VIDEO-COLORIMETRY MEASUREMENT OF CIE 1931 XYZ BY DIGITAL CAMERA
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1 VIDEO-COLORIMETRY MEASUREMENT OF CIE 1931 XYZ BY DIGITAL CAMERA Yoshiaki Uetani Dr.Eng., Associate Professor Fukuyama University, Faculty of Engineering, Department of Architecture Fukuyama , JAPAN ABSTRACT A new colorimetry technique by a digital camera is developed and named "Video-Colorimetry". To eliminate the difference in products, the digital camera is colorimetrically calibrated using a spectra-colorimeter, a xenon lamp, and color samples. The calibrated results are described as a series of regression functions. In the actual videocolorimetry, the colorimetric calibration functions transfer the RGB signals on a digital color image into the absolute values of the CIE 1931 tristimulus values XYZ pixel by pixel. The XYZ values of each pixel are transferred into the absolute luminance Y, color coordinates xy, correlated color temperature, etc. The validation by the spectracolorimeter shows reasonable accuracy of the video colorimetry. 1. INTRODUCTION To evaluate the color in the interior or exterior of buildings, the spatial distribution of color in a visual field should be measured colorimetrically. Though a conventional telescopic colorimeter could measure the color of a field point by point, it might take a long time to finish a scanning and the obtained distribution could be too coarse to analyze the spatial distribution of color. For the application of colorimetry in research and practice of architecture, the author has developed the video-colorimetry systems using color CCD video cameras. The first system was composed of a CCD color video camera and a video capture board with a desktop computer 1), 2). It was colorimetrically calibrated with a tri-filtered colorimeter. The RGB values of each pixel on a color video image were converted into the absolute values of CIE 1931 color coordinates (x,y). The color coordinates were transferred into the correlated color temperature (CCT) for the measurement of the CCT distribution of the sky to estimate the cloud cover. 374
2 Session VII: Applications of Colorimetry The second system was composed of a precision color CCD camera and interface board with a desktop computer 3). The system was colorimetrically calibrated with a spectra-colorimeter. The RGB values of each pixel on a color video image were converted into the absolute values of CIE 1931 color coordinates (x,y) for the colorimetry of building interiors and exteriors. This paper describes the third system in which the colorimetric calibration technique is applied to a digital camera 4). The latest colorimetry system measures the absolute values of CIE 1931 tristimulus values XYZ of each pixel on captured images. The XYZ values are converted into the absolute luminance Y, color coordinates (x,y), and correlated color temperature (CCT). 2. METHODOLOGY 2.1 Basic formula The CIE 1931 tristimulus values X, Y, Z and R, G, B are related by the following equations, X = R G B Y = R G B (1) Z = R G B where the value Y is identical with the luminance, which has the unit of candela per square meters [cd/m 2 ]. The National Television System Committee (NTSC) in USA recommended the color television standards in Countries as USA, CANADA, Japan, and Mexico adopted this standard. Many other countries have chosen different system as SECAM or PAL. The transformation equations from the normalized RGB video signals Rv, Gv, Bv of the NTSC system to the normalized CIE 1931 tristimulus values Xn, Yn, Zn for the illuminant C are expressed as, Xn = Rv Gv, Bv Yn = Rv Gv, Bv (2) Zn = Rv Gv, Bv The transformation equations for the illuminant D 65 are given as follows 5). Xn = Rv Gv, Bv Yn = Rv Gv, Bv (3) Zn = Rv Gv, Bv Uetani Y.: Video-Colorimetry Measurement of CIE 1931 XYZ by Digital Camera 375
3 The parameters in the transformation equations were decided by the colors of CRT phosphors available when the NTSC system was proposed a half century ago. Recent TV systems tend to adopt the new standards by the Society of Motion Picture and Television Engineers (SMPTE) and European Broadcasting Union (EBU) which propose closer colors to modern phosphors. In this paper, the NTSC equations (3) for the illuminant D 65 is adopted through the preliminary calibration with the digital camera to compare the formulae including the NTSC (C), NTSC (D 65 ), SMPTE(C), EBU, and HDTV standards. The NTSC formulae are so popular that a lot of image analysis software and hardware have utilized them to convert RGB images to device independent CIE XYZ images. However, simple applications of these formulae provide no more than relative values of CIE XYZ, though the absolute XYZ values are essential to the applications of colorimetry in research and practice of architecture. On the other hand, the new method described in this paper converts the RGB values of each pixel on a color image into the absolute values of CIE XYZ by the colorimetric calibration of the digital camera. 