Why We Don't Know How Many Colors There Are

There have been many attempts to answer the question of how many distinct colors there are, with widely varying answers. Here we present an analysis of what it would take to arrive at a reliable answer and show how currently available models fail to make predictions under the wide range of conditions that needs to be considered. Gamut volumes are reported for a number of light sources and viewing modes and the conclusion is drawn that the only reliable data we have comes from psychophysical work. The color gamut of the LUTCHI data in CIECAM02 is therefore shown as an alternative to the gamut of all possible colors. Introduction The question of how many colors there are has occupied enquiring minds for a long time and has been a tempting topic to apply color science methods and models to. Key papers here are those of Schrödinger (1920) who posited the Object Color Solid as encompassing all possible surface colors, Pointer (1980), who measured a set of natural surfaces and whose findings have been the benchmark ever since, McCann (1999) who emphasized the importance of color spaces in gamut computation, Morovic et al. (2001) who illustrated how color gamuts change with viewing conditions, Inui et al. (2004) who showed how the SOCS database – a new set of measured (‘real’) samples – compares to Pointer’s data, Heckaman et al. (2005) who demonstrated the existence of new colors that come about when illuminant and adapted white are decoupled and Nascimento (2008), whose estimate of the color volume occupied by natural scenes and the OCS in CIELAB, again showed similar results to Pointer’s findings. Instead of being after a number (‘How does 16.8 million sound?’), the aim of this paper is to present a framework for answering the question and to show that the question is either unanswerable or that its answer is the expression of predictions made by models under conditions for which they were never intended and under which they have no empirical basis or known predictive powers. Nonetheless the limits of color are relevant both due to their intrinsic scientific interestingness and due to their value in engineering decision processes as a means of judging the approach of diminishing returns. The remainder of this paper will present a framework for how to count all possible colors ‘by hand’, introduce a computational and modeling based solution, analyze its predictions and conclude with thoughts on the limitations of gamut computation and appearance prediction. What does ‘all possible colors’ mean? In order to address the question of how many colors there are, it is necessary to define what is meant by the term color. The CIE system of 1931 provided a method for specifying a color using a trichromatic system that takes into account the spectral properties of light reflected or emitted by an object and the spectral response of the human visual system. A typical RGB display device accepts in excess of 16 million unique color–channel inputs ((2) – 8 bits per each of 3 channels), potentially each with a unique trichromatic specification. However, some studies have suggested that our visual system can only distinguish about 2 to 10 million colors (e.g. Judd and Wyszecki, 1975; Hardin, 1992; Goldstein, 1996). The set of ~16 million unique stimuli (according to the CIE system) that an RGB imaging device can generate defines the tristimulus gamut of the device. The lower estimates for the number of colors suggests that some of these colors are visually indistinguishable. The suggestion that color is essentially the property of an object does not explain the many so-called, known color illusions. For example, it is well known a gray patch displayed on a black background will look brighter than a physically identical gray patch on a white background. This ‘illusion’ occurs because color is a perceptual response. Our visual system does not operate like a device that records and reproduces internally a replica of what it is presented with. Rather, the purpose of the visual system is to extract information from the environment and to create an internal representation. The ‘illusion’ of the identical gray patches described above occurs precisely because the visual system computes spatial contrast in what it views, which helps it to extract invariant information in its environment (Jameson and Hurvich, 1964). The phenomenon of spatial contrast indicates that color is not something that can be represented by a one-to-one mapping. Rather, color depends upon context. However, spatial contrast is only one way that color varies. The process of how the visual system perceives color is complex; not least, there is an opposite effect to spatial contrast in which color tends to be more similar to the background. It is known as White’s effect (White, 1979) or, generally, assimilation. Furthermore, color also depends upon temporal contrast or after-image effects (Koenderink, 1972), spatial frequency (Campbell and Robson, 1968), stimulus size including the factors of viewing angle and viewing distance (Fairchild, 2005), etc. It should now become clear that although the number of distinguishable colors is significantly lower than the number of physically different stimuli, the perceptual color gamut may be much larger than the gamut of physically–distinct stimuli. For example, one might imagine that the most red that can be obtained on a display would be where the red primary is maximally and uniquely activated (e.g. RGB = [255 0 0]). However, it may be possible to generate an even more colorful red by displaying the ‘full primary’ red on a green background, or after having viewed a scene under a greenish light source. Counting all possible colors ‘by hand’ To consider counting all possible colors, we could imagine someone laying out infinitely many colored cards, having spectral properties that represent all variation in the visible range, on a uniformly gray surface. Next, the observer would group together those that are indistinguishable, and then counting the resulting groups. Unfortunately, this exercise would only tell us about how many colors there are on the grey background and when viewed from a certain distance, in a certain sequence, under a certain light source, etc. Changing the configuration (e.g. background) or the viewer’s adaptation state (e.g. by looking at a different color beforehand) would change some or all of the color experiences that this set of cards give rise to. Therefore, given the complexity of the context, the prospect of counting the total number of indistinguishable colors is practically impossible. One might interpret this impossibility as being due to the large number of factors involved. For example, Fairchild (2010) argued that the generally accepted estimate of 10 million unique distinguishable colors are for a single viewing condition and for a particular observer. The change of viewing conditions and observers will lead to different / new distinguishable colors and, therefore, the number of possible colors is infinity. However, this argument may be too extreme, given the tendency of the visual system to saturate. This can be illustrated using the following thought experiment: Given three colors along a line in color space: A, B and C, let A be just distinguishable from B and B just distinguishable from C under some viewing conditions. If the viewing conditions change, B’ (the color of the stimulus having color B under the original viewing conditions) may either end up remaining indistinguishable from A’ and C’ or end up matching one or both of them. This new set of between 1 and 3 colors may in turn be either distinct from the original colors A, B and C or match some of them (Figure 1). Therefore, 1000 different viewing conditions do not necessarily correspond to 1000 new / unique / distinguishable colors. How many new colors they give rise to is the question that needs to be answered though to know how many distinct color appearances can be had. Figure 1: Impact of viewing condition change on number of distinguishable