Spectrophotometer measurements are precise, but time- ... camera RGB values to device independent CIELAB ... One way to improve the Pseudo-Inverse.
Digital Camera Characterization for Color Measurements Martin Solli*, Mattias Andersson**, Björn Kruse*, Reiner Lenz* *Center for Creative Media Technology, Linköping University (Sweden) **Digital Printing Center, Mid Sweden University (Sweden) Abstract The use of spectrophotometers for color measurements on printed substrates is widely spread among paper producers as well as within the printing industry. Spectrophotometer measurements are precise, but timeconsuming procedures and faster methods are desirable. Colorimetrically calibrated flatbed scanners have been proved to provide a fast and fairly accurate alternative to spectrophotometers. Moreover, the rapid development of digital cameras has made it possible to transfer successfully implemented methods for color calibration of flatbed scanners to a camera-based system. Earlier presented methods for color calibration of trichromatic devices have been implemented in the camera-based system and improving modifications are proposed. Furthermore, the performance of the calibration can further be enhanced if the spectral sensitivities of the color filters in the camera sensor can be characterized. Methods for filter characterization are presented together with methods that utilize the camera characteristics to enable color measurements. The findings of this study show how a moderately priced consumer digital camera can be used as a fast and inexpensive alternative to spectrophotometers for color measurements on printed substrates.
Introduction In this work, color test charts from the NCS color atlas and charts printed with inkjet on matte-coated substrate, are used for the camera characterization. These charts are illuminated with a light source with known spectral distribution, and each color is measured with both, a camera and a spectrophotometer. Measured values are used as input data in the generation of approximated transformation functions from the device dependent camera RGB values to device independent CIELAB values. Two different methods to find transformation functions are presented, evaluated and compared. The first method is based on regression, and the second method use a characterization of the camera filters to approximatively recover the spectral distribution from the camera RGB values.
Regression A method for colorimetric calibration of scanners proposed by Hardeberg [1] is implemented and used for the camera system. The method features a non-linear cubic root transformation of camera RGB values (eq. 1)
followed by a third order three-dimensional polynomial regression directly to CIELAB values (eq. 2-5). RGB=[RGB]1/3
(1)
Lab=g(RGB)
(2)
G=v’a
(3)
where v=[h0(x), h1(x),…]’, contains measured camera RGB values, and a=[a0, a1,…]’, is a vector of coefficients to be optimized. The result is highly dependent on the choice of v. With a second-order polynomial, v becomes v = [1 R G B R2 RG RB G2 GB B2]’
(4)
Finally, a can be calculated from V and y a = pinv(V) y
(5)
where pinv(V) is the Moore-Penrose pseudo inverse of V=[v1, v2,…] , and y is the observed output data (CIELAB). Hardeberg found that the third-order polynomial regression gave the best result. In this work another vector v is used in the regression. The modified method is called Signal Dependent Regression. The idea behind the new vector is that since different light sources have different energy in different wavelengths, the result of the regression may be improved by using channels recording high energy more than those recording lower energy. The base of the new vector is the third-order polynomial. Then some terms from the fourth-order are added, but only for the two signals, from R, G and B, having the largest energy.
