Improving the Color Constancy of Prints by Ink DesignYongda Chen, Roy S. Berns, and Lawrence A. Taplin, Munsell Color Science Laboratory,Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology, Rochester, New York, USAAbstractA computer simulation was performed to investigate optimal four- and five-ink sets in order to minimize color inconstancy while maintaining a large color gamut. The effect of including a spectrally-flat black ink on color constancy was explored. The relationship between ink shape and the color constancy of prints was also analyzed. The results show that the ink shape in the middle wavelength region is very important for the color constancy of prints. The minimum and maximum color inconstancy indices that the different ink sets can achieve, which were optimized by different objective functions, were explored. The results show that color constancy can be improved by both ink design and lookup table creation.IntroductionColor constancy is the general tendency of the color of an object to remain constant when the level and color of the illumination are changed.1 It is a result of both physiological and psychological compensations. Conversely color inconstancy is the undesirable change in color caused by changes in illumination. There does not yet exist a computational theory sufficient to explain the mechanism of color constancy of human vision. For many applications, it is very important that colored materials exhibit color constancy. However they often deviate significantly in hue when viewed under different light sources. In fact, color inconstancy is unavoidable. That means the perceived color always changes under different illuminants.Color inconstancy is a very important factor to evaluate for the image quality of prints since prints are viewed under many different lighting conditions. The color constancy of neutral has always been a design criterion for photographic dyes.2 Ohta3 explored the optimum combination of cyan, magenta, and yellow dyes to create stable grays under different illuminants. Because of the popularity of ink-jet printing technologies, fortuitous color constancy is less commonplace. The practices of only using CMY for pictorial images and using dye-based black inks with long wavelength reflectance “tails” result in appreciable color inconstancy. A s a consequence, in addition to color gamut expansion,4-6 color constancy should be an ink-design criterion.This paper is divided into two sections. In the first section, the theoretical ink design for color constancy was described. In the second section, color constancy properties of lookup tables combined by the optimized ink sets were evaluated. Optimizing the Ink Spectra while Minimizing Color InconstancyAs mentioned above, color inconstancy depends on the ink spectral properties and can be minimized by optimizing the ink spectral properties while maintaining a relative large color gamut. MethodIn this section, the different parts of the optimization algorithm are described. These metrics and models include the color inconstancy metric, theoretical ink curve function, printing model, gamut calculation, and optimization objective function.Color Inconstancy IndexGenerally a color inconstancy index (CII) is used as a metric to evaluate the extent of color inconstancy. The color inconstancy index is the total color difference between a sample’s colorimetric coordinates under reference and test illuminants using a perceptually uniform color-difference equation. The calculation of the color inconstancy index is described in references 1, 7 and 8: Tristimulus values are calculated for illuminants of interest from an object’s spectral reflectance. Using a chromatic-adaptation transform such as CIECAT02,9 corresponding colors are calculated from each illuminant to D65. The corresponding-color tristimulus values are converted to CIELAB using D65 as the reference white.A weighted CIE94 color difference is calculated with kL= kC= 2 between pairs of corresponding colors. In this manner, hue inconstancy is penalized twice as much as lightness or chroma inconstancy. A s a rule-of-thumb, samples with excellent color constancy have CII values below unity.Absorption Bands of Hypothetical Inks by Symmetric Cubic Spline FunctionIn order to perform ink curve optimization, several different functions were considered to model ink spectra, including a Gaussian function, symmetric cubic-spline function, triangular function, line function, etc. All of these functions can model both one and two peak reflectance curves. A t first, the Gaussian functions were used to simulate hypothetical ink curves.5 Six parameters, two sets each of height, width, and peak wavelength, were necessary to simulate one ink curve in reflectance space. The advantage of this model is that it is very flexible when simulating different ink curves. The disadvantage is that the model has so many parameters that convergence and optimization speeds were slow. Moreover, some parameters became useless in some situations. The width and the peak wavelength were not useful when the height is zero, for example.From previous research, we found that these optimized inks were not as complicated as real ink curves, the ink curves are close to13th Color Imaging Conference Final Program and Proceedings159

Improving the Color Constancy of Prints by Ink Design