2.2 The Inverse Matrix Colorimetric Calibration The purpose of the colorimetric calibration is to obtain the calibration functions that convert the normalized values of RGB signals captured by a digital camera into the absolute values of CIE 1931 tristimulus values XYZ which might be measured by a spectra-colorimeter as the reference. In the colorimetric calibration of the former studies by the author 1) 2) 3), captured video values Rv, Gv, Bv are transferred into the normalized CIE 1931 tristimulus values Xv, Yv, Zv by the NTSC formula (2) or (3) at first. Then the regression analyses were applied between the normalized values Xv, Yv, Zv and the absolute values X, Y, Z measured by the reference spectra-colorimeter. This straightforward calibration was accurate but not efficient in collecting sample data. If any of the captured video values Rv, Gv, Bv beyond the range of digitization, all the normalized values Xv, Yv, Zv must be discarded. This problem occurred frequently for the color chips of high chromatisity (e.g. red, green, blue, etc.). In this paper, a new technique, "the Inverse Matrix Colorimetric Calibration" is introduced as follows. 2.2(a) Normalized values of RGB signals A digital camera captures the video images of color samples illuminated by a reference lamp at 376
4 Session VII: Applications of Colorimetry various illuminance levels. The settings of exposure (e.g. shutter speed, f-stop of the lens, gain control of the CCD, etc.) and white balance (e.g. daylight, incandescent lamp, fluorescent lamp, etc.) must be recorded for each video image. The normalized values of RGB signals Rv, Gv, Bv of each color sample on captured video images are read numerically by image analysis software. 2.2(b) Absolute values of CIE XYZ and the reference RGB signal values A reference spectra-colorimeter measured the absolute values of CIE 1931 tristimulus values Xs, Ys, Zs of each color sample at the same conditions of illumination as the video images. The inverse functions of equations (3) convert the absolute values of Xs, Ys, Zs into the reference RGB signal values Rvs, Gvs, Bvs as follows. Rvs = Xs Ys Zs Gvs = Xs Ys Zs (4) Bvs = Xs Ys Zs 2.2(c) Regression functions The regression analysis between the Rvs, Gvs, Bvs and Rv, Gv, Bv decides the set of regression functions Fr, Fg, Fb. Rvs = Fr(Rv, E, W) Gvs = Fg(Gv, E, W) (5) Bvs = Fb(Bv, E, W) where E and W are the parameters of exposure and white balance controls of the digital camera. Though most digital cameras have the functions of automatic controls, the video-colorimetry described here requires a digital camera that has repeatable manual controls of white balance and exposure. 2.3 Video colorimetry in practice In the actual video colorimetry, the digital camera captures the video images of objects. The image analysis software read normalized RGB signal values Rv, Gv, Bv first, then convert them to the reference RGB signal values Rvs, Gvs, Bvs by the regression functions (5), and finally obtains the absolute values of CIE 1931 tristimulus values X, Y, Z by the transformation equations (3). Uetani Y.: Video-Colorimetry Measurement of CIE 1931 XYZ by Digital Camera 377
5 The values X, Y, Z of each pixel are transferred into the color coordinates (x,y) and the correlated color temperature T 6) as follows. x = X / (X + Y + Z) y = Y / (X + Y + Z) (6) T = -437 n n n (7) where, n = (x ) / (y ) 3. COLORIMETRIC CALIBRATION AS A CASE STUDY 3.1 Instruments The digital still camera (Nikon, E2n) used for the case study is capable of capturing a 24bit color images of 1280 by 1000 pixels through a conventional still camera lens (e.g. Nikon, AF Zoom Nikkor 35-70/2.8D). Each of the RGB signals of a pixel is expressed by an 8-bit integer between 0 and 255. The installed special optics reduce a whole circle image by the fisheye lens (Nikon, Fisheye 8mm F2.8S, Figure 1) to fit the 2/3 inch CCD array. Figure 1 The digital still camera with the fisheye lens 378
6 Session VII: Applications of Colorimetry The white balance is manually set to CLOUDY position, which corresponds to 6500K in CCT according to the user s manual 7). The shutter speed, and f-stop are also manually controlled and unified to the exposure value Ev as a parameter of the brightness. Ev = log 2 (F 2 /T) (8) where, F is the f-stop value of the iris, T is the shutter speed [sec]. The images are stored in a PC card. The RGB values of images are read and processed by an image analysis software (NIH Image, on a note-type PC (Apple, PowerBook 1400c). The colorimetric reference for the calibration is a spectra-colorimeter (Photo research, PR650, Figure 2). The 24 chips of color samples (Macbeth, Color checker, Figure 3) are illuminated by a Xenon lamp (Ushio, UXL-500D) in a dark room. The illuminance values on the color samples are changed from 353 lx to 4867 lx by controlling the distance to the lamp. Figure 2 The spectra-colorimeter (left) and the digital still camera with the zoom lens Uetani Y.: Video-Colorimetry Measurement of CIE 1931 XYZ by Digital Camera 379
