Tuesday, July 31, 2012

0 Three-Channel Arrays



Inside Canon
   This section discusses spectral sensitivity and color correction for three-channel systems
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.
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. 
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.

Monday, July 30, 2012

0 Color and tone correction block details

Color and tone correction block details


   Many different approaches have been developed to acquire trichromatic color images.
Some cameras scan a scene with a trilinear sensor incorporating color filters to capture
three channels of color information for every pixel in the scene [51], [52].  These cameras
can achieve very high spatial resolution and excellent color quality.  Because the exposure
of each scan line of the scene is sequential, the exposure time for each line must be a small
fraction of the capture time for the whole scene. These cameras often take seconds or even
minutes to acquire a full scene,  so they work poorly for recording scenes that have any
motion or variation in lighting.  Some cameras use a single panchromatic area sensor and
filters in the lens system to sequentially capture three color channels for every pixel in the
scene. These are faster than the linear scanning cameras, since all pixels in a color channel
are  exposed  simultaneously,  although  the  channels  are  exposed sequentially.            

These  are commonly used and particularly effective in astronomy and other scientific applications
where motion is not a factor.         Some cameras use dichroic beam splitters and three area
sensors to simultaneously capture three channels of color for each pixel in the scene [53],
[54].  This is particularly common and successful in high-quality video cameras, where a
high pixel rate makes the processing for demosaicking difficult to implement well.  These
are the fastest cameras, since all color channels are exposed simultaneously. Each of these
approaches can perform well, but they increase the cost and complexity of the camera and
restrict the range of camera operation.


Cost and complexity issues drive consumer digital color cameras in the direction of a
single sensor that captures all color information simultaneously.                Two approaches based
on single array sensors are presently used.           One approach fabricates a sensor with three
layers of photodiodes and uses the wavelength-dependent depth of photon absorption to
provide spectral sensitivity [55], [56]. This system allows sampling three channels of color
information at every pixel,  although the spectral sensitivity poses several challenges for
image processing. The approach more commonly used is the fusion of multiple color chan-
nels from a sensor with a color filter array into a full-color image.  This fusion approach,
specifically with a four-channel color filter array, is the focus of this chapter.

  A camera embodying this approach includes a single lens, a single area array sensor with
a color filter array, and a processing path to convert pixel values read from the sensor to
a suitable image for color reproduction.          The image processing chain used is shown as a
block diagram in Figure 1.4.  The block labeled as color and tone processing is examined
in more detail here, as shown in Figure 1.5.  This figure breaks the overall color and tone
processing down into three distinct steps.  The first, white balance, applies gain factors to
each color channel of camera pixel values to provide an image with equal mean code values
in each color channel for neutral scene content. The second, color correction, converts the
white balanced image to a known set of color primaries,  such as the primaries used for
sRGB. The final step applies a tone correction to convert the image to a rendered image.

 

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