Detail Preserving Reproduction of Color Images for Monochromats and Dichromats Karl Rasche, Robert Geist, James Westall
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IEEE CG&A SPECIAL ISSUE:SMART DEPICTION FOR VISUAL COMMUNICATION 1 Detail Preserving Reproduction of Color Images for Monochromats and Dichromats Karl Rasche, Robert Geist, James Westall Abstract— In spite of the ever increasing prevalence of low- algorithm is mapping to luminance. Mapping to luminance, Y, cost, color printing devices, grayscale printing devices remain for the NTSC model is given by: in widespread use. In its current grant proposal guide, the US National Science Foundation warns investigators that they Y = 0:299 × R2:2 + 0:587 × G2:2 + 0:114 × B2:2 (1) “should not rely on colorized objects to make their arguments.” Authors producing documents with color images must account Here the gamma value for the model is 2.2, and the coefficients for the possibility that color images may be reduced to grayscale are derived from the chromaticity values for the primaries before they are viewed and that the standard reduction used by grayscale printers, map color to luminance, may fail to as well as the reference white, which for this model is CIE preserve important image detail. This paper suggests a new Illuminant C, designed to represent daylight. Chromaticity color to grayscale transformation that preserves image detail values are defined in terms of the CIE XYZ color space of by maintaining distance ratios during the reduction. Multiple the standard observer. The XYZ color space was designed in examples attest to its effectiveness. An extension of the new 1931 by the CIE for matching the perceived color of any given transformation that reduces three-dimensional color space to a two-dimensional surface is also suggested. Such reductions are spectral energy distribution. Three primaries, X, Y, and Z, important for color-deficient observers. and three associated matching functions, x¯λ , y¯λ , and z¯λ , were identified with the property that, given any spectral energy Index Terms— color-deficient vision, color mapping, conjugate- λ gradient optimization, grayscale transform distribution, P( ), the non-negative weights X = k P(λ)x¯λ dλ Y = k P(λ)y¯λ dλ Z = k P(λ)z¯λ dλ I. INTRODUCTION Z Z Z can be used to construct a color, c = XX+YY+ZZ, that will N spite of the ever increasing prevalence of low-cost, match P(λ) up to human perception. The scaling constant, k, color printing devices, grayscale printing devices remain I depends on the spectrum of the reference white. Chromaticity in widespread use. In its current grant proposal guide, the US values are then two-dimensional, normalized coordinates (x;y) National Science Foundation warns investigators: “For cost given by and technical reasons, the Foundation cannot, at this time, X Y reproduce proposals containing color. PIs, therefore, generally x = y = X +Y + Z X +Y + Z should not rely on colorized objects to make their arguments.” Authors producing documents with color images for any venue Different color models, e.g. the sRGB model commonly must account for the possibility that the color images may be used to describe color monitors, with different chromaticities, reduced to grayscale before they are viewed. Since conversion reference white, or gamma, will yield mappings to luminance to grayscale reduces the number of color dimensions, some that differ slightly from (1). Details on color space definitions loss of visual information is generally unavoidable. Ideally, may be found in [1]. this loss can be restricted to features that vary minimally When mappings such as (1) are used, colors that have within the color image. Nevertheless, with standard procedures very small differences in luminance but large differences in in widespread use, this objective is not often achieved, and chrominance are mapped to similar shades of gray. Colors important image detail is often lost. Consequently, algorithms that were easily distinguishable in the original image, due to that convert color images to grayscale in a way that preserves chrominance variation, can become indistinguishable in the information remain important. grayscale image. An example is shown in Figure 1. The left A grayscale conversion algorithm is a dimension-reducing image is an (R;G;B) digital photograph. The center image is function that maps points in color space, typically RGB produced by applying (1) to produce an encoded luminance, Y, tristimulus values, (R;G;B) 2 ℜ3, to a subset of ℜ1. Any such and then linearly mapping the Y values to pixel gray levels. mapping assumes a color model, which includes specification The red berries, which stand out markedly from the green of chromaticity values for red, green, and blue primaries leaves in the color image, are effectively lost in the gray image. as well as a reference white spectrum and a linearizing A