An Efficient Perception-Based Adaptive Color to Gray
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Computational Aesthetics in Graphics, Visualization, and Imaging (2007) D. W. Cunningham, G. Meyer, L. Neumann (Editors) An Efficient Perception-based Adaptive Color to Gray Transformation † ‡ § L. Neumann 1 and M. Cadíkˇ 2 and A. Nemcsics 3 1ICREA, Barcelona, and VICOROB, University of Girona, Spain 2Department of Computer Science and Engineering, Czech Technical University in Prague, Czech Republic 3Technical University of Budapest, Hungary Abstract The visualization of color images in gray scale has high practical and theoretical importance. Neither the existing local, gradient based methods, nor the fast global techniques give a satisfying result. We present a new color to grayscale transformation, based on the experimental background of the Coloroid system observations. We regard the color and luminance contrasts as a gradient field and we introduce a new simple, yet very efficient method to solve the inconsistency of the field. Having a consistent gradient field, we obtain the resultant image via fast direct integration. The complexity of the method is linear in the number of pixels, making it fast and suitable for high resolution images. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Picture Image Generation]: Display Algorithms, Viewing Algorithms; I.4.3 [Image Processing and Computer Vision]: Enhancement-Filtering 1. Introduction changes (gradients) and values. The problem combines var- ious aspects of color vision and spatial vision. How does Nowadays, except for a few artistic and scientific applica- the visual effect of chrominance and luminance contrasts de- tions, the vast majority of captured images are color pho- pend on spatial frequencies? tographs. On the other hand, many laser printers are still black-and-white, and most of the pictures in daily newspa- The above questions do not have simple solutions, as pers published in the world are predominantly gray-scale im- adaptive color to gray transformations are not generally ages. Thereby the practical importance of color to grayscale found in nature. We believe that global transformation ap- transformations is clear. The theoretical challenge is also ev- proaches cannot give a full answer to the above questions, al- ident. The color to gray transformation is a mapping of a 3D though they appear to offer some fast and acceptable results. set with spatial coherences to a one dimensional (1D) space The adaptive local methods hold the promise of a much bet- and it necessarily leads to some information loss. What is the ter solution, although they suffer from theoretical problems best way? Which way gives the highest perceptual equiva- in perceptual modeling and practical difficulties in numerical lence? Does there exist a universal approach? calculations. In this paper, we present a perceptually-based adaptive approach using the experimental background of the The solution requires the preservation of chromatic con- Coloroid observations. We investigated the relative equiva- trasts during the conversion to luminance contrasts and the lent luminance differences for a set of chromatic differences associated evaluation of the luminance and chrominance at a given spatial frequency, using 10 × 10 cm solid color samples. However, a comprehensive spatio-chromatic anal- † ysis still demands further investigation. [email protected] ‡ [email protected] The paper is structured as follows. We review previous § [email protected] work on color to gray image transformation in Section 2. Full color versions of the images and other materials are online: In Section 3, we describe the Coloroid color system and we http://www.cgg.cvut.cz/~cadikm/color_to_gray present our new observations based on the Coloroid. Sec- c The Eurographics Association 2007. 74 L. Neumann & M. Cadíkˇ & A. Nemcsics / An Efficient Perception-based Adaptive Color to Gray Transformation tion 4 introduces an efficient gradient-based color to gray transformation algorithm powered by a new gradient incon- sistency correction method. Then, in Section 5, we show and discuss the results of the presented transformation algorithm. Finally, in Section 6, we conclude and suggest some ideas for future research. 