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Models of Color Perception and Color Naming

As outlined in the introduction, the working hypothesis of this dissertation is that the characteristics of the underlying neurophysiological color vision process explain phenomena like the universality of basic color category foci and graded membership of color samples in color categories. In other words, both universal basic color foci and graded membership properties must follow directly from the properties of the used color model, if we want the color model to explain human color naming behavior. It is not sufficient for a color model to merely categorize all possible color percepts in a systematic way; it must also explain why some color percepts are more salient than others, and why category membership judgments are graded. I hypothesize that when learning basic color names, some points in the learning space are more salient than others and act as ``attractors'' for category foci. These properties must follow from the color model, and it is against these criteria that I will judge the usefulness of any particular color model. None of the existing color models meets these criteria.

In the light of the requirements for color vision models set forth above, we can immediately disqualify a number of simplistic models of color naming that might be intuitively appealing:

• Extensions of color names as intervals on the wavelength line: Clearly, this kind of model does not accommodate or explain the existence of universal foci or graded membership functions. In addition, this model does not allow for non-spectral colors like purple or brown at all. It is this kind of arbitrary model that Berlin and Kay (successfully) sought to disprove in their study [Berlin \& Kay 1969].

• RGB-based models: RGB models are loosely based on the three types of photoreceptors and their spectral sensitivities in the human retina (Section ). As such, they model a very early stage in the human color vision process, probably too early to be useful for our purpose. Indeed, already at the LGN level, RGB-like signals have been transformed into an opponent coding (yellow--blue and red--green), which continues to the cortical level [Dow 1990]. As [Hurlbert 1991] points out, RGB codes perceived colors neither uniquely nor efficiently. Since the cones adapt to the intensity and spectral composition of the ambient light (including surrounding image areas), RGB values do not uniquely specify colors. In addition, the ranges of wavelengths that the three cone types are sensitive to overlap greatly, especially for the R and G cones. This makes for rather inefficient coding of color. According to Hurlbert, the brain has evolved a second-stage mechanism to transform cone triplets into more reliable and discriminatory code, which discounts redundancies and enhances differences in cone responses. She claims that few color scientists would disagree that this color-opponent processing occurs, but there is disagreement on exactly which directions the opponent-color axes take in color space. To summarize, although opponent representations are usually thought of as ``merely'' linear transforms of RGB space, the opponent representation is much more suitable for modeling perceived color than RGB is.

From a psychological point of view, the inappropriateness of RGB as a color model is clearly demonstrated by the difficulty people experience in manipulating RGB color coding in a consistent and intuitive way, and by the recent interest in different kinds of color models (among which are opponent models) in computer graphics research [Scheifler \& Gettys 1992][Robertson \& O'Callaghan 1986][Turkowski 1986][Rogers 1985][Naiman 1985][Meyer \& Greenberg 1980]. [Rogers 1985] points out that RGB and all of the linear transforms thereof (CIE XYZ, YIQ, CMY) are difficult for users to specify subjective color concepts in. A closer look at the properties of RGB representations provides independent evidence. The RGB color solid has the shape of a unit cube, with the achromatic (grey level) dimension going from to , and the maximally saturated colors red, green, and blue at a lower brightness level than the maximally saturated colors yellow, cyan, and purple, all of which are situated at corners of the cube (Figure ).

This kind of organization does not match the color naming data very well. As [Shepard 1987] points out, the representation of stimulus data is of major importance for the interpretation of experimental psychological results. He cites the example of generalization across stimuli, which can exhibit a non-monotonic increase between stimuli separated by certain special intervals in a metric space, for example, between tones separated by an octave, between hues at opposite ends of the visible spectrum (red and violet), and between shapes differing by particular angles related to inherent symmetries of those shapes. If we use a circular hue representation rather than a wavelength interval representation, as in the Munsell color space, for instance, red and violet become neighbors rather than opposites, and the apparent nonmonotonic effect disappears. Similar conceptions of psychological spaces exist for pitch [Patterson 1986] and shape [Walters 1987].

The same holds, mutatis mutandis, for lookup tables specifying RGB values indexed by color names (as found in the X-windows system, for instance), or the other way around. This kind of ``model'' does not even provide a name for every point in the space, and graded membership or learning names in a productive way is even harder to model in this context, not to mention the existence of universal color foci.

Other kinds of existing color models (CIE chromaticity, opponent models, psycho-physical and colorimetric models in general) all suffer from the same disadvantage of not being able to explain the existence of universal foci, and to a lesser extent, the graded category membership functions.

The only existing models of color naming based explicitly on the neurophysiology of color vision and attempting to explain the universality of foci and graded membership functions are [Cairo 1977] and [Kay \& McDaniel 1978]. Apart from not being defined or implemented as full-fledged computational models, both of these have important drawbacks. Kay and McDaniel's model interprets (stylized versions of) the response functions of four types of color-sensitive cells in the LGN [De Valois et al. 1966] as characteristic functions of four fuzzy sets corresponding to the categories red, green, yellow, and blue. As such, the model explains the existence of universal foci (which correspond to maxima of the characteristic functions) and the graded membership functions (which correspond directly to the characteristic functions) of these four basic color categories. But the model has to be tweaked to account for other basic color categories (requiring the introduction of new and ad hoc fuzzy set operations and a nonlinear compression of the wavelength dimension that is without apparent external motivation), and it is not clear at all how non-spectral basic color categories like brown or purple are to be dealt with, nor how to model the learning of color names in this model. It also does not adequately explain the hierarchy of languages with respect to the lexical encoding of basic color categories. Another objection that can be brought against the model is that it predicts that a flat-spectrum white stimulus light is a good example of every basic color category, since there is no opponent mechanism that cancels out opponent primaries. This prediction is clearly not born out by experience or by psychophysical experimentation.

Cairo's model of color naming [Cairo 1977] is also based on findings in the physiology of the pre-cortical visual system. It is four-dimensional: wavelength, intensity, purity, and a fourth dimension representing the adaptation state of the retina. All of these dimensions are defined as physical parameters of the stimulus, rather than as perceptual dimensions. Cairo introduces a ``data-reduction model'' of analog-to-digital conversion in the pre-cortical visual system, and represents Berlin and Kay's eleven basic color categories as specific combinations of quantized values on the four dimensions. In addition, he predicts four potential new basic color categories beyond Berlin and Kay's eleven, which he calls sky-blue, turquoise, lime, and khaki.

Although this model is interesting for its attempt to take adaptation into account, it suffers from a number of important drawbacks. For instance, the discrete nature of the model and the use of wavelength as one of the dimensions forces complex stimuli to be treated as if they were monochromatic, and this is done using the ``dominant wavelength'' to represent an entire spectrum. While this may work in limited circumstances, it is clearly a gross simplification which cannot hold in general (e.g., which is the ``dominant wavelength'' of the spectra of Figure ?). In addition, Cairo claims that Berlin and Kay's finding of universal foci of categories is a mere artifact introduced by the use of the Munsell color system for the stimulus material used in the experiment. This conclusion does not seem to be supported by the wealth of psychological and linguistic research done since Berlin and Kay's initial study (cf. the bibliography of recent research in [Berlin \& Kay 1969]). On the contrary, it seems that it is rather Cairo himself who is forced to deny the evidence because of the discrete nature of his model, which does not allow for graded categories. The discretization of the model itself seems to be fueled by a desire to make color notation the subject of algebraic analysis, requiring a complete ordering of a discrete number of possible color values. While that may be a noble cause, it also requires most of the data on actual color naming behavior to be ignored, which is too much of a price to pay for a convenient analysis. Berlin and Kay's hierarchy of languages is explained in a rather circular fashion by Cairo in terms of the ``perceptual salience'' of the four underlying dimensions, but without explaining where their salience derives from. In general, this model seems overly biased by an extreme information processing view of psychology that regards cognition quite literally as a digital computational process.

[Harnad et al. 1991] present a rather different approach to the categorization problem, using artificial neural networks. They consider the problem of separating lines into two classes. After training an auto-associator network (one that essentially reproduces its input as its output), they add a categorization task to the same net. The result is that the ``similarity space'' derived from the net's hidden nodes' activations is warped to reflect categorial boundaries. The analysis of the network representations is interesting, and the authors provide a good discussion of network representations, but the applicability of the approach seems limited. An interesting thing to note is that the representations used by this network seem just as ungrounded as the symbolic representations that the first author criticizes in some of his other work [Harnad 1990].