1.3.5 Colour Profiles

Now that we have seen a representation of the entire colour gamut
perceivable by the eye, it is straightforward to understand the
statement that it is not possible to reproduce all colours perceivable
by the eye using three primaries of red, green and blue light; the
visible gamut does not form a triangle, and so no additive mixture
of three real primary colours can possibly span the gamut.
Nevertheless, digital displays do use three real primary colours. In
order to ensure that these displays reproduce the intended colours
from image files, a standard colour profile, sRGB, was developed by
HewlettPackard
and Microsoft.
Converting from CIE XYZ tristimulus values to sRGB involves two
transformations. The first is an axis transformation, to convert from
the CIE XYZ primaries into specific red, green and blue primaries;
we can express this transformation as a matrix multiplication:


Rl
Gl
Bl


= 

3.2410 −1.5374 −0.4986
−0.9692 1.8760 0.0416
0.0556 −0.2040 1.0570 



X
Y
Z 

(1.13)
where the tristimulus values are scaled so that Y = 1.0 corresponds
to the maximum brightness of the display hardware.
The second transformation adjusts (with gamma correction) for the
nonlinear nature of brightness on computer monitors and similar
digital displays; in Cathode Ray Tube monitors, for example, the
physical processes involved in the emission of electrons and the
excitation of the phosphors to produce the image on the screen give
a perceived brightness that is not linearly related to the input signal,
but related by an approximate powerlaw
instead. Liquid Crystal
Displays have a very complicated relationship between input voltage
and perceived brightness; however, they incorporate hardware to
22
Colour Spaces and Profiles
mimic the powerlaw
behaviour of a CRT. If C refers to each of R, G
and B in turn,
CsRGB = � 12.92Cl Cl < 0.00304
1.055C1/2.4
l − 0.055 otherwise
(1.14)
The CsRGB values are clamped to be between 0 and 1, and then
scaled to whatever colour resolution is required; for 8bit
colour
channels, such as are found in Processing, Cascading Style Sheet
colour specifications, and PNG images (among other uses), the
CsRGB values are multiplied by 255.
Apart from the clamping of values to between 0 and 1, the
transformation from CIE XYZ to sRGB is reversible; to convert from
sRGB coordinates to XYZ tristimulus values, first invert the transfer
function to yield linear values Cl with
Cl = � CsRGB
12.92 CsRGB < 0.04045
�CsRGB+0.055
1.055 �2.4
otherwise
(1.15)
and then invert the matrix multiplication:


X
Y
Z 

= 

0.4124 0.3576 0.1805
0.2126 0.7152 0.0722
0.0193 0.1192 0.9505 



Rl
Gl
Bl


(1.16)
y
x 0 0.5
0
0.5
Figure 1.9: A representation of sRGB (solid triangle) and Adobe RGB
(dashed triangle) colour space gamuts, relative to the CIE standard
observer chromaticity gamut of figure 1.7.
As well as sRGB, there are other standardized colour spaces,
intended for example for professional printing workflows. One such
is Adobe RGB, which has a larger gamut of colours than sRGB
(compare the dashed triangle in figure 1.9 to the solid triangle);
however, all image manipulation software and printing hardware
must be aware of the choice of colour space, otherwise colour
manipulation operations will not do what is intended.
23
CC227 Creative Computing II Perception and Information Retrieval
1.4 Motion
The perception of motion by the visual system is exploited in the
construction of video and animation artifacts, with the illusion of
motion generated from the presentation of a succession of static
images. This section describes some of the perceptual effects behind
the illusion of motion. Regarding the algorithmic detection of
motion, note that not everything is fully understood, to the extent
that it is difficult to characterise computationally the particular
motion that will be perceived from a digital video stream. We will
return to this when we discuss Multimedia Information Retrieval.
1.4.1 Philosophy of Motion
Even the concept of motion has certain philosophical difficulties, as
it is bound up in the continuity of self over time: to perceive motion,
an observer must understand that an object observed twice, once at
a later time than the other, is the same underlying object. Zeno’s
paradoxes12 illustrate those difficulties, which even if they have 12Zeno of Elea (490 BC? – 430 BC?),
Greek philosopher. mathematical resolutions might remain troubling from a
philosophical perspective. Zeno is said to have devised his paradoxes
in support of the philosophy of his teacher Parmenides, saying
amongst other things that change and motion are only illusions.
Two related paradoxes devised by Zeno – the Dichotomy paradox,
and the paradox of Achilles and the Tortoise – essentially illustrate
that an infinite process needs to be achieved before any motion can
be deemed to have taken place.
The dichotomy paradox begins by considering motion from a point
A to a different point B. In order to perform that motion, a point C
halfway between A and B needs to be visited. But to move from A
to C, a point D halfway between them must be reached; iterating
this argument leads to the conclusion that motion between any two
points requires an infinite number of steps.
The paradox of Achilles and the Tortoise is somewhat similar; the
scenario involves fleetfooted
Achilles racing a tortoise: to make the
race fair, the tortoise is given a head start. Now, by the time that
Achilles reaches the tortoise’s initial position, the tortoise will have
moved along a certain distance. For Achilles to overtake the tortoise,
he must additionally cover that distance, by which time the tortoise
will have moved forward again – and each time Achilles covers the
remaining distance, the tortoise inches forward, with the conclusion
that Achilles needs to reach the tortoise’s current position an infinite
number of times before he can overtake13. 13Achilles and the Tortoise are used
as characters in the dialogues in
Godel, Escher, Bach: an Eternal
Golden Braid by Douglas
Hofstadter, a book exploring the
relationships between creativity,
mind and computation.
A third paradox due to Zeno explores a slightly different aspect of
the difficulty of motion: the Arrow paradox considers the
relationship of motion and time. The scenario involves an arrow in
flight towards a target; consider isolating an instant of time in that
flight. In that snapshot, the arrow is not in motion – but then how
can a succession of instants lead to the arrow progressing in its
path? The resolution of this apparent paradox lies in a careful
mathematical treatment of infinitesmal quantities; however, the
24
Motion
paradox is also related to an illusion allowing the visual perception
of motion to arise from a succession of still images, discussed in the
next section.