成像系统中的光谱反射率重建
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摘要
随着计算机图像处理技术的飞速发展,彩色图像和多光谱图像越来越多地应用于颜色信息的展现、传递以及复制。不同的成像设备具有各自的色彩特征,而且所获得及传递的颜色信息都是设备相关的。为了能够精确地得到颜色信息,需要对成像设备进行色彩表征,得到与设备无关的所成像物体的光谱反射率。本文对在非线性成像系统下的光谱反射率重建方法和在反射率重建过程中代表颜色的选取方法进行了研究。
当成像系统为非线性或测量过程受到噪声干扰时,已有的光谱反射率重建方法都无法得到较高的重建精度。例如,线性的维纳估计法无法很好地处理非线性的问题。为了很好地处理系统非线性和测量噪声,本文研究了文献中结合多项式的普通最小二乘法和正则化最小二乘法。实验结果表明,在光谱误差和色度误差方面,正则化最小二乘法明显优于维纳估计法和普通最小二乘法。
色彩表征过程中通常会用到标准色卡,但由于标准色卡的颜色样本数量较大,在实际成像系统中使用时有诸多不便。考虑到颜色样本之间存在较大冗余,可从中选出具代表性的少数样本用于光谱表征。本论文提出了一种代表颜色的分步选取算法,即首先通过假设一个虚拟成像系统,根据全局误差最小的原则,挑选出部分最具代表性的颜色,估计出实际成像系统的光谱响应函数,然后在此基础上继续选择其余的代表颜色。实验表明,本论文所提出的方法在光谱精度及色度方面均优于先前方法。
With the rapid development of modern computer image processing technologies, color images and multispectral images have been widely used in the presentation, transfer and copying of color information. Different imaging systems have different characteristics, and all the color information they get and transfer are device-dependent, so it is necessary to find a way to get the device-independent color information. Spectral reflectance reconstruction, also referred as spectral characterization, aims to recover accurate spectral reflectance of object surface by employing standard color charts. This dissertation studies the methods for spectral reflectance reconstruction and the methods for selection of representative colors.
When the imaging process is not a linear system or influenced by the measurement noise, the spectral reconstruction methods in hand cannot work very well. For instance, Wiener estimation only works well under linear systems. In order to cope with the nonlinearity and measurement noise, we studied the polynomial regression solved by ordinary least squares and regularized least squares. Experiment results show that, in terms of spectral and colorimetric error metrics, the regularized method performs better than Wiener estimation and ordinary polynomial regression.
As there are always a large number of color samples on a color chart, spectral characterization becomes a time-consuming process for practical application. Some methods have been presented to selected representative color samples based on the redundancy of the colors on a chart. However, these methods only consider the distribution of spectral reflectance, and thus the selected colors may not be optimal for a specific imaging system. To deal with this problem, we proposed a sequential method for the selection of most representative colors, which consists of two steps. In the first step, a part of representative colors is selected according to the minimization of mean spectral root-mean-square error, by assuming a virtual imaging system. The spectral sensitivity of the real imaging system is then calculated based on these selected samples. In the second step, additional representative colors are selected based on the characteristics of the real imaging system. Experiment shows that the proposed method outperforms the previous methods in terms of both spectral and colorimetric accuracy.
