PhD Thesis DECREASING COLORIMETRIC ERROR IN CASE OF CALIBRATING TRISTIMULUS COLORIMETERES, AND CHARACTERIZING COLOUR SCANNERS AND DIGITAL CAMERAS

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1 Zsolt T. Kosztyán DECREASING COLORIMETRIC ERROR IN CASE OF CALIBRATING TRISTIMULUS COLORIMETERES, AND CHARACTERIZING COLOUR SCANNERS AND DIGITAL CAMERAS PhD Thesis Supervisor: János Schanda DSc University of Pannonia Doctoral School of Information Science and Technology Veszprém 2011

2 Abstract For colorimetric imaging the tristimulus technique is still the best practical method to keep the measurement time within reasonable limits. As a further new demand to the above considerations came the request to be able to measure the colour not only in one spot, but in the entire scene, thus image taking colorimeters had to be developed. Due to the fact that the number of coloured glasses that are available to adjust the detector responsivity to the CIE colour matching functions (CMF) is limited and the number of the filters used in a channel can not be increased without limits to decrease the adjustment error, as this would decrease the sensitivity of the colorimeter, the systematic errors of such instruments is substantial. The systematic of colorimetric error could be very high in case of measuring narrowband solid state lights, for instance colour light emission diodes (LEDs). In this study I investigated how to reduce the systematic error drastically using different kind of matrix-based calibration methods when measuring different kind of light sources. Determining colorimetric error of characterizing colour scanners and digital cameras is very important task for colour accuracy in colour management. At characterizing colour scanners and digital cameras usually the responsivities of the detectors cannot be determined directly. When using indirect methods for spectral and colour characterizations the optimal selection of the reflectant samples can be the key of adequate characterization process with as possible as lowest colorimetric error. The aim of the dissertation was to create new methods for optimal colour sample selection, which can be used for ii

3 colorimetric and spectral characterization too. Matrix correction methods for calibrating tristimulus colorimeters are also introduced. With these matrix correction and optimal colour sample selection methods the colorimetric error of calibration and characterization can be decreased significantly. Using Matrix Correction Methods for Decreasing Colorimetric Error of Tristimulus Colorimeters Due to the fact that the number of coloured glasses that are available to adjust the detector responsivity to the CIE colour matching functions (CMF) is limited and the number of the filters used in a channel can not be increased without limits to decrease the adjustment error, as this would decrease the sensitivity of the colorimeter, the systematic errors of such instruments is substantial. An approach for decreasing the systematic errors is to increase the number of the colorimeter channels (or filters) used for a measurement, i.e. to use one or more additional channels in addition to the, X 1 =X long, X 2 =X short Y, and Z channels. In my dissertation I introduce matrix correction methods for minimizing colorimetric errors when measuring different kind of test-sources. The optimum correction matrix depends on the (test) light source to be measured. If such optimum matrix is used the systematic measurement error will be reduced drastically. The noise propagation with the applied matrix corrections is also investigated. iii

4 Adaptive Statistical Methods for Optimal Colour Selection and Spectral Characterization of Colour Scanner and Cameras The main goal is to decrease colorimetric error also in case of characterizing colour scanners and digital cameras. Despite scanners and digital cameras usually are not used in colorimetric measures the accurate characterization of these devices is one of the most important task of colour management process. There are two different types of the broadband method: the spectral and the colorimetric characterization. The applicability of these methods is highly dependent on the reflectance spectra of the selected colour samples. The additional problem is that the characteristics (i.e. spectral responsivity) of the detectors are not known, and usually cannot be determined directly. The (broadband) colorimetric characterization method handles the input device as a black-box. In this method we do not examine the functioning of the different parts of the device (it is not necessary to determine the spectral power distribution of the source, the spectral transmission of the colour filters and the spectral responsivity of the detectors). Only the input and the output values are known, the transformation function between device dependent RGB and device independent CIE XYZ or CIELAB colour space has to be determined with linear or polynomial regression. In the colorimetric characterization it is very relevant to question the nature of the optimal colour sample set. The spectral responsivity of the detector can be determined directly using a monochromator or interference filters. This will be called the direct or narrowband spectral characterization method. In one hand this method is very iv

