that the usual video gamut is desired, since many real world colors
extend beyond the gamut of sRGB. Two of the RIMM primaries are also hypothetical, lying
outside the spectral locus.
The curves shown are the standard
CIE XYZ color matching functions (CMFs) corresponding to the XYZ primaries. Linear combinations of these curves are also color matching functions, orresponding to other sets of primaries. Data captured with any set of color matching functions can be converted to another set of color matching functions using a 3 3 matrix as PC MPO, where PC and PO are 3 1 vectors of converted pixel values and original
color pixel values, respectively. This matrix operation is also referred to as color correction.
Color matching functions and approximations: (a) sRGB, and (b) RIMM.
Each set of primaries has a corresponding set of color matching functions.
Because cameras cannot provide negative spectral sensitivity, cameras use all-positive ap-
proximations to color matching functions (ACMF) instead.
Note the RIMM color matching functions have
smaller negative lobes than the sRGB color matching functions. The size of the negative
excursions in the color matching functions correspond to how far the spectral locus lies
outside the color gamut triangle. Cameras with spectral sensitivities that
are not color matching functions produce color errors because the camera integration of
the spectrum is different from the human integration of the spectrum. In a successful color
camera, the spectral sensitivities must be chosen so these color errors are acceptable for the
intended application.
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| Computational Photography- Three Channel Arrays |
Digital camera images are usually corrected to one of several standardized RGB color
spaces, such as sRGB [58], [59], RIMM RGB [57], [60], and Adobe RGB (1998) [61],
each with somewhat different characteristics. Some of these color spaces and others are
compared in Reference [62].
The deviation of a set of spectral sensitivities from color matching functions was consid-
ered in Reference [63], which proposed a q factor for measuring how well a single spectral
sensitivity curve compared with its nearest projection onto color matching functions. This
concept was extended in Reference [64], to the factor, which considers the projection of
a set of spectral sensitivities (referred to as scanning filters) onto the human visual sensi-
tivities. Because q and are computed on spectral sensitivities, the factors are not well
correlated to color errors calculated in a visually uniform space, such as CIE Lab.
Several three-channel systems are used to illustrate the impact of spectral sensitivity on
image noise. These examples use sample spectral sensitivity curves for a typical RGB
camera from Reference [56] converted to quantum efficiencies and cascaded with a typical
infrared cut filter. The resulting overall quantum efficiency curves are shown, together
with the quantum efficiency of the underlying sensor. One way to improve
the signal-to-noise ratio of this camera would be to increase the quantum efficiency of
the sensor itself. This is difficult and begs the question of selecting the optimal quantum
efficiencies for the three color channels. Given the sensor quantum efficiency as a limit for
peak quantum efficiency for any color, widening the spectral response for one or more color
channels is the available option to significantly improve camera sensitivity. The effects of
widening the spectral sensitivity are illustrated in this chapter by considering a camera
with red, panchromatic, and blue channels and a camera with cyan, magenta, and yellow
channels. The CMY quantum efficiencies were created by summing
pairs of the RGB quantum efficiency curves and thus are not precisely what would normally
be found on a CMY sensor. In particular, the yellow channel has a dip in sensitivity near
a wavelength of 560 nm, which is not typical of yellow filters. The primary effect of this
dip is to reduce color errors rather than change the color correction matrix or sensitivity
significantly.
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| Computational Photography- Three Channel Arrays |
Reference [65] considers the trade-off of noise and color error by examining the sensitiv-
ity and noise in sensors with both RGB and CMYG filters. It is concluded that the CMYG
system has more noise in a color-corrected image than the RGB system. Reference [66]
proposes optimal spectral sensitivity curves for both RGB and CMY systems consider-
ing Poisson noise, minimizing a weighted sum of color errors and noise. Fundamentally,
the overlap between color matching functions drives use of substantial color correction
to provide good color reproduction. All three systems in the current illustration produce
reasonable color errors, so the illustration will compare the noise in the three systems.
This chapter focuses on random noise from two sources. The first is Poisson-distributed
noise associated with the random process of photons being absorbed and converted to
photo-electrons within a pixel, also called shot noise.
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