7 Figure 3 The 24 chips of color samples Figure 4 Scatter diagrams of the Rvs-Rv, Gvs-Gv, and Bvs-Bv 3.2 Regression functions Figure 4 shows the scatter diagrams of the Rvs-Rv, Gvs-Gv, and Bvs-Bv. The regression analysis resulted in the following equations (9), and the parameters shown in Table 1. In most cases, the correlative coefficients Rr, Rg, and Rb beyond 0.9. The regression functions are also drawn in Figure
8 Session VII: Applications of Colorimetry Table 1 Parameters for the regression functions Ev a r0 (Ev) a r1 (Ev) a r2 (Ev) R r a g0 (Ev) a g1 (Ev) a g2 (Ev) R g a b0 (Ev) a b1 (Ev) a b2 (Ev) R b e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e Rvs = a r0 (Ev) + a r1 (Ev)*Rv + a r2 (Ev)*Rv 2 Gvs = a g0 (Ev) + a g1 (Ev)*Gv + a g2 (Ev)*Gv 2 (9) Bvs = a b0 (Ev) + a b1 (Ev)*Bv + a b2 (Ev)*Bv 2 The following equations obtain the absolute values of CIE 1931 tristimulus values X, Y, Z pixel by pixel. The equations (6) and (7) transfer the values X, Y, Z of each pixel into the color coordinates (x,y) and the correlated color temperature T. The regression functions and parameters are described as a macro program for the image analysis software. X = Rvs Gvs Bvs Y = Rvs Gvs Bvs (10) Z = Rvs Gvs Bvs 4. APPLICATION The video-colorimetry technique was applied to measure the luminance and the color coordinates on the interior and exterior of the university hall at Fukuyama University (Figure 5), as well as the luminance and correlated color temperature of the sky (Figure 6). The color images captured by the digital camera are transferred to the PC. The macro program on the image analysis software read the R, G, B values pixel by pixel, and convert into the absolute values of the CIE 1931 XYZ, the color coordinates, and the correlated color temperature. For the validation, the spectra-colorimeter measures the XYZ values at the same time. Figure 7 and Figure 8 show the comparison of the CIE XYZ values and the color coordinates measured by the video-colorimeter and the spectra-colorimeter on the interior and exterior of the university hall. Though the video-colorimetry slightly overestimates, the errors are small enough for the application to evaluate the colors of buildings. Uetani Y.: Video-Colorimetry Measurement of CIE 1931 XYZ by Digital Camera 381
9 Figure 5 Video-colorimetry of the XYZ and (x,y) on the exterior and interior of a building Figure 6 Video-colorimetry of XYZ, (x,y) and CCT of the sky 382
10 Session VII: Applications of Colorimetry Figure 7 Comparison of CIEXYZ values measured by the video-colorimeter and the spectra-colorimeter Figure 8 Color coordinates measured by the video-colorimeter and the spectra-colorimeter Uetani Y.: Video-Colorimetry Measurement of CIE 1931 XYZ by Digital Camera 383
11 5. CONCLUTION A new colorimetry technique is developed. The system is simply composed of a digital camera, a note-type PC, and a macro program on image analysis software. The digital camera is calibrated with a spectra-colorimeter. At the actual colorimetry, the color image of the scene captured by the digital camera is transferred to the PC. The macro program converts the RGB values on color images into the absolute values of CIE 1931 XYZ pixel by pixel. The XYZ values are also transferred to the color coordinates and the correlated color temperature. Finally, the author names this new colorimetry technique as "Video-Colorimetry". Acknowledgment The image processing is performed using the NIH Image program written by Wayne Rasband at the U.S. N.I.H. Nomenclature X, Y, Z Absolute values of the CIE 1931 tristimulus values XYZ. R, G, B Absolute values of the CIE 1931 tristimulus values RGB. x, y Color coordinates T Correlated color temperature Xn, Yn, Zn Normalized values of the CIE XYZ Rv, Gv, Bv Normalized values of the video signals RGB. Xs, Ys, Zs Absolute values of the CIE XYZ measured by the reference spectra-colorimeter Rvs, Gvs, Bvs Reference values of the video signals RGB as the inverse functions of Xs, Ys, Zs References (1) Uetani Y., et.al.: Cloud Cover Measurement Using Colour Video Images, Proceedings of the VIIth European Lighting Conference LUX EUROPA 1993, Vol.2, pp , (2) Uetani Y.: Colorimeter by Color Video Image and its Application, Proceedings of CIE 23rd Session, Vol.1, pp , (3) Uetani Y.: Measurement of color coordinates by color video camera, Proc. of Annual Meeting of Chugoku Branch of A.I.J., March 1996 (in Japanese). (4) Uetani Y.: Measurement of Luminance and color coordinates by a Digital Camera, Annual conference of IEIJ, 1998 (in Japanese). (5) K.B.Benson, J.C.Whitaker: Television Engineering Handbook Featuring HDTV System, McGraw-Hill, (6) McCamy, C. S.: Correlated color temperature as an explicit function of chromaticity coordinates, Color Res. Appl. 17, pp , (7) Nikon E2/E2n Operation manual, Nikon, 1997 (in Japanese). 384
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