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78 2 Image formation

Unfortunately, for both computer vision and computer graphics, the presence of gamma
in images is often problematic. For example, the proper simulation of radiometric phenomena
such as shading (see Section 2.2 and Equation (2.87)) occurs in a linear radiance space. Once
all of the computations have been performed, the appropriate gamma should be applied before
display. Unfortunately, many computer graphics systems (such as shading models) operate
directly on RGB values and display these values directly. (Fortunately, newer color imaging
standards such as the 16-bit scRGB use a linear space, which makes this less of a problem
(Glassner 1995).)
In computer vision, the situation can be even more daunting. The accurate determination
of surface normals, using a technique such as photometric stereo (Section 12.1.1)orevena
simpler operation such as accurate image deblurring, require that the measurements be in a
linear space of intensities. Therefore, it is imperative when performing detailed quantitative
computations such as these to first undo the gamma and the per-image color re-balancing
in the sensed color values. Chakrabarti, Scharstein, and Zickler (2009) develop a sophisti-
cated 24-parameter model that is a good match to the processing performed by today’s digital
cameras; they also provide a database of color images you can use for your own testing. 23
For other vision applications, however, such as feature detection or the matching of sig-
nals in stereo and motion estimation, this linearization step is often not necessary. In fact,
determining whether it is necessary to undo gamma can take some careful thinking, e.g., in
the case of compensating for exposure variations in image stitching (see Exercise 2.7).
If all of these processing steps sound confusing to model, they are. Exercise 2.10 has you
try to tease apart some of these phenomena using empirical investigation, i.e., taking pictures
of color charts and comparing the RAW and JPEG compressed color values.

Other color spaces
While RGB and XYZ are the primary color spaces used to describe the spectral content (and
hence tri-stimulus response) of color signals, a variety of other representations have been
developed both in video and still image coding and in computer graphics.
The earliest color representation developed for video transmission was the YIQ standard
developed for NTSC video in North America and the closely related YUV standard developed
for PAL in Europe. In both of these cases, it was desired to have a luma channel Y (so called
since it only roughly mimics true luminance) that would be comparable to the regular black-
and-white TV signal, along with two lower frequency chroma channels.
In both systems, the Y signal (or more appropriately, the Y’ luma signal since it is gamma
compressed) is obtained from
Y =0.299R +0.587G +0.114B , (2.112)

601
where R’G’B’ is the triplet of gamma-compressed color components. When using the newer
color definitions for HDTV in BT.709, the formula is

Y =0.2125R +0.7154G +0.0721B . (2.113)
709

The UV components are derived from scaled versions of (B −Y ) and (R −Y ), namely,

U =0.492111(B − Y ) and V =0.877283(R − Y ), (2.114)

23 http://vision.middlebury.edu/color/.