1. 中国科学院西安光学精密机械研究所, 陕西 西安 710119
2. 中国科学院大学, 北京 100049
3. 西安电子科技大学, 陕西 西安 710071
*通讯联系人 e-mail: xuebin@opt.ac.cn

Method for Obtaining Truth Color Values Based on Relative Spectral Power Distribution of Light Source
WANG Hong1,2, YANG Jian-feng1, XUE Bin1,*, SONG Yan-song1,2, XIE Pei-yue3
1. Xi’an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi’an 710119, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China
3. Xidian University, Xi’an 710071, China;
Abstract

Chang’E-3 panoramic camera is designed for color imaging, and a color calibration has to be performed before the launch of the detector. The first step when calibrating the camera is to obtain the ground truth color values of the samples. The color values measured by the traditional method have some significant deviations with the actual values and differ at the color difference and human visual perception. When the values are used to perform calibration, the color differences are not ideal, and the images have a negative effect on human perception. In this study, the white reference coordinates adopted in transformation matrix between XYZ and sRGB color space are redefined by using the relative spectral power distribution of D65 calibration light source. After that, based on the CIE color-computing formula and H. Grassmann color mixing law, the transformation matrix to recalculate RGB color values from XYZ color space is modified. In addition, by means of calculating spectral tristimulus values in sRGB with modified matrix, we give analysis to the factors that caused color distortions. The results of the ground experiment showed that the color differences DE76 for cameras A and B after calibration reduced 0.8 and 0.73 respectively compared with those achieved using traditional method. And when the calibrated matrix is used to correct images taken on lunar surface, color difference reduced 26.50% and 34.47% respectively, and the images have a positive effect on human perception.

Keyword: Chang’E-3;; truth color values; Spectral power distribution; Tristimulus values; Color calibration

1 样本选取

 Figure Option 图1 麦克白经典色卡(a): 24色块的编号; (b): 24色在CIE 1931色品图上的分布Fig.1 Macbeth classic color checker(a): Number of each color patch; (b): Distribution of 24 colors in CIE 1931 color chromaticity diagram

 Figure Option 图2 (a)第13到18色块反射谱; (b)麦克白色卡反射谱和D65光源相对功率谱测试实验平台Fig.2 (a) Reflection spectrum of 13 to 18 color patch; (b) Test platform for measuring reflection spectrum of Macbeth color checker and relative power spectrum of D65 light source

$Xj=k∑λφj(λ)x̅(λ)ΔλYj=k∑λφj(λ)y̅(λ)ΔλZj=k∑λφj(λ)z̅(λ)Δλ(1)$

XYZ空间与sRGB空间之间的标准转换关系式, 如式(2)

$sRsGsB=t11t12t13t21t22t23t31t32t33XYZ=TXYZ→sRGBGXYZ=3.2405-1.5371-0.4985-0.96931.87600.04160.0556-0.20401.0572XYZ(2)$

 Figure Option 图3 根据XYZ与sRGB颜色空间之间的标准 转换矩阵计算得到的RGB颜色值Fig.3 RGB values obtained by the standard transform matrix between XYZ and sRGB color space

2 光源修正法

 Figure Option 图4 D65光源相对功率谱分布的CIE标准值和测试值Fig.4 The relative power spectrum of D65 light source for CIE standard and measured

$[R]=Xr[X]+Yr[Y]+Zr[Z][G]=Xg[X]+Yg[Y]+Zg[Z][B]=Xb[X]+Yb[Y]+Zb[Z](3)$

$C[C]=sR[R]+sG[G]+sB[B](4)$

$X=sRXr+sGXg+sBXbY=sRYr+sGYg+sBYbZ=sRZr+sGZg+sBZb(5)$

$XYZ=CrxrCgxgCbxbCryrCgygCbybCrzrCgzgCbzbsRsGsB(6)$

$sRsGsB=ygzb-ybzgCrΔxbzg-xgzbCrΔxgyb-xbygCrΔybzr-yrzbCgΔxrzb-xbzrCgΔxbyr-xrybCgΔyrzg-ygzrCbΔxgzr-xrzgCbΔxryg-xgyrCbΔXYZ=T'XYZ→sRGB[X Y Z]T(7)$

$Δ=xr(ygzb-ybzg)+xg(ybzr-yrzb)+xb(yrzg-ygzr)(8)$

$T'XYZ→sRGB=7.3725-3.4972-1.1342-2.51144.86070.10770.1772-0.64973.3664(9)$

$sR=k'∑λφj(λ)sr̅(λ)ΔλsG=k'∑λφj(λ)sg̅(λ)ΔλsB=k'∑λφj(λ)sb̅(λ)Δλ(10)$

$sR=t11X+t12Y+t13Z(11)$

$k∑λφj(λ)sr̅(λ)Δλ=t11k∑λφj(λ)x̅(λ)Δλ+t12k∑λφj(λ)y̅(λ)Δλ+t13k∑λφj(λ)z̅(λ)Δλ=k∑λφj(λ)(t11x̅(λ)+t12y̅(λ)+t13z̅(λ))Δλ$(12)

$sr̅sg̅sb̅=t11t12t13t21t22t23t31t32t33=x̅y̅z̅(13)$

 Figure Option 图5 (a)修正前后sRGB颜色空间的三刺激值曲线; (b)D65光源CIE标准XYZ值和测试值在CIE1931色品图上位置Fig.5 (a) Tristimulus values curve in sRGB color space before and after modification; (b) The position of CIE standard XYZ values and measured values for D65 light source at CIE 1931 chromaticity diagram

3 光源修正法流程

 Figure Option 图6 光源修正法流程图Fig.6 Flow chart of light source modified method

 Figure Option 图7 光源修正法计算得到的RGB颜色值Fig.7 RGB color values of Macbeth color checker calculated by light source modified method

4 实验验证

4.1 地面试验图像评价

$rtruthgtruthbtruth=M11M12M13M21M22M23M31M32M33rcamgcambcam(14)$

 Figure Option 图8 校正后室外图像: (a)标准转换矩阵和(b)光源修正法Fig.8 Outdoor images after correction using different truth color values obtained by (a) standard transform matrix method and (b) light source correction method

4.2 在轨图像评价

 Figure Option 图9 (a)厂商给定值, (b)标准转换矩阵法和(c)光源修正法, 校正后在轨图像Fig.9 Image taken on lunar surface after color correction using different truth color values obtained by (a) manufacturing plant, (b) standard transform matrix method and (c) light source correction method

5 结论

The authors have declared that no competing interests exist.

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