View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Repositorio Institucional de la Universidad de Alicante Concerning the Calculation of the Color Gamut in a Digital Camera Francisco Martı´nez-Verdu´,1* M. J. Luque,2 P. Capilla,2 and J. Pujol3 1Department of Optics, University of Alicante, Apartado de Correos n° 99, 03080 Alicante, Spain 2Department of Optics, University of Valencia, Dr. Moliner s/n, 46100 Burjassot, Valencia, Spain 3Department of Optics and Optometry, Center for Development of Sensors, Instrumentation and Systems (CD6), Technical University of Catalonia, Rambla de Sant Nebridi n° 10, 08222 Terrassa, Barcelona, Spain Received 3 January 2004; revised 25 November 2005; accepted 11 January 2006 Abstract: Several methods to determine the color gamut of INTRODUCTION any digital camera are shown. Since an input device is additive, its color triangle was obtained from their spectral Color devices1–7 are basically divided into input or capture sensitivities and it was compared with the theoretical sen- devices (scanners and digital cameras) and output devices sors of Ives-Abney-Yule and MacAdam. On the other hand, (softcopy, such as displays, and hardcopy, such as printers). the RGB digital data of the optimal or MacAdam colors Scanners, digital cameras, and displays (CRT, LCD/TFT, were simulated to transform them into XYZ data according plasma, etc.) are additive color devices. However, most to the colorimetric profile of the digital camera. From this, printing devices8 (inkjet, electro-photography, offset, etc.) the MacAdam limits associated to the digital camera are perform by additive and subtractive color mixing. Success- compared with the corresponding ones of the CIE-1931 ful color management5–11 depends on knowing the color XYZ standard observer, resulting that our color device has gamut and the color profile of the device used. Determining much smaller MacAdam loci than those of the colorimetric the gamut of output devices (displays, projectors, and print- standard observer. Taking this into account, we have esti- ers) is relatively easy, both when colors in display or in mated the reduction of discernible colors by the digital paper are generated systematically12 and when color profiles camera applying a chromatic discrimination model and a are applied.13 However, the conceptual problems inherent to packing algorithm to obtain color discrimination ellipses. determining the gamut of input devices (scanners and digital Calculating the relative decrement of distinguishable colors cameras) are numerous. Displays, projectors, and printers by the digital camera in comparison with the colorimetric are electro-optical devices, that is, they generate color dig- standard observer at different luminance factors of the ital images by physical and electronic procedures that are optimal colors, we have found that the camera distinguishes finally seen in a medium (display, screen, or paper), and so considerably fewer very dark than very light ones, but each RGB or CMYK digital data triad corresponds to a relatively much more colors with middle lightness (Y be- single color-stimulus. Scanners and digital cameras are op- tween 40 and 70, or L* between 69.5 and 87.0). This toelectronic devices,14–16 that is, they encode and generate a behavior is due to the short dynamic range of the digital digital image from the light projecting over them from the camera response.© 2006 Wiley Periodicals, Inc. Col Res Appl, 31, original image by means of physical and electronic proce- 000–000, 2006; Published online in Wiley InterScience (www.interscience. dures. Then, this digital image is seen on display and saved wiley.com). DOI 10.1002/col.00000 in some image file format. Key words:digital camera; color triangle; MacAdam limits; The key factor in the performance of input devices is the color discrimination ellipses univariance principle: spectrally different color stimuli may give rise to identical RGB digital data. Therefore, it is very difficult to determine what color-stimulus corresponds to a Correspondence to: Francisco martı´nez-verdu´ (e-mail: [email protected]) RGB triad if the captured scene is not previously known. If Contract grant sponsor: Ministerio de Educacio´n y Ciencia (Spain), we capture a reference scene of known colors (taken from, Contract grant number: DPI2002–00118, DPI2005–08999-C02. for example, a color atlas such as Munsell’s or the NCS) and Volume 31, Number 5, October 2006 1 determine the corresponding RGB values, the next step is to the camera response can be translated to the same space as transform the RGB digital data into XYZ data to determine the reference stimulus by means of a model. For these how the input device encodes these color-stimuli in com- reasons, the gamut obtained with the first procedure may be parison with the human eye. To do this, we must apply the called “input device alone gamut,” whilst the second is input-device’s color profile to the RGB values to derive the rather an “input device plus transform gamut.” corresponding XYZ values. Therefore, the color gamut of an Two different approaches will be carried out to under- input device depends on a color transform (“input device stand better this subject using a real digital camera. In the plus transform” gamut). So, it is not clear a priori if any type first place, if an input device is additive, it is possible to plot of color transform might be associated with the “input into a chromaticity diagram the color triangle associated to device alone” gamut, or if it can be calculated by means of this device and to compare it with the theoretical color other alternative procedures. Note that the color gamut of triangles of sensors that fulfill Luther’s condition (Ives- output devices can be obtained far more simply. Abney-Yule, (Ref. 1, p 128), MacAdam22). RGB triangles In principle, this work would not be necessary if all input are usually used to represent graphically the color gamut of devices were completely linear in an optoelectronic manner displays, but we can use them likewise with input devices and satisfied the Luther condition,17,18 that is, if their color- because they also are additive. Therefore, this approach, that matching functions or scaled spectral sensitivities were ex- disregards the color profile of the digital camera as it will be act linear combinations of the color-matching functions of seen below, is the simplest calculation to understand ini- the CIE standard observer. Let TRGB and TXYZ be the tially the “camera alone” gamut of the input device. color-matching functions of an input device and the color- The second approach to this subject, based on determin- imetric standard observer, respectively, with 41 rows (from ing the “camera plus transform” gamut using a color profile, 380 to 780 nm at 10 nm step) and 3 columns. The nonful- is to select previously the color-stimuli in the scene, either fillment of Luther condition implies that there is a 3 ϫ 41 real (Munsell or NCS chips, IT8 or ColorCheckerDC charts, nonzero matrix C that links both capture systems as follows: etc.) or simulated (vector decomposition,19,23,24 optimal or MacAdam colors,25–27 etc.). This implies in turn that the t t TXYZ ϭ M ⅐ TRGB ϩ C (1) illuminance level, the chromaticity of the light source and the source/detector geometry, are initially fixed. To simulate where M is the basic color profile or connection matrix color capture in these initial conditions, we must use the relating both color spaces,19–21 which is one of the basic spectral power distributions of the color-stimuli of the scene components of any characterization model for these color to estimate the RGB digital data of the input device. It is devices. (AT is transpose matrix of matrix A). assumed that the optoelectronic spectral functions of the If matrix C (or Luther bias) were zero, the XYZ tristimu- input device are known a priori, either by direct measure- lus values derived from the color profile would coincide ment or by simulation under some assumptions about the with the real values and the input device would work as a basic performance of the color device. Then, we should colorimeter, and colors metameric for the eye would also be finally have a set of colors encoded according to the color- so for the camera and vice versa. But, in fact, matrix C is not imetric standard observer in any CIE color space, linear zero, so this initial error is dragged down all of the complete (XYZ, UЈVЈWЈ, etc.) or nonlinear (L*a*b*, etc.) and the color profile (from capture to image editing) and finally it is same set of colors encoded by RGB digital data. In the mixed with the reproduction errors caused by the optoelec- discussion, we address in detail the comparison between this tronic limitation of the dynamic response range, that is, the procedure, where the performance of the camera is “trans- nonlinear errors associated to response clipping due to noise lated” in terms of the color space of the human observer, and saturation. Consequently, due to the nonideal optoelec- and a previous method28 proposed by Morovicˇ and tronic performance and the nonfulfillment of the Luther Morovicˇ, where the optimal colors of the camera are com- condition, the input devices, in raw performance (without puted directly. color rendering to standard output-referred representations), Finally, the number of discernible colors of the camera will always show a color gamut different from that of the and that of the colorimetric standard observer can be com- colorimetric standard observer. puted by assuming that both have the same color metric. A The gamut of the camera can be determined directly by priori, this is achieved by estimating the number of the measuring (or predicting) its optimal colors, that is, by discrimination ellipsoids filling the color solid, which in the determining in each direction of color space the highest human case is associated to the MacAdam limits or Ro¨sch- colorfulness the stimulus can attain without saturating the MacAdam color solid.25–28 Usually, the problem is simpli- camera response.