当成像系统为非线性或测量过程受到噪声干扰时,已有的光谱反射率重建方法都无法得到较高的重建精度。例如,线性的维纳估计法无法很好地处理非线性的问题。为了很好地处理系统非线性和测量噪声,本文研究了文献中结合多项式的普通最小二乘法和正则化最小二乘法。实验结果表明,在光谱误差和色度误差方面,正则化最小二乘法明显优于维纳估计法和普通最小二乘法。
色彩表征过程中通常会用到标准色卡,但由于标准色卡的颜色样本数量较大,在实际成像系统中使用时有诸多不便。考虑到颜色样本之间存在较大冗余,可从中选出具代表性的少数样本用于光谱表征。本论文提出了一种代表颜色的分步选取算法,即首先通过假设一个虚拟成像系统,根据全局误差最小的原则,挑选出部分最具代表性的颜色,估计出实际成像系统的光谱响应函数,然后在此基础上继续选择其余的代表颜色。实验表明,本论文所提出的方法在光谱精度及色度方面均优于先前方法。
With the rapid development of modern computer image processing technologies, color images and multispectral images have been widely used in the presentation, transfer and copying of color information. Different imaging systems have different characteristics, and all the color information they get and transfer are device-dependent, so it is necessary to find a way to get the device-independent color information. Spectral reflectance reconstruction, also referred as spectral characterization, aims to recover accurate spectral reflectance of object surface by employing standard color charts. This dissertation studies the methods for spectral reflectance reconstruction and the methods for selection of representative colors.
When the imaging process is not a linear system or influenced by the measurement noise, the spectral reconstruction methods in hand cannot work very well. For instance, Wiener estimation only works well under linear systems. In order to cope with the nonlinearity and measurement noise, we studied the polynomial regression solved by ordinary least squares and regularized least squares. Experiment results show that, in terms of spectral and colorimetric error metrics, the regularized method performs better than Wiener estimation and ordinary polynomial regression.
As there are always a large number of color samples on a color chart, spectral characterization becomes a time-consuming process for practical application. Some methods have been presented to selected representative color samples based on the redundancy of the colors on a chart. However, these methods only consider the distribution of spectral reflectance, and thus the selected colors may not be optimal for a specific imaging system. To deal with this problem, we proposed a sequential method for the selection of most representative colors, which consists of two steps. In the first step, a part of representative colors is selected according to the minimization of mean spectral root-mean-square error, by assuming a virtual imaging system. The spectral sensitivity of the real imaging system is then calculated based on these selected samples. In the second step, additional representative colors are selected based on the characteristics of the real imaging system. Experiment shows that the proposed method outperforms the previous methods in terms of both spectral and colorimetric accuracy.
引文
[1]J.Y.Hardeberg,Acquisition and reproduction of color images:colorimetric and multispectral approaches(Universal Publishers,2001),dissertation.com
[2]张伟峰,基于小框架核的支持向量回归理论及在光谱反射率重建中的应用,[中山大学博士学位论文],广州,中山大学,2008,75-82
[3]徐海松,颜色信息工程,杭州:浙江大学出版社,2005年12月
[4]Go Series cameras,http://www.qimaging.com/products/cameras/publication/index.php
[5]M.D.Fhirchild,Color Appearance Models,Addison-Wesley,New Jersey,1998
[6]G.W.Hong,M.R.Luo,P.A.Rhodes,A study of digital camera colorimetric characterization based on polynomial modeling.Color Research and Application,26(1),2001,76-84
[7]P.C.Hung,Colorimetric calibration in electronic imaging devices using a look-up-table in interpolations.Journal of Electronic Imaging,2(1),1993,53-61
[8]H.R.Kang,P.G.Anderson,Neural network application to color scanner and printer calibrations.Journal of Electronic Imaging,1(2),1992,125-135