5 expensive on the other hand monochromator cannot be used for determine spectral responsivity of colour scanners. The responsivities of the detectors can also be determined indirectly using reflecting colour samples this method is called as broadband spectral characterization methods. Using both broadband (colorimetric/spectral) characterization methods colour samples of known reflectance spectra are scanned. One would expect that the characterization process would be very simple applying a regression method. Using more reflectance spectra in the regression model should improve the estimation of the detector responsivity determination. Applying earlier published methods experiments have shown that with some samples one could improve the estimation, but with other colour samples this was not possible. For example, there are many redundant colour samples in the Munsell-, or the NCS-atlases. The use of these violates, in the regression methods, the condition of independent variables (avoiding correlation) of the characterization process. In my dissertation I show that colorimetric characterization error of both broadband characterization methods are strongly dependent of adequate selected colour reflectant samples. I show how to select colour samples in order to decrease systematic characterization error. The conditions of the regression model using colorimetric and broadband spectral characterization for scanners and cameras is investigated in my dissertation. If these conditions are not satisfied, the estimation of detector responsivity would be distorted and/or the determination would be inefficient. The importance of optimal colour sample selection is emphasized. Selection methods, which improve the condition of the characterization method are judged to be effective. The v

6 selection method, based on statistical classification, introduced in my dissertation improves all broadband (colorimetric and spectral) characterization methods based on a regression analysis. In this case the error of estimation can be decreased very significantly, because the conditions of the regression models are improved. The selection method can be used for any arbitrary colour sample set. The selecting methods improve the assumptions of the characterization method directly. In this way the error of the estimation of sensitivity curves can be very significantly decreased. Hypothesises and Theses of my Research The aim of my research was to create new algorithms and methods to decrease systematic colorimetric error when measuring tristimulus values of different kind of light sources especially narrowband solid state light sources. The main idea of the research was that in case of using tristimulus colorimeter the systematic colorimetric error can be reduced significantly when applying extra channels and responsivity of all channels are taken into account as appropriate coefficients in a correction matrix. This assumption is described in hypothesis H1. H1 Systematic error of tristimulus colorimeter can be decreased if appropriate linear combinations of channel outputs are considered. In my dissertation matrix correction methods have been introduced for decreasing systematic error of tristimulus vi

7 colorimeters determining extra channels responsivities and considering the optimal linear combination of all channel outputs. Results of my research described in my thesis T1. T1 Global matrix correction method was introduced for decreasing systematic error of tristimulus colorimeter considering any arbitrary channel responsivity. By means of this method the optimal linear matrix correction of channel outputs and ideal channel responsivities of extra channels can be determined simultaneously [3][9][10]. Even better results can be obtained with the unique matrix method (decreasing the systematic measurement errors) when different matrices are used to measure different source types. This method can be recommended for four-channel tristimulus colorimeters, where significant reduction of the systematic errors can be obtained. Results of my research described in my thesis T2. T2 Unique matrix correction method was introduced for decreasing systematic error of tristimulus colorimeter. By means of this method unique matrices can be determined for different kind of light sources. This method also can be used for traditional (four-channel) tristimulus colorimeter [3][11]. The adaptive matrix correction method can be used for color LEDs measurements when the method can be combined with different LED spectral distribution approximations. In this case, the matrix values are set up adaptively. vii

8 Results of my research described in my thesis T3. T3 Adaptive matrix correction and spectral characterization method was introduced for decreasing systematic error of tristimulus colorimeter. By means of this method the spectral power distribution of colour solid state light sources can be estimated and optimal linear matrix transformation also can be determined simultaneously [3][4][7]. Unique and adaptive matrix correction methods can be used for traditional 4-filters tristimulus colorimeters. With the discussed (global/unique/adaptive matrix transformation) methods, the chromaticity errors can be eight to hundred times smaller than with detector-based calibration. The other goal of my research was to create new algorithms for decreasing characterization error of different kind of computer input devices (colour scanners and digital cameras). One can see that there are a number of characterization methods, which are different from each other in their detector responsivity error estimation and demands on computation and cost. However, most broadband characterization methods (both spectral and colorimetric) use a regression calculation scheme. The question is whether the conditions of the regression methods are satisfied, or not satisfied. I showed in my dissertation that the applied broadband characterization methods are very sensitive to the fulfillment of their conditionals. Therefore the adequate selected colour samples for characterization process will improve the fulfillment of conditionals and in this way the colorimetric error of viii

