IEEE Consumer Electronics Magazine - October 2015 - 76

Normalized Sensitivities of Cones

1
Long
Medium
Short

0.8
0.6
0.4
0.2

0
350 400 450 500 550 600 650 700 750 800 850
Wavelength λ (nm)

FIGURE 5. The normalized response of cones to different light
wavelengths.

to the reference color using color-matching functions. The
results of such an experiment using the red (645.2 nm),
green (525.3 nm), and blue (444.4 nm) primaries (RGB)
[10] are plotted in Figure 10. Note that to achieve certain
colors, it is necessary to supply a negative amount of one of
the primaries. Since providing a negative amount is highly
impractical, the Commission Internationale de l'Eclairage
(CIE) defined the CIE 1931 XYZ color space [11]. For a given
color composed of different wavelengths m, the XYZ tristimulus value corresponds to the sum of the xr , yr , and zr spectral distribution over the full visible gamut (see Figure 11). Note that yr
directly matches the photopic luminous efficiency curve (say, the
HVS sensibility to white light in the photopic regime). This is
obviously an intentional choice since it allows the information
to be divided in a luminance channel (Y) and two chrominance ones (X and Z). This representation that combines
several primaries is referred to as the additive color system. For a more comprehensive review of color-matching
functions, we refer to [1].
Regardless of which representation is used (i.e., XYZ or
RGB), storing floating point values as uncompressed data
results in using 32 b per color channel and 96 b per pixel (bpp).
This is four times the amount of space needed compared to standard LDR images. To address this issue, several file formats have
been designed to encode floating point values with minimal quantization loss. To this end, Greg Ward [12] proposed the XYZE/
RGBE format, where the exponent is shared among the three

color channels. This representation is valid only because color
channels are usually highly correlated. In this representation, each
pixel is stored in 32 b, with 8 b representing each color mantissa
and another 8 b for the common exponent. This format covers 76
orders of magnitude while using 32 bpp (see Table 2). The RGBE
or XYZE format covers a huge range of luminance, more than
what the human eye can perceive.
By redistributing the quantization steps in a more human
restricted dynamic range, it is possible to achieve a finer quantization over a more restrictive range. That solution is provided
by the IEEE 754 16-b float standard [13] (half-float), which is
part of the specification of the OpenEXR file format [14]. This
representation covers around 10.7 orders of magnitude while
using 48 bpp (see Table 3). The half-float pixel representation
is used in the new Academy Color Encoding System standard,
which is currently undergoing industrywide production trials
by major Hollywood studios and standardization by the Society of Motion Picture and Television Engineers (SMPTE).
OpenEXR images can have an arbitrary number of channels,
each with a different data type, adequately covering the storing
needs of future imaging technologies such as plenoptic [15] or
spectral images [16].

STANDARD COLOR PIXEL REPRESENTATION

Capturing color information in floating point representation
allows for the accurate depiction of the full range of luminance and color values present in real life. However, these
representations are mostly used for processing content in
such a way that quantization errors do not propagate during
the postprocessing stage. Once content has been mastered,
it needs to be distributed to end users in a cost-efficient
way. Cost in this context means sending the smallest
amount of information while achieving the lowest perceivable distortion. To this end, content in floating point is
encoded to a standard color pixel representation with a
limited bit depth, optimizing the representation of light
intensity and color information on a subspace of what the
HVS can perceive (see Figure 12).
Optimizing the light intensity information corresponds to
perceptually encoding luminance in a way that information
that would be invisible after decoding (visual noise) is
removed. In the case of LDR, perceptual encoding is performed by an inverse electro optic transfer function called
gamma encoding (ITU Recommendation BT.1361 [17]), whose design was
based on psychophysical studies for
luminance levels ranging from 0.1 to
Rods Active
100 cd/m 2 (capacity of CRT display
Cones Active
technology). Although the existing monScotopic Vision Regime
Photopic Vision Regime
itors achieve lower black and higher
Mesopic Vision Regime
white levels than this range, for a while,
0.01
0
10
106
10-6
the BT.1361 recommendation was the
2
only available standard used for encodLuminance (cd/m )
ing luminance. Recently, to address this
FIGURE 6. The approximate range of luminance values where cones and rods are recep- issue, another perceptual encoding,
known as perceptual quantizer (PQ)
tive as well as the different vision regime.

76 IEEE Consumer Electronics Magazine

october 2015

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