As a method for developing a sense of the ordering of color, Rood [Rood 1879] suggested gluing two pyramids base to base and then attempting to paint the surface of the resulting tetrahedral solid. White was to be painted at one tip and black at the other tip, a spectral color wheel was to be painted around the joint between the two pyramids, and then the faces were to be filled in so as to make smooth transitions along all surfaces. Albert Munsell, a painter and the inventor of the daylight photometer, took Rood's advice and after much elaboration on this early experiment developed the Munsell Color System [Munsell 1923]. This representation has been widely used in reflectance models, and presaged the development of the CIE color space.
Figure 9. Schematic diagram of the three axes of the Munsell color system [from Hall 1979].
The Munsell Color System has been thoroughly investigated with respect to small perceptual differences parallel to each of its three axes as shown in Figure 9. A Subcommittee of the Colorimetric Committee of the Optical Society of America performed the first systematic investigation of the psychophysical properties of the Munsell system and formulated what has come to be known as the Renotation Munsell [see Indow 1988 for a review].
Studying the Renotation Munsell system by holding two dimensions of the representation constant while varying the remaining dimension says nothing about the scaling of the axes with respect to one another. In order for a uniform scaling for the Munsell Color Solid to exist, it is necessary that perceptual color space be a metric space. Thus, the discovery of a uniform scaling would be evidence in support of perceptual color space being metric.
Figure 10. Multidimensional scaling of 361 small color difference pairs of 178 Munsell color chips as judged by 5 subjects. This slice of the Munsell Color Solid comprises a plane of equal value ($V=5$) [from Indow & Aoki 1983].
Recent studies of the Munsell Color Solid have used multidimensional scaling techniques to analyze small difference comparative color judgements and have found that the Renotation Munsell is neither as uniform or as smooth as was originally claimed. Figure 10 shows data from one such experiment [Indow & Aoki 1983] in which 178 Munsell color chips were shown as 361 color difference pairs and judged twice by each of 5 subjects. If the Munsell Color Solid were an accurate description of perceptual color space, these data would be plotted as a set of concentric circles with equally spaced spokes radiating from the center. Although the Munsell system captures some of the nature of the perceptual color space, it is not a uniform color scaling. McCamy McCamy93a has proposed a reformulation of the Munsell color solid to attempt to remove these anomalies while still retaining some of the intuitive appeal of the system.