[9]B.Hill,The history of multispectral imaging at Aachen University of Technology,2002,http://www.multispectral.org
[10]H.L.Shen,J.H.Xin,Spectral characterization of a color scanner by adaptive estimation,Journal of the Optical Society of America A,21(7),2004,1125-1130
[11]W.K.Pratt,Digital I4maging Processing,4th edition,Wiley,New York,2007
[12]N.Shimano,Recovery of spectral reflectances of objects being imaged without prior knowledge,Image Processing,IEEE Transactions on,15(7),2006,1848-1856
[13]H.L Shen,P.Q.Cai,S.J.Shao,J.H.Xin,Reflectance reconstruction for multispectral imaging by adaptive Wiener estimation,Optics Express,15(23),2007,15545-15554
[14]H.Halleishi,T.Hasegawa,A.Hosoi,Y.Yokoyama,N.Tsumura,Y.Miyake,System design for accurately estimating the reflectance spectra of art paintings.Appl Opt.39,2000,6621-6632
[15]N.Shimano,K.Terai,M.Hironaga,Recovery of spectral reflectances of objects being imaged by multispectral cameras,Journal of the Optical Society of America A,24,2007, 3211-3219
[16] J. Y. Hardeberg, F. Schmitt, and H. Brettel, Multispectral color image capture using liquid crystal tunable filter, Optical Engineering. 41 ,2002, 2532-2548
[17] L. Maloney, Evaluation of linear models of surface spectral reflectance with small number of parameters, Journal of the Optical Society of America A, 3, 1986, 1673-1683
[18] M. Shi, G. Healey, Using reflectance models for color scanner calibration. Journal of the Optical Society of America A, 19(4), 2002, 645-656
[19] J. Cohen, Dependency of spectral reflectance curves of the Munsell color chips. Appl. Opt. 39,1964,6621-6632
[20] L. Maloney, Evaluation of linear models of surface spectral reflectance with small numbers of parameters, J. Opt. Soc. Am. A3, 1986, 1673-1683
[21] L. Maloney, B. A. Wandell, Color constancy: a method for recovering surface spectral reflectance, J. Opt. Soc. Am. A 3, 1986, 29-33
[22] R. Schettini, S. Zuffi, A computational strategy exploiting genetic algorithms to recover color surface reflectance functions, Neural Comput. & Applic. 16, 2007, 69-79
[23] H. L. Shen, John. H. Xin, Spectral characterization of a color scanner based on optimized adaptive estimation, J. Opt. Soc. Am. A, 23(7), 2006, 1566-1569
[24] V. Cheung, S. Westland, C. J. Li, J. Hardeberg, D. Connah, Characterization of trichromatic color cameras by using a new multispectral imaging technique, J. Opt. Soc. Am. A, 22(7), 2005,1231-1240
[25] V. Cardei, B. Funt, Committee-based color constancy, in Proc. IS&T/SID Seventh Color Imaging Conf.: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Virginia, 1999), 1999, 311-313
[26] H. Stokman, T. Gevers, Selection and fusion of color models for image feature detection, IEEE Trans. Pattern Anal. Mach. Intell. 29, 2007, 371-381
[27] H. L. Shen, J. H. Xin, S. J. Shao, Improved reflectance reconstruction for multispectral imaging by combining different techniques, Optics Express, 15(9), 2007, 5531-5536
[28] R. McDonald, K. J. Smith, CIE94 - a new colour difference formaula, J. Soc. Dyers Colour. 111, 1995,376-379
[29] V. Cheung, S. Westland, Methods for optimal color selection, Journal of Imaging Science and Technology, 50,2006, 481-488
[30] M. Mohammadi, M. Nezamabadi, R. S. Berns, L A. Taplin, Spectral imaging target development based on hierarchical cluster analysis, in Proceedings of Twelfth Color Imaging Conference, (IS&T, 2004), 59
[31] H. L. Shen, H. G. Zhang, J. H. Xin, S. J. Shao, Optimal selection of representative colors for spectral reflectance reconstruction in a multispectral imaging system, Applied Optics, 47(13), 2008, 2494-2502
[32] 张贤达,矩阵分析与应用,北京：清化大学出版社,2006 年12月, 341-401
