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Color Naming

Color naming also belongs in the domain of psychology. I define color naming as a mapping from visual stimuli to pairs of color terms (or symbols or names) and ``confidence'', ``goodness'', or ``typicality'' measures.

More precisely, since I am not interested in spatial characteristics of visual stimuli, I will represent stimuli as spectral distributions associated with single points in the visual field only. The domain of is thus the set of all such distributions:

where represents wavelength in nm, and represents a spectral distribution. The functions will not be further defined. They need not be continuous or differentiable, for instance. A pure monochromatic stimulus would be represented as an impulse function, and mixtures of several monochromatic primaries would be represented as multi-modal distributions. The mapping can then be defined as

where is an enumerable set of undefined terms, and is the closed unit interval .

Informally, the preferred interpretation of the model is that represents the set of spectral distributions that function as input to the visual system, represents a set of basic color terms, e.g. , which is the set of basic color terms described in [Berlin \& Kay 1969], and represents the set of ``confidence'', ``goodness'', or ``typicality'' measures.

If we ignore the part of the , we might think of as representing a partition of the set of all possible color percepts into a number of equivalence classes, one for each color term. If we do take the part into account, we could model the response to any given stimulus , i.e. , as a fuzzy partition of the set of color terms [Kay \& McDaniel 1978][Zadeh 1971], which constrains the numbers of the pairs to sum to 1, or

where is the selector of the second element of an n-tuple, for any . The mapping then defines a set of membership or characteristic functions , one for each color category , on the universe . It is not clear what the advantage of such a model would be, however, or how well it fits the data on human color categorization.

The definition of implies that I will not be concerned with recovering or from , as noted above. A practical consequence of this is that changing the lighting of a scene may yield a different value of . I don't consider this a problem as long as the change is consistent with human performance on the same task.

From the brief discussion of the physiology of color vision above, it follows that if we want to model the relation between the domain of and a set of color terms, i.e. if we want to model color naming, it is not sufficient to define the extensions of color terms as intervals on the wavelength range between 380 and 770 nm. In particular, this approach could only work for pure monochromatic stimuli, which are very rare in real-world situations, and it would not explain the typical graded membership functions one finds in anthropological and linguistic research when subjects are asked to identify best examples and maximal extensions of color terms with respect to a set of color chips with known properties [Berlin \& Kay 1969]. This approach would also leave out non-spectral colors like purple or brown altogether. But perhaps the biggest objection against such an approach would be that it would constitute a system-external semantic model of color names, while our interest is in system-internal semantics, to be explained below. I claim that to model human color naming it is necessary to take human color perception into account, just as [Ronchi 1957] claims that it is necessary to take human physiology and psychology into account when studying optics, if that is defined with respect to visible light, i.e. implicitly with respect to an observer.