فضاهای طیفی و فضا های رنگی Spectral Spaces and Color Spaces

INTRODUCTION In recent years interest in spectral spaces representing in a limited number of dimensions (usually three) the reflectances of color chips defining perceptual color spaces [those of Munsell or Swedish Natural Color System (NCS)] and other data has increased.1– ۶ Different mathematical techniques have been used for the dimensionality reduction with varying results. Color spaces are usually defined as geometrical models of human color experiences. Perceptual color spaces are geometrical arrangements of color chips (or geometrical models thereof) found under given conditions to differ from each other in specific ways. In the case of the Munsell system, for example, the color chips differ in terms of the color attributes hue, chroma (saturation) and value (lightness) by unit differences that vary by attribute. In the case of NCS they vary by unique hue component, blackness and whiteness. Psychophysical color spaces are based on the weighting of the spectral return (the products of a normalized spectral power function defining the light source and the spectral reflectance function of the objects viewed) entering the eye that views samples in a given surround by cone response or color matching functions, and additional manipulation. These spaces assume the premise that there is a direct and unique relationship between the spectral return entering the eye and the resulting color experience. At least since Land’s experiments it is known that this premise is not generally valid because a given spectral return can result in widely differing color experiences depending on the complexity of the surround. Reasonably good correlation between spectral return and experience can be obtained when maximally simplifying the surround to a single, uniform achromatic field. There is a fundamental difference between spectral spaces and color spaces, the former being based on implicit weighting by functions derived from mathematical analysis of spectral returns, the latter on the explicit weighting by functions based on results of color-matching experiments, i.e., psychological data. The purpose of this article is to compare the two kinds of spaces and to demonstrate the differences that are critical from the point of view of color vision. BACKGROUND Historically, psychological color spaces are geometrical Euclidean three-dimensional (3D) arrangements of color chips that vary in a given perceptual fashion. A Euclidean arrangement is only possible if the unit differences of the different attributes used for the arrangement are not of equal size. In the Munsell system, for example, the scale units of hue, value and chroma scales are all of different perceptual size. For the last 100 years the most sought after color space has been the perceptually uniform one, with no fully satisfactory solution as yet. Another well-known space is based on constant change in perceived unique hues, blackness and whiteness (the so-called Hering natural color space). In terms of perceptual distance this space varies between and within attributes. Psychophysical Color Spaces Psychophysical color spaces are based on spectral returns and cone sensitivity or color-matching functions. In human color vision the spectral returns are subject, among other things, to lightness and chromatic adaptation effects. These tend to discount, to a smaller or larger extent, the effect of the spectral composition of the light source. It is reasonable to assume that adaptation to a (synthetic) equal energy light source would lead to color experiences very similar to those of, say, daylight illuminant D55 and that as a first approximation an average daylight source can be discounted and spectral returns (on a relative basis) can be considered to be the spectral reflectance functions. The colorimetric system reduces the many dimensions (typically 31 at 10 nm intervals) of spectral returns to three by subjecting them to the filters or weights of the standardized color-matching functions. Color matching bears some relationship to color appearance since matched lights or objects have the same appearance. However, matching does not provide explicit information about the relationship between reflectance function and appearance (in the highly relativized condition where a systematic relationship can be expected). When placing Munsell system reflectance functions into the CIE tristimulus space they form an irregular, slanted double cone, with the perfect black color at the origin of the space. Planes of constant value are horizontal slices through the slanted double cone. In order to make the lightness axis perpendicular to the constant value planes, the additional assumption of an operating opponent color system is made. This is achieved by normalizing by subtracting (and application of a weighting factor) the X and Z tristimulus values from Y. A plane chromatic diagram results in which perfectly horizontal reflectance functions under an equal energy light source, regardless of their luminous reflectance, fall on the origin. Fair agreement with the psychological space is still not obtained because the (relativized) relationship between reflectance function and color experience is not linear. Appropriate power functions applied to the tristimulus values or the opponent color values improve the agreement considerably. If the filters used are cone-response functions rather than color-matching functions an additional transformation is required to convert the former to the latter (or approximations thereof). The several steps discussed generate points in a 3D space from reflectance functions, the distribution of which indicates a degree of agreement with the distribution of points representing, say, Munsell chips in a psychologically derived hue, value, chroma space.