[33] M. J. Vrhel, R. Gershon, and L. S. Iwan, Measurement and analysis of object reflectance spectra, Color Res. Appl., 19, 1994, 4-9
[34] M. G. A. Thomson, S. Westland, Colour-imager calibration by parametric fitting of sensor responses, Color Res. Appl. 26, 2001,442-449
[35] J. M. DiCarlo and B. A. Wandell, Spectral estimation theory: beyond linear but before Bayesian, Journal of the Optical Society of America A, 20(7), 2003, 1261-1270
[36] Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction, Applied Optics, 41(23), 2002,4840-4847
[37] D. R. Connah and J. Y. Hardeberg, Spectral recovery using polynomial models, in Proc. of SPIE-IS&T Electronic Imaging, SPIE 5667,2005,65-75
[38] V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, T. Jaaskelainen, and S. D. Lee, Regularized learning framework in the estimation of reflectance spectra from camera responses, Journal of the Optical Society of America A, 24(9), 2007, 2673-2683
[39] A. Bjorck, Numerical Methods for Least Squares Problems, SIAM, 1996
[40] A. Neumaier, Solving ill-conditioned and singular linear systems, a tutorial on regularization, SIAM Rev. 99, 1998, 636-666
[41] M. L. Luo, G. Cui, and B. Rigg, The development of the CIE 2000 color-difference formula: CIEDE2000, Color research and application, 26,2001 , 340-350
[42] L. W. Macdonald, M. R. Lou, Color Imaging: Vision and Technology, Chichester, UK: Wiley, 1999
[43] K. Barnard, B. Funt, Camera characterization for color research, Color Research and Application,27,2002,152-163
[2]张伟峰,基于小框架核的支持向量回归理论及在光谱反射率重建中的应用,[中山大学博士学位论文],广州,中山大学,2008,75-82
[3]徐海松,颜色信息工程,杭州:浙江大学出版社,2005年12月
[4]Go Series cameras,http://www.qimaging.com/products/cameras/publication/index.php
[5]M.D.Fhirchild,Color Appearance Models,Addison-Wesley,New Jersey,1998
[6]G.W.Hong,M.R.Luo,P.A.Rhodes,A study of digital camera colorimetric characterization based on polynomial modeling.Color Research and Application,26(1),2001,76-84
[7]P.C.Hung,Colorimetric calibration in electronic imaging devices using a look-up-table in interpolations.Journal of Electronic Imaging,2(1),1993,53-61
[8]H.R.Kang,P.G.Anderson,Neural network application to color scanner and printer calibrations.Journal of Electronic Imaging,1(2),1992,125-135
[9]B.Hill,The history of multispectral imaging at Aachen University of Technology,2002,http://www.multispectral.org
[10]H.L.Shen,J.H.Xin,Spectral characterization of a color scanner by adaptive estimation,Journal of the Optical Society of America A,21(7),2004,1125-1130
[11]W.K.Pratt,Digital I4maging Processing,4th edition,Wiley,New York,2007
[12]N.Shimano,Recovery of spectral reflectances of objects being imaged without prior knowledge,Image Processing,IEEE Transactions on,15(7),2006,1848-1856
[13]H.L Shen,P.Q.Cai,S.J.Shao,J.H.Xin,Reflectance reconstruction for multispectral imaging by adaptive Wiener estimation,Optics Express,15(23),2007,15545-15554
[14]H.Halleishi,T.Hasegawa,A.Hosoi,Y.Yokoyama,N.Tsumura,Y.Miyake,System design for accurately estimating the reflectance spectra of art paintings.Appl Opt.39,2000,6621-6632
[15]N.Shimano,K.Terai,M.Hironaga,Recovery of spectral reflectances of objects being imaged by multispectral cameras,Journal of the Optical Society of America A,24,2007, 3211-3219
[16] J. Y. Hardeberg, F. Schmitt, and H. Brettel, Multispectral color image capture using liquid crystal tunable filter, Optical Engineering. 41 ,2002, 2532-2548
[17] L. Maloney, Evaluation of linear models of surface spectral reflectance with small number of parameters, Journal of the Optical Society of America A, 3, 1986, 1673-1683
[18] M. Shi, G. Healey, Using reflectance models for color scanner calibration. Journal of the Optical Society of America A, 19(4), 2002, 645-656
