摘要： 基于相机RGB预测物体光谱反射率的研究一直备受研究者们的关注。传统方法都是通过单一光源下的信息进行光谱反射率恢复。最近，Zhang等在Color Research & Application报道了一种基于单光源相机RGB信息预测物体光谱反射率的两步方法。首先基于单个光源下的相机响应RGB值，挑选出一定量的训练数据，采用多项式模型和伪逆的方法预测出不同光源下的CIE XYZ值；然后根据预测的多光源下的CIE XYZ值及整体训练数据预估光谱反射率，再通过预估的光谱反射率挑选一定量训练样本，通过伪逆方法预测出物体光谱反射率。尽管仍然基于一个光源下的相机响应RGB，但通过映射到多光源下的色度值XYZ，提高输入信息的维度来优化光谱反射率的重建精度。受Zhang等工作的启发，提出新的基于单一光源下相机的raw RGB响应信息，通过三阶多项式模型扩展的加权最小二乘方法对多光源下的CIE XYZ值进行预测，然后根据预测出的多光源下的CIE XYZ值再通过维纳估计的方法进行光谱反射率重建，通过这样的两步方法实现从相机响应RGB到光谱反射率的重构。该新方法，采用全体训练数据，应用十分方便，避免了Zhang等的方法需要挑选一定量的局部训练样本的问题。同时Zhang等的方法挑选出的局部训练样本同等重要，而该方法在第1步中，根据训练样本与给定的测试样本的接近程度，赋予训练样本不同的权重，以提高预测精度。通过采用140色色卡作为训练样本，24色色卡和自制的44色印刷品样本进行测试，以判断预测和实测反射率接近程度的均方根误差（RMSE）和人感知色差为评价标准进行比较，结果表明，该方法明显优于Zhang等的方法，而且预测精度随着光源数量的增加而提高，当光源个数达到6时，表现最佳。
关键词：多光源；光谱反射率重建；加权；维纳估计
Abstract：The research on predicting the spectral reflectance information of objects based on the camera RGB value has always attracted researchers’ attention. The traditional method is to restore spectral reflectance through the information under a single light source. Recently, Zhang et al. [Color Research & Application, 2017, 42: 68] proposed a two-step method for predicting reflectance based on camera RGB information under a single light source. Firstly, the camera response RGB value under a single light source is transformed to CIE XYZ values under different light sources through a polynomial model with local training samples using a pseudo-inverse method. Then the reflectance can be estimated based on the predicted CIE XYZ values under multiple light sources using local training samples and pseudo-inverse method. Though the method still uses camera RGB information under a single light source, obtaining CIE XYZ values under multiple illuminants improves the reconstruction accuracy of the spectral reflectance. Motivated by Zhang et al., a new two-step method is proposed for reconstructing spectral reflectance based on the raw camera RGB. Firstly, camera raw RGB is transformed to CIE tristimulus values under multi-illuminants via polynomial expansion of order 3 and weighted least square approach. Reflectance of the object is predicted based on the transformed CIE tristimulus values under multi-illuminants using the Wiener estimation. The prosed method uses the full set of training samples in order to avoid selecting a certain number of training samples that existed with the method of Zhang et al. Hence the proposed method is easy to be applied. Furthermore, in the method of Zhang et al., selected training samples are considered as equalimportant, while the proposed method assigns different weights to each of the training samples depending on the closeness to the given test sample in the first step so that prediction accuracy is increased. Comparison between the proposed method and the method given by Zhang et al. is considered. Both methods are trained using the X-Rite Color Checker Standard Digital (SG) chart and tested using the Color Checker Classic Chart and self-made 44 printed samples. Comparison results have shown that the proposed method outperforms the method given by Zhang et al. in terms of root mean square error (RMSE) and CIEDE2000 colour difference. Furthermore, the prediction accuracy of the proposed method is improved with the increase of the number of illuminants used, and the proposed method performs the best with 6 illuminants.
Key words：Multi-illuminants; Spectral reflectance reconstruction; Weighting coefficients; Wiener estimation
李富豪，李长军. 基于相机rawRGB通过加权多项式和维纳估计方法重建光谱反射率[J]. 光谱学与光谱分析, 2021, 41(10): 3281-3285.
LI Fu-hao, LI Chang-jun. Spectral Reflectance Reconstruction Based on Camera Raw RGB Using Weighted Third-Order Polynomial and Wiener Estimation. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2021, 41(10): 3281-3285.
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