Computational Color Harmony Based on Coloroid System

Institut fur¨ Computergraphik und Institute of Computer Graphics and Algorithmen Algorithms Technische Universitat¨ Wien Vienna University of Technology Karlsplatz 13/186/2 email: A-1040 Wien [email protected] AUSTRIA other services: Tel: +43 (1) 58801-18601 http://www.cg.tuwien.ac.at/ Fax: +43 (1) 58801-18698 ftp://ftp.cg.tuwien.ac.at/ TECHNICAL REPORT Computational Color Harmony based on Coloroid System Laszl´ o´ Neumanna, Antal Nemcsicsb, Attila Neumannc a Grup de Grafics` de Girona, Universitat de Girona, Spain Institucio´ Catalana de Recerca i Estudis Avançats, ICREA, Barcelona email:[email protected] : Corresponding author b Budapest University of Technology and Economics, Hungary email:[email protected] c Institute of Computer Graphics and Algorithms, University of Technology, Vienna, Austria email:[email protected] TR-186-2-05-05 (revised) June 2005 Computational Color Harmony based on Coloroid System Laszl´ o´ Neumanna, Antal Nemcsicsb, Attila Neumannc a Grup de Grafics` de Girona, Universitat de Girona, Spain Institucio´ Catalana de Recerca i Estudis Avançats, ICREA, Barcelona email:[email protected] : Corresponding author b Budapest University of Technology and Economics, Hungary email:[email protected] c Institute of Computer Graphics and Algorithms, University of Technology, Vienna, Austria email:[email protected] June 26, 2005 Figure 1: Visualization of the overall appearance of a dichromatic color set with ‘caleidoscope’ option of the Color Plan Designer software ABSTRACT Figure 2: Interactive color selection of a dichromatic color set in multi-layer mode, applying rotated regular The paper presents experimentally based rules and grid methods creating harmonic color sets. Firstly, dichromatic rules will be presented which concern color harmony relationships of only two hues. For an arbitrarily given hue pair, we define the just harmonic saturation values, resulting in just harmonic color pairs. These 2 1 THE COLOROID COLOR-ORDER SYSTEM values express the fuzzy border between harmony and disharmony regions by a single scalar, most appropri- ately. Secondly, the value of harmony will be defined corresponding to the contrast of lightness, i.e. the difference of perceptual lightness values. Thirdly, we formulate the harmony value of the saturation contrast, depending on hue and lightness. Results of these investigations form a basis for a unified, coherent dichromatic harmony formula as well as for analysis of polychromatic color harmony. Introduced color harmony rules are based on Coloroid, which is one of the 5 − 6 main color-order systems and furthermore it is an aesthetically uniform continuous color space. Coloroid has simple closed forward and backward transformation formulas with the color space of CIE XYZ. It relies on a huge number of observations and experiments, and it is a very suitable tool of color dynamics for describing aesthetical relationships. It had Figure 3: The aesthetically uniform 48 limit-colors of supported also numerous color plans of great architec- the Coloroid system built 7 hue groups with the non- tural projects having been realized in the practice. The uniform numbering: 10,...16, 20,...26, 30,...35, 40,...46, experimental data and information to be retrieved from 50,...56, 60,...66, 70,...76, according the yellow, orange, them are just partly processed and published so far. Our red, purple, blue, cold-green, warm-green intervals article utilizes a ’slice’ of this database, together with additional complementary observations. This paper is an issue of a planned series of articles, dealing with rules Most important results of experiments have been pub- and coherences of color harmony based on the Coloroid lished in periodicals and books. Many results have been system. employed to create the aesthetically uniform Coloroid dH Keywords: Color Order System, Coloroid, Computa- color-order system relying on “harmony threshold”, tional Aesthetics, Color Dynamics, Color Harmony, En- or within many others, to create the system of the color vironmental Color Design preference indices. Most of the experiments have inves- tigated the perceptual attributes of hue, saturation and lightness, the role of aesthetical uniformity, the color preferences, color associations and other factors of color 1 The COLOROID color-order harmony. system Data are already processed, partly processed and raw, respectively. Catalog of circumstances of the experi- 1.1 Historical survey ments have been documented in the Library of Technical University of Budapest and a survey of experiments is in A series of experiments of great dimensions have been a recently written report [1]. This set of data, being dig- processed between 1962 and 1996 at the Technical Uni- itally stored unfortunately just partly, promises answers versity of Budapest, Hungary, and also in other coun- and formulas on several further questions. Some com- tries, in order to formulate rules of color harmony and