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Before we can apply the category model described in the previous section to
Berlin and Kay's color naming data, we need to quantify the stimulus set
they used for their experiments. As described in Section , they
used a set of 329 Munsell color chips consisting of 40 equally spaced hues
at 8 equally spaced brightness (Value) levels each, all at maximum
saturation (Chroma), and a gray scale consisting of nine equally spaced
brightness (Value) steps. They asked subjects to point out both the extent
and the foci of the basic color categories of their native language on the
array of color chips, viewed under a light source approximating the CIE
standard source A (Figure
).
In the following sections I will always use the CIE XYZ space, the CIE
L*a*b* space, and the NPP color space for comparative purposes. The XYZ
space is in a sense ``the mother of all RGB spaces'', since the various RGB
spaces are simple linear transforms of it. It is generally accepted as an
approximation to the spectral sensitivities of the human cone
photoreceptors, and thus a ``primary'' representation, as close to the
sensor as we can hope to get. The L*a*b* space is defined by the CIE to be
perceptually equidistant across (most of) the color gamut, and is often
used as a reference in color work. It is a non-linear transform of the XYZ
space. It also performs very well for our purpose, as shown below. The NPP
space is of course the one that we derived from neurophysiological
measurements in Chapter , and is also a non-linear
transform of the XYZ space. We use this space to attempt to link the
category model to the underlying neurophysiology.
The conversion from Munsell coordinates, in which the stimulus set is
defined, to CIE XYZ coordinates, which is the basis for the color spaces we
are interested in, is non-trivial, and there is no simple mathematical
conversion possible. Fortunately, the Munsell set of standard color
reference chips, from which the Berlin and Kay set is chosen, has been
measured spectrophotometrically and converted to CIE xyY coordinates in the
past [Newhall et al. 1943]. After
conversion from CIE xyY, we obtain unnormalized CIE XYZ coordinates for
each of the stimuli contained in the Berlin and Kay set. To normalize the
coordinates to the unit cube, with the gray axis going from
to
, I used Von Kries
adaptation:
where is the vector representing the unnormalized stimulus
values, and
is the vector representing the unnormalized
white reference stimulus values. Although Berlin and Kay's gray axis only
runs from Munsell Value 1 to 9, I used the coordinates of Munsell Value 10
as white reference, since that is the maximum Munsell Value defined,
i.e. the ``whitest white'' available. Although Von Kries adaptation cannot
theoretically be shown to exactly undo all the effects of a non-flat
spectrum light source, it works well enough in practice to be allowable,
especially with a light source that is as close to a flat spectrum as the
CIE C source used in these measurements [Wyszecki \& Stiles 1982]. The
obtained stimulus set is shown in Figure
,
represented in CIE XYZ, CIE L*a*b*, and NPP coordinates.
Some interesting things to note about this figure are:
In particular, note the irregularities in the lower blue region. I have added Munsell Values 0 and 10 to the gray axis, for a total of 11 stimuli.
Combining the information from Figure with the derived
color space coordinates of the stimuli, we can now describe the boundary of
a Basic Color category as a polygon passing through the coordinates of each
of the boundary stimuli, and the focus of a Basic Color category as the
center of mass of the points indicated as focal points.
Figure
shows the boundaries and foci obtained in
this way.
Note that the shape and size of the polygons is different in different color spaces, and that in general a straight line on the Berlin and Kay chart does not necessarily translate into a straight line in the color space, since the stimuli are lying on or near a curved surface.