more dramatic, if contrived, example is shown in Figure 2, gamma value. The most common RGB model is probably the where the colored blocks in the original image (left) were NTSC standard, and the most common grayscale conversion chosen to have nearly identical luminance. All image detail is lost when the luminance mapping (1) is applied. The authors are with Clemson University, Clemson, SC 29634-0974 An effective grayscale conversion method should preserve Email: [email protected] the detail in the original color image. Our fundamental premise is that this is best achieved by a perceptual match of relative IEEE CG&A SPECIAL ISSUE:SMART DEPICTION FOR VISUAL COMMUNICATION 2 (a) (b) (c) Fig. 1. Conversion to Grayscale: Substantial image detail is lost when the color photo (a) is converted to the grayscale photo (b) by the standard NTSC map to luminance. An alternative mapping (c) preserves some of the detail. color differences between the color image and the grayscale error-diffusion [3], but such diffusion does not compensate image. In particular, the perceived color difference between for a problematic palette. When a standard error diffusion any pair of colors should be proportional to their perceived mapping is applied to the color image of Figure 1(a), the result gray difference. is visually indistinguishable from the image of Figure 1(b). In this paper we describe a new approach to the grayscale Color gamut mapping for printing with a small set of inks conversion problem that is built on this premise. The method is similar to our problem. Here, colors are reproduced using 3 1 automatically constructs a linear mapping from ℜ to ℜ only one or two base ink colors. The entire color gamut of an that preserves, to the extent possible, the perceived distances image to be printed is generally not available, and an image 3 between those points in ℜ that comprise a specific color must be mapped into the available gamut in a meaningful 1 image and their mapped values in ℜ . The derived mapping way. Stollnitz et al. [4] examine the case of printing with function depends upon the characteristics of the input image an arbitrary number of base ink colors. For the case of a and incorporates information from all three dimensions of the single ink, they seek to preserve luminance contrast by using color space. After describing our detail-preserving grayscale a monotonic mapping of input luminance to ink density. This transform, we show that a straightforward extension can be method ignores chrominance of the input image and thus will used to re-color images in a way that preserves detail for suffer the same loss of chrominance-based detail that (1) does. viewers with color-deficient vision. The reduction of high dimensional data to a lower dimen- sion is also a well studied problem. A standard linear technique A. Related Work is principal component analysis (PCA). In PCA, a set of This problem is similar to the tone mapping problem of orthogonal vectors, the principal components, lying along the displaying high dynamic range images on low dynamic range directions of maximal data variation is found. To reduce the displays [2]. In both cases, the objective is to preserve an dimensions of the data, a subset of the principal components abundance of visual information within the constraints of a are used to form a subspace onto which the original data is limited gamut, and our approach to grayscale conversion, like projected. While preserving the color variation is necessary for Tumblin and Rushmeier’s tone mapping, seeks a perceptual pleasing grayscale images, it is not sufficient. Consider again match. Nevertheless, tone mapping is generally concerned with the example color image in Figure 1. If we have an image compression of the gamut range, whereas we are interested in with most of the colors clustered in two regions, here red and compression of gamut dimensionality. green, we can envision a “dumbbell”-shaped distribution of The problem might also be compared to color quantization, pixels in color space. By preserving variance, one end of the as it attempts to display a large number of colors with a “dumbbell” will be mapped to the light end of the grayscale small palette. Nevertheless, palette selection is an integral gamut while the other will be mapped to the dark end. If part of color quantization methods. Palette colors are most we then examine the histogram of the resulting grayscale often selected from a large gamut, which at least includes the image, we will find a large number of empty gray bins in gamut of the original image. In our problem, the palette is the center of the range. As such, any detail within the red fixed to a gray ramp, and so the principal task, as well as and green “dumbbell” clusters will be reproduced over a very the flexibility available, for any color quantization method has small gray range and may not be perceived.