plementary experiments have been performed in the last describe aesthetic relationships. Nearly 80 thousand ob- years, like in the case of this article. servers performed 26 million elementary observations and brought elementary decisions during this unique 1.2 Basics of the Coloroid series of experiments. Observers have been classified by various points of view, covering a wide spectrum Conditions of observations and basic concept of the Col- of different aspects, like gender, age, as well as socio- oroid differ from other color order systems. “The aim cultural points of view, as educational qualification, cul- is to provide a system in which the colors are spaced tural identity, habitation, and also physical and mental evenly in terms of their aesthetic effects, rather than of health, and so on. color differences as in the Munsell system, or perceptual 1.2 Basics of the Coloroid 3 Figure 4: A cylindrical projection of the continuous Figure 5: The continuous version of a yellowish-orange limit-color curve of the Coloroid constant hue page content as in the NCS.” [2]. In typical Coloroid experi- √ 3. Lightness V = 10 · Y. It does not contain a ments, the observer can see in a wide view field simulta- 3rd root or logarithmic formula, like the ds line- neously with a set of larger, often not neighboring color element based spaces contain them. samples, and they have to answer relative quickly, not after a long adaptation time. These conditions make it Every hue plane‘s perceptual metric is Euclidean, but it similar to an observation of a complex image in the real fulfills just within hue planes. Color difference formulas life. Under this view conditions the human vision sys- between two different hues are not so simple, and hues tem can distinguish less colors, especially in the darker are equidistant only in a general sense [4]. regions. Thereby the dH esthetical threshold in Col- oroid is 1...4 times greater than the ds line element, Fine structure of perceptual metrics in the 3D Coloroid which is the “unit” of just noticeable difference in other space is under investigation, but the preliminary results systems [3]. A rotating Maxwell wheel was applied in a are very interesting. We obtained not just color differ- great number of experiments, ensuring an arbitrary ad- ences for local and large scales, but also geodetic lines ditive mixture of the black, white and the limit-color, or shortest paths. Latter ones have deep and practical by ratios s, w, and p, respectively, where s + w + p = 1. aesthetical meaning. The limit-colors were the available most saturated solid- Details of the Coloroid will not be presented in this pa- colors instead of spectral colors. per. Just definitions of hue, saturation and lightness, signed by A, T, V respectively, have been recalled. The Due to the very great number of observations and also basic arrangement is similar to other color-order sys- to the obtained good correlations, we consider the basic tems. Fig 3 shows the circle of 48 limit-colors, while concepts of Coloroid like “axioms”, which are valid for fig 4 shows the continuous 3D limit-color line. Fig the above mentioned view-conditions as: 5 illustrates a yellowish orange hue page of Coloroid, where the horizontal axis is the psychometrical satura- 1. Surface of a constant Hue (A) form a plane, con- tion, which in near to the ‘chroma’ of several systems, taining the neutral axis and a hue dependent limit- and the vertical axis depicts the lightness. Fig 6 demon- color, unlike most of the other systems having strates the typical shape of the Coloroid gamut at a fixed curved hue-surfaces, like e.g. the Munsell system. hue value. The two Coloroid gamuts represent the limit- color selections. The larger one corresponds to the spec- 2. Saturation T = const · ratio of the limit-color, trum and purple limit-colors and smaller to the most sat- where the constant depends on the hue. urated solid-colors. 4 1 THE COLOROID COLOR-ORDER SYSTEM Figure 6: A hue plane of the Coloroid with the greater and smaller gamut according to the limit-colors, using Figure 8: The color space of the Coloroid illustrated spectral and solid-color, respectively by its cylindrical projection: the inner gamut is defined by solid-colors, while the large, theoretical gamut is defined by spectral and appropriate purple colors Concepts and formulas of Coloroid can be found in several basic publications [5], [6], [2] and [3]. Fig 7 art- work shows the spatial arrangement of the colors, while fig 8 shows the borderlines of the Coloroid space and its cylindrical arrangement. A deep survey of applica- tion areas can be found in [7], which is a revised and significantly extended edition. Article [8] contains a concise introduction to the basics of the Coloroid, con- necting to a gamut mapping method. The Coloroid has been already successful also in practice by designing new buildings and by contributing in restoration of old parts of cities, e.g.

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