2. Related work Figure 1: Left: shape of the Coloroid gamut at a fixed hue value. Right: turquoise hue plane of the Coloroid space. There are several approaches available in the literature that aim to convert color images to grayscale. Strickland et al. [SKM87] proposed a local color image enhancement technique used to sharpen images based on saturation feed- back. Zhang and Wandell [ZW96] devised a spatial exten- sion of the CIELab color model (S-CIELab) that is useful for measuring color differences between images. Using the pattern-color separable transformation, the S-CIELab differ- ence measure reflects both spatial and color sensitivity. Bala and Eschbach [BE04] presented spatial color to gray trans- formation that locally preserves the chrominance edges by introducing high-frequency chrominance information into Figure 2: Left: 48 limit colors of the Coloroid system. Right: the luminance channel. The method applies a spatial high- curve of Coloroid limit colors in 3D. pass filter to the chromatic channels, weighs the output with a luminance dependent term, and finally adds the result to the luminance channel. Grundland and Dodgson [GD05] pro- posed the decolorize algorithm for contrast enhancing, color 3. The Coloroid system to grayscale conversion. The method applies a global color The Coloroid is a color-order system and color space with to grayscale conversion by expressing grayscale as a con- conversion formulas to and from CIE XYZ system. The tinuous, image dependent, piecewise linear mapping of the Coloroid system is based on huge number of observa- RGB color primaries and their color saturation. The authors tions [Nem01] and represents perhaps the most adequate tool calibrate the behavior of their method by using three param- or “natural language” to describe harmony relationships and eters to control contrast enhancement, scale selection, and other psychometric attributes between colors [NNN05]. The noise suppression. The authors suggest image independent experimental arrangement of the observations of the color default values for these parameters. Gooch et al. [GOTG05] harmony relationships is an ideal tool to study the basic presented a Color2Gray algorithm which iteratively adjusts questions of the color to gray transformation, especially to the gray value of each pixel to minimize an objective func- find the chrominance-luminance equivalent attributes on a tion based on local contrasts between pixels. The method relative scale. applies three free parameters (θ, α, μ), but the authors do not provide image independent default values. Moreover, the Conditions of observations and basic concept of the Col- complexity of the method is O(N4). Hence, the method is oroid system differ from other color order systems. In typi- very slow and it is difficult to apply to high resolution im- cal Coloroid experiments, the observer is given a wide field ages. Rasche et al. [RGW05] presented a color to gray tech- of view to observe a large set of often non-neighboring nique that aims to preserve the contrast while maintaining color samples, and must give their responses relative quickly. luminance consistency. Authors approach the problem by These conditions make it similar to an observation of a com- means of constrained multidimensional scaling which scales plex image in the real life. Under these viewing conditions badly with the number of colors, and therefore the color the human vision system can distinguish a reduced num- quantization is suggested. However, due to the necessary ber of colors, especially in the darker regions. The colors in quantization of colors the method produces quantization-like Coloroid can be obtained by additive mixture of the black, artifacts. Therefore, the usage of this method is very ques- white and the limit-color, by ratios s, w, and p, respectively, tionable for images with continuous tones (e.g. real-world where s + w + p = 1. The limit-colors were the most satu- photos). Moreover, the time-demands are enormous (even a rated solid-colors instead of spectral colors. Due to the very low-res image transformation takes minutes) and depend on great number of observations and also to the obtained good the number of colors. correlations, we consider the basic concepts of Coloroid to c The Eurographics Association 2007. L. Neumann & M. Cadíkˇ & A. Nemcsics / An Efficient Perception-based Adaptive Color to Gray Transformation 75 be axioms, which are valid for the above mentioned view- A λϕ conditions: 10 570.836 58.040 20 582.640 32.898 1. Surfaces of a constant Hue (A) form a plane, containing 30 602.717 5.533 the neutral axis and a hue dependent limit-color, unlike 40 -504.836 -46.209 most of the other systems that have curved hue-surfaces 50 450.000 -116.628 (e.g. the Munsell system). 60 490.371 -174.503 = ∗ ( ) 2. Saturation T const ratio p of the limit-color, where 70 536.295 103.890 the constant depends on the hue. / 3. Lightness V = 10 ∗ Y 1 2. Unlike the ds line-element Table 1: Definition of the seven basic Coloroid hues based spaces, the Coloroid does not contain a 3rd root or a logarithmic formula here. A/A 10 20 30 40 50 60 70 Fig. 2 (left) shows the circle of 48 limit-colors, while 10 0.0 -2.5 -5.0 -7.0 -10.0 -5.0 -2.0 Fig. 2 (right) shows the continuous 3D limit-color line. 20 2.5 0.0 -2.5 -5.0 -8.0 -3.0 1.5 Fig. 1 (left) demonstrates the typical shape of the Coloroid 30 5.0 2.5 0.0 -3.0 -5.0 -3.0 3.5 gamut at a fixed hue value. The lightness of the most satu- 40 7.0 5.0 3.0 0.0 -2.5 1.0 4.0 rated point depends on the hue according to Fig.