Color filter characterization The aim of this method is to recover approximate spectral distributions from the camera RGB values acquired with the camera. Thereafter, the spectral distributions can be converted to any color space, such as CIELAB. An estimation of W, a matrix containing the spectral sensitivity of each color filter, can be written as W = pinv(R’)’ C
(6)
where R’ is a matrix with spectral reflectances for color patches, and C=[R G B], is a matrix containing the corresponding camera RGB values. Without noise, this solution would be perfect. But under real-world conditions, the method needs improvements. Singular Value Decomposition (SVD), also referred to as principal eigenvector solution, can improve the inverse problem. Hardeberg [1] among others has proved that this method reduces the noise sensitivity a lot. For further improvements, three constraints proposed by
Finlayson et. al. [2] can be added. The first uses Fourier transform to ensure smoothness by restricting the filter spectral sensitivities to being linear combinations of Fourier basis functions. The second is positivity, since a device cannot have negative response to a stimulus. Finally, the third one is modality; the number of peaks in a sensor curve is restricted. Furthermore, the filter characteristics can be used to reproduce the input spectrum from measured camera RGB values. One way to improve the Pseudo-Inverse approach is to take advantage of a priori knowledge of the spectral reflectances that are to be recovered [1]. A set of basis functions is created, well representative of the spectral reflectances that assumingly will be encountered in the measurements. Out of 365 colors, 50 colors with the most different spectral distributions are selected. Thereafter, the most significant components from these 50 colors are extracted using SVD. Finally, the Fourier basis and positivity constraints are applied to further improve the result. The idea of the second new method developed in this work, called MultiSensor, is to extend the matrix C described in equation 6 with combinations of the existing signals from each filter thus creating a new matrix C = [R G B R+G R+B G+B]
(7)
This extended matrix improves the result, the maximum errors in particular, are decreased.
Equipment & measurements Table 1. The used equipment. Camera: Canon EOS 10D (CMOS) Light cabinet: Largo Minispectra Spectrophotometer measurements: Inkjet color charts: PR-650 SpectraColorimeter NCS color charts: MacBeth ColorEye 700 When the Canon RAW image format is used, the sensor response is linear to incoming light intensity.
Results For calibration and evaluation of the regression methods, 365 colored patches from the NCS system are used, evenly distributed throughout the NCS color space. Every second color is used for calibration, and the remaining colors for evaluation. The difference between the reference spectrophotometer measurements and the camera measurements for third-order regression and Signal Dependent Regression are shown in table 2. With the SDR method, 5 % of the measured colors display an error greater than 3 ∆E from the reference measurements. For the color filter characterization, 22 inkjet colors are used for calibration, and 365 NCS colors for evaluation. Figure 1 shows the calculated functions. For an easier evaluation of color errors, the CIE Color Matching Functions translate spectral distributions to CIELAB values. The color differences are shown in table 2. For the MultiSensor method, 60 % has an error less than 3 ∆E, and only 8 % of them an error greater than 6 ∆E.
400
700
400
700
Figure 1. Original RGB functions and MultiSensor functions.
Table 2. Color errors converted to ∆E. Regression methods: Third-order SDR Mean 1.32 1.27 Max 4.56 4.44 Spectrum prediction: Original MultiSensor Mean 2.84 2.84 Max 12.30 9.81
Conclusion This article shows that a moderately priced digital camera can be used for color measurements. Methods for transformation between camera RGB values and device independent color representations are presented. The Signal Dependent Regression shows the best result among the regression methods. It was observed that the most difficult colors to measure were mainly dark and green colors. A disadvantage with regression methods is that it requires a large number of calibration colors, which makes it a time-consuming process. In addition, new calibrations need to be done for each new illumination or type of printed substrate. The filter characterization methods show larger errors than the regression methods, but it has one advantage, the spectral distribution is reproduced. Moreover, when colors with different spectral distributions are selected, fewer colors are necessary in the calibration procedure. In order to reduce the maximum errors, the MultiSensor technique developed in this work is useful. Both methods displayed difficulties to measure the same type of colors. The best reproduction was found for neutral colors, followed by bright colors. Dark and highly saturated colors were the most difficult to measure.
Acknowledgment The support from the Swedish national research program T2F is greatly acknowledged.
References 1.
2.
Hardeberg, Jon Yngve, "Acquisition and Reproduction of Color Images", Ecole National Supérieure des Télecommunications, Départment TSI, France, (1999). Finlayson, et. al, "Recovering Device Sensitivities with Quadratic Programming", 6th Color Imaging Conference: Color Science, Systems, and Applications, IS&T, (1998).
Biography Martin Solli has a MS degree in Media Technology and Engineering from Linköping University, Sweden, where he currently is working with scanner calibrations.