9 characterization can be reduced. This assumption is described in hypothesis H2. H2 The optimal colour sample selection is required for appropriate broadband characterization process. The sample selection process must be fit to the characterization method and must be improve conditionals of characterization method in order to reduce the systematic error of characterization error. In my dissertation I compare most broadband characterization methods in case of different kind of light sources and reflectant samples and show these methods sensitivity of conditional fulfillments. I show that the most robust methods are regression and relaxed regression (i.e. principal eigenvectors) methods. In the introduced statistical selection method the color samples are separated into two batches. The first group, classed as so called representative color samples, the second group to serve as test color samples. Sensitivity curves can be estimated with the representative color samples, but the color differences will be calculated using all color samples. This SCRS (Statistical Clustering method for Reflectances and Sources) method has three steps. The introduced (SCRS) selection method improves the condition of the characterization method are judged to be effective. When using this method the error of estimation can be decreased very significantly, because the conditions of the characterization methods based on regression models are improved. The selection method can be used for any arbitrary color sample set. The selecting methods improve the assumptions of the characterization method directly. In this ix

10 way the error of the estimation of sensitivity curves can be very significantly decreased. Results of my research described in my thesis T4. T4 The systematic error of the broadband characterization process based on regression models can be reduced by the introduced statistical colour sample selection method [2][5][6][8]. The introduced algorithms and methods decrease the systematic error of characterization and calibration processes. In one hand the systematic error of tristimulus colorimeter can be reduced drastically with the suggested matrix correction method. On the other hand the colorimetric error of characterization of colour scanners and digital cameras can be decreased when using introduced optimal colour sample selection algorithm. These methods and algorithms was published in scientific journals, and in conference proceedings. x

11 Publication List about this Research SCI Journals [1] Cecilia Sik Lányi, PhD, Zsolt Kosztyán, PhD, Balázs Kránicz, PhD, János Schanda, PhD, DrS, and Mojtaba Navvab, PhD, FIES: Using Multimedia Interactive E-teaching in Color Science, LEUKOS The Journal of the Illuminating Engineering Society of North America 4 (1) pp ISSN: , (Impakt faktor: 0.286) [2] Zsolt Tibor Kosztyán, János Schanda: Adaptive Statistical Methods for Optimal Color Selection and Spectral Characterization of Color Scanners and Cameras. Journal of Imaging Science and Technology 53 (1) pp (Impakt faktor: 0.522) [3] Zsolt T. Kosztyán, George P. Eppeldauer, János D. Schanda: Matrixbased color measurement corrections of tristimulus colorimeters, Applied Optics 49 (12) pp (Impakt faktor: 1.767) Posters [4] Zsolt T. Kosztyán, János Schanda: Using Adaptive Matrix Transformation for Decreasing Colour Measuring Systematic Error in Image Taking Tristimulus Colorimeters, Light and Lighting Conference with Special Emphasis on LEDs and Solid State Lighting May 2009 Budapest, Hungary Hungarian Conference Proceedings [5] Kosztyán Zsolt Tibor, Prof. Dr. Schanda János, Kreschka Miklós: Síkágyas szkennerek színképi jellemzőinek meghatározása, színi transzformáció készítése színhelyes megjelenítéshez. XXX. Jubileumi Kolorisztikai Szimpózium, Eger, május 30. június 1. (a kéziratok lektorált CD-mellékletben jelentek meg) [6] Kosztyán Zsolt Tibor. Statisztikai kiválasztási módszerek színes kamerák és szkennerek karakterizálására. XXXI. Kolorisztikai Szimpózium, Eger, május 7-9. [7] Dr. Kosztyán Zsolt Tibor, Prof. Schanda János: Tristimulusos színmérők színi hibájának csökkentése adaptív mátrixtranszformációval május Eger xi

12 International Conference Proceedings [8] Zs. Kosztyán, J. Schanda: Flatbed scanners and CCD-cameras: colorimetric characterization and uncertainties, 2nd Expert Symposium on Measurement Uncertainty, June 11-17, 2006, pp [9] Zs. Kosztyán, S. Sturm, D. Müller, J. Schanda: Decreasing Colour Measuring Systematic Error in Image Taking Tristimulus Colorimeters, CIE Expert Symposium on Advances in Photometry and Colorimetry, 7-8 July 2008, Turin (Torino), Italy, pp [10] J. Schanda, Zs. Kosztyán: Industrial colorimetry with image resolution, Bulg. Colour Conference, Varna September 27-27, 2008, pp. 1-5 [11] George Eppeldauer, Zs. Kosztyan, J. D. Schanda, G. Schanda, C. C. Miller, T. C. Larason, Y. Ohno, Extension of the NIST Tristimulus Colorimeter for Solid-state Light Source Measurements, Light and Lighting Conference with Special Emphasis on LEDs and Solid State Lighting May 2009 Budapest, Hungary xii