[19] J. Cohen, Dependency of spectral reflectance curves of the Munsell color chips. Appl. Opt. 39,1964,6621-6632
[20] L. Maloney, Evaluation of linear models of surface spectral reflectance with small numbers of parameters, J. Opt. Soc. Am. A3, 1986, 1673-1683
[21] L. Maloney, B. A. Wandell, Color constancy: a method for recovering surface spectral reflectance, J. Opt. Soc. Am. A 3, 1986, 29-33
[22] R. Schettini, S. Zuffi, A computational strategy exploiting genetic algorithms to recover color surface reflectance functions, Neural Comput. & Applic. 16, 2007, 69-79
[23] H. L. Shen, John. H. Xin, Spectral characterization of a color scanner based on optimized adaptive estimation, J. Opt. Soc. Am. A, 23(7), 2006, 1566-1569
[24] V. Cheung, S. Westland, C. J. Li, J. Hardeberg, D. Connah, Characterization of trichromatic color cameras by using a new multispectral imaging technique, J. Opt. Soc. Am. A, 22(7), 2005,1231-1240
[25] V. Cardei, B. Funt, Committee-based color constancy, in Proc. IS&T/SID Seventh Color Imaging Conf.: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Virginia, 1999), 1999, 311-313
[26] H. Stokman, T. Gevers, Selection and fusion of color models for image feature detection, IEEE Trans. Pattern Anal. Mach. Intell. 29, 2007, 371-381
[27] H. L. Shen, J. H. Xin, S. J. Shao, Improved reflectance reconstruction for multispectral imaging by combining different techniques, Optics Express, 15(9), 2007, 5531-5536
[28] R. McDonald, K. J. Smith, CIE94 - a new colour difference formaula, J. Soc. Dyers Colour. 111, 1995,376-379
[29] V. Cheung, S. Westland, Methods for optimal color selection, Journal of Imaging Science and Technology, 50,2006, 481-488
[30] M. Mohammadi, M. Nezamabadi, R. S. Berns, L A. Taplin, Spectral imaging target development based on hierarchical cluster analysis, in Proceedings of Twelfth Color Imaging Conference, (IS&T, 2004), 59
[31] H. L. Shen, H. G. Zhang, J. H. Xin, S. J. Shao, Optimal selection of representative colors for spectral reflectance reconstruction in a multispectral imaging system, Applied Optics, 47(13), 2008, 2494-2502
[32] 张贤达,矩阵分析与应用,北京：清化大学出版社,2006 年12月, 341-401
[33] M. J. Vrhel, R. Gershon, and L. S. Iwan, Measurement and analysis of object reflectance spectra, Color Res. Appl., 19, 1994, 4-9
[34] M. G. A. Thomson, S. Westland, Colour-imager calibration by parametric fitting of sensor responses, Color Res. Appl. 26, 2001,442-449
[35] J. M. DiCarlo and B. A. Wandell, Spectral estimation theory: beyond linear but before Bayesian, Journal of the Optical Society of America A, 20(7), 2003, 1261-1270
[36] Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction, Applied Optics, 41(23), 2002,4840-4847
[37] D. R. Connah and J. Y. Hardeberg, Spectral recovery using polynomial models, in Proc. of SPIE-IS&T Electronic Imaging, SPIE 5667,2005,65-75
[38] V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, T. Jaaskelainen, and S. D. Lee, Regularized learning framework in the estimation of reflectance spectra from camera responses, Journal of the Optical Society of America A, 24(9), 2007, 2673-2683
[39] A. Bjorck, Numerical Methods for Least Squares Problems, SIAM, 1996
[40] A. Neumaier, Solving ill-conditioned and singular linear systems, a tutorial on regularization, SIAM Rev. 99, 1998, 636-666
[41] M. L. Luo, G. Cui, and B. Rigg, The development of the CIE 2000 color-difference formula: CIEDE2000, Color research and application, 26,2001 , 340-350
[42] L. W. Macdonald, M. R. Lou, Color Imaging: Vision and Technology, Chichester, UK: Wiley, 1999
[43] K. Barnard, B. Funt, Camera characterization for color research, Color Research and Application,27,2002,152-163