相机响应函数定标的正则化方法
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摘要
相机响应函数是真实场景辐射量与图像灰度值之间的映射关系,对相机响应函数的标定具有重要的研究价值。根据相机的成像原理给出了相机响应函数的数学模型,分析了最小二乘法标定相机响应函数存在的病态问题。为了获得稳定、精确的相机响应函数,提出了一种正则化方法对相机响应函数进行标定,该方法在索波列夫空间中设置不同的正则算子。通过实验分别论证索波列夫参数不同时相机响应函数的稳定性,确定了索伯列夫空间参数,应用L曲线法确定了正则化参数。验证结果表明,正则化方法能够显著提高相机响应函数标定的稳定性和精确性。
Camera response function is the mapping between the real scene radiation and the image gray value,and it is significant to the calibration of the camera response functions.According to the imaging principle of the camera,the mathematical model of the camera response function was given,and the ill-posed problem of the least squares method for the calibration of the camera response function was analyzed.To obtain a stable and accurate camera response function,a regularization method using the variable regular operators set in the Sobolev space was proposed to calibrate the camera response function.The stability of camera response function was demonstrated under different Sobolev operators.The regularization parameters were determined by the L curve method and verified by experiments.The results indicate that the regularization method can improve the stability and accuracy of the calibration of the camera response function significantly.
Camera response function is the mapping between the real scene radiation and the image gray value,and it is significant to the calibration of the camera response functions.According to the imaging principle of the camera,the mathematical model of the camera response function was given,and the ill-posed problem of the least squares method for the calibration of the camera response function was analyzed.To obtain a stable and accurate camera response function,a regularization method using the variable regular operators set in the Sobolev space was proposed to calibrate the camera response function.The stability of camera response function was demonstrated under different Sobolev operators.The regularization parameters were determined by the L curve method and verified by experiments.The results indicate that the regularization method can improve the stability and accuracy of the calibration of the camera response function significantly.
引文
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[2]HSU Y F,CHANG S F.Camera response functions for image forensics:an automatic algorithm for splicing detection[J].IEEE Transactions on Information Forensics and Security,2010,5(4):816-825.
[3]SHEN F,ZHAO Y M,JIANG X Z,et al.Recovering high dynamic range by Multi-Exposure Retinex[J].Journal of Visual Communication and Image Representation,2009,20(8):521-531.
[4]TAI Y W,CHEN X,KIM S,et al.Nonlinear camera response functions and image deblurring:theoretical analysis and practice[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(10):2498-2512.
[5]张伟,谢蓄芬,王付刚,等.变积分时间的红外相机单点绝对辐射定标法[J].红外与激光工程,2012,41(8):2090-2095.
[6]都琳,孙华燕,张廷华,等.克服动态问题影响的相机响应函数标定[J].光学精密工程,2016,24(6):1510-1519.
[7]MANDERS C,AIMONE C,MANN S.Camera response function recovery from different illuminations of identical subject matter[C]//International Conference on Image Processing.Singapore:IEEE,2004:2965-2968.
[8]MANDERS C,MANN S.Determining camera response functions from comparagrams of images with their raw datafile counterparts[C]//Proceedings of2004International Symposium on Intelligent Multimedia,Video and Speech Processing.Hong Kong:IEEE,2004:418-421.
[9]TAKAMATSU J,MATSUSHITA Y.Estimating camera response functions using probabilistic intensity similarity[C]//2008IEEE Conference on Computer Vision and Pattern Recognition.Anchorage:IEEE,2008:1-8.
[10]MANN S,PICARD R W.Being undigital with digital cameras:extending dynamic range by combining differently exposed picture[C]//Proceedings of IS&T 48th Annual Conference.Washington:Society for Imaging Science and Technology,1995:422-428.
[11]MITSUNAGA T,NAYAR S K.Radiometric self calibration[C]//Proceedings 1999IEEE Computer Society Conference on Computer Vision and Pattern Recognition.Fort Collins:IEEE,1999:374-380.
[12]DEBEVEC P E,MALIK J.Recovering high dynamic range radiance maps from photographs[C]//SIGGRAPH’97proceedings of the 24th annual conference on computer graphics and interactive techniques.New York:ACM Press,1997,97:369-378.
[13]方华猛,易本顺,甘良才,等.高动态范围图像合成中相机响应函数的快速标定[J].光子学报,2013,42(6):737-741.
[14]章卫祥,周秉峰.一个稳健的用于HDR图像的相机响应函数标定算法[J].计算机学报,2006,29(4):658-663.
[15]GOOSSENS B,LUONG H,AELTERMAN J,et al.Reconstruction of high dynamic range images with poisson noise modeling and integrated denoising[C]//IEEE International Conference on Image Processing.Brussels:IEEE,2011:3429-3432.
[16]孙新志,李小林.复变量移动最小二乘近似在Sobolev空间中的误差估计[J].应用数学和力学,2016,37(4):416-425.
[17]吴淑君.Orlicz-Sobolev空间中几类Kirchhoff型方程解的研究[D].上海:上海大学,2016.
[18]AKYZ A O,GENTAV A.Special section on HDR imaging:a reality check for radiometric camera response recovery algorithms[J].Computers and Graphics,2013,37(7):935-943.
[20]STICKEL J J.Data smoothing and numerical differentiation by a regularization method[J].Computersand Chemical Engineering,2010,34(4):467-475.
[21]KIM K,LEEM K H,PELEKANOS G.An alternative to Tikhonov regularization for linear sampling methods[J].Acta Applicandae Mathematicae,2010,112(2):171-180.