B. Hill
Abstract
This article discusses the CIELAB color spave within the limits of optimal colors including the complete volume of object colors. A graphical representation of this color space is composed of planes of constant lightness L* with an net of lines parallel to the a* and b* axes. This uniform net is projected onto a number of other color spaces (CIE XYZ, tristimulus RGB, predistorted RGB, and YCC color space) to demonstrate and study the structure of color differences in these spaces on the basis of CIELAB color difference formulas. Two formulas are considered: the CIE 1976 formula *** and the newer CiE 1994 formula ***. The various color spaces considered are uniformly quantized and the grid of quantized points is transformed into CIELAB colordinates to study the distribution of color differences due to basic quantization steps and to spacify the areas of the colors with the highest sensitivity to color discrimination. From a threshold value for the maximum color difference among neighboring quantized points searched for in each color space, concepts for the quantization of the color spaces are drived. The results are compared to quantization concepts based on average values of quantization errors published in previous work. In addition to color spaces bounded by the optimal colors, the studies are also applied to device-dependent color spaces limited by the range of a positive RGB cube or by the gamut of colors of practical print processes (thermal dye sublimation, chromalin, and match print). For all the color spaces, estimation of the number of distinguishable colors are given on the basis of a threshold value for the color difference perception of *** = 1 and *** = 1.
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Index Terms
Comparative analysis of the quantization of color spaces on the basis of the CIELAB color-difference formula
Reviews
Svetlana Segarceanu
The main goal of this study is to describe the range of optimal colors in a specified grid of the CIELAB space and to point out how these colors are represented when transformed into a number of other typical color spaces. A second aim is to compare the quantization of the different spaces. Therefore, the quantization based on the CIELAB difference formulas is applied to several other color spaces. The introduction briefly presents previous research in this field and describes the authors' approach. The second section defines the basic concepts of the analysis, namely the CIELAB system and the two difference formulas used to compare two colors. The first, D E ab , assumes a mathematical approximation by which these differences are given in terms of L * , the perceived lightness, and the coordinates a * and b * on the opponent color axes green-red and blue-yellow, respectively. The second, D E * 94 , is more complicated and is expressed in terms of differences of lightness, chroma, and hue. The optimal color space is represented as being composed of planes of constant lightness. Section 2.3 discusses the problem of establishing a threshold value for color differences in order to quantize the color space. Next, a general frame for defining a quantization box is presented. In any quantization, the step between a color point and one of its neighbors produces a color difference. The authors take into account the maximum difference produced by a diagonal step, denoted by D E worst . One aim of the study is to find D E max for all the color points, and to find a quantization concept that keeps it below a fixed value. This maximum value is computed for the CIELAB space and the general D E ab formula, assuming certain quantization conditions. Section 3 establishes the number of distinguishable colors and the type of quantization for a given threshold. Section 4 presents graphical representations of the uniform grid of colors of the CIELAB space when it is transformed into the primary color spaces CIEXYZ and RGB ITU-RBT , the predistorted R ?G ?B ? color space, and the YTU color space. The variations of D E worst and D E max for both difference formulas, along lines of optimal colors in each of these color spaces, are plotted against hue angle and lightness, and suitable quantization concepts for color spaces are derived from the maximum color quantization step obtained in each color space. In section 5, the authors present the CIELUV color space and compare the CIELUV and CIELAB spaces by evaluating the color differences in the CIELUV space using the CIELAB color difference formulas. Section 6 is devoted to device-dependent color spaces. In the last part of the paper, the authors discuss<__?__Pub Caret> the results. The study is interesting, neatly presented, and beautifully illustrated. It is useful for people working with three-dimensional graphics and those interested in the analysis of color spaces.
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