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Naming Color Samples
The complete process required for naming the color of an object (or a blob)
in one's field of view is schematized in Figure 
.
The sensing device, e.g. a color camera, color scanner, or special-purpose
color sensor, typically outputs RGB (Red, Green, Blue) values for each
pixel in its sensor array, which are transformed into the color space
coordinates of choice (e.g. XYZ, L*a*b*, or NPP). This transform is
usually, but not always, reversible (this is especially easy when dealing
with a simple linear transform such as the RGB to XYZ conversion). A blob
of a uniform color in the field of view thus corresponds to a point in
color space, 
. Once we have determined 
, we
determine its membership (or goodness) value with respect to each of the
defined color categories 
:
where 
is the set of all membership values, 
is the
membership value for category 
, and 
is the set of all
defined (non-null) categories.
is the normalized Gaussian function from Section
with the corresponding parameters 
(the focus) and 
, and 
is the label (name) associated with category . Note that it is always
possible to get a non-zero membership value for any category, because the
normalized Gaussian is strictly positive everywhere except at infinite
distance from the focus. This property is important in forced-choice
identification tasks, as we will discuss below.
Next we select all categories for which the membership value exceeds the
threshold for category membership 
, and the corresponding membership
values:
These are the candidates to provide a name for the color of the
stimulus. More than one
membership value can potentially exceed the threshold, so there may be more
than one element in this set (the set may be empty too, as the combined
extent of the categories does not cover the entire color space, at least
when thresholded). This is particularly the case for overlapping categories
such as red and orange (Figure p. ).
Next we sort the candidates by decreasing membership value:
and the first element of this n-tuple is our categorization judgment with
the corresponding membership or goodness value. The name corresponding to
the perceived color is then simply 
.
Using a particular threshold value amounts to doing a free choice
naming experiment with 11 named basic color categories and one null
category for everything that does not exceed the threshold for any of the
named categories. Using a zero (or no) threshold amounts to a forced-choice
experiment where we will always assign one of the 11 named categories to
the stimulus, regardless of how low the best membership value might be.
This technique has been used by [Hurvich \& Jameson 1957] for instance,
using only the four primary colors red, green, blue, and yellow, to obtain
psychophysical measurements of the color-opponent processes assumed to
underlie color perception.