基于光谱色差权重函数的多光谱降维方法研究  

Research on Multispectral Dimension Reduction Method Based on Weight Function Composed of Spectral Color Difference

作　　者：曹前 麻祥才 白春燕 苏娜[1] 崔庆斌 CAO Qian;MA Xiang-cai;BAI Chun-yan;SU Na;CUI Qing-bin(Department of Printing and Packaging Engineering,Shanghai Publishing and Printing College,Shanghai 200093,China)

机构地区：[1]上海出版印刷高等专科学校印刷包装工程系,上海200093

出　　处：《光谱学与光谱分析》2023年第9期2679-2686,共8页Spectroscopy and Spectral Analysis

基　　金：上海市自然科学基金项目(21ZR1422100)资助。

摘　　要：光谱反射率维度高,与光照和观察条件无关,能够真实、客观地描述物体的颜色信息,由物体本身特性决定,因此被称为物体的“指纹”。但是,光谱反射率数据量超过传统三色系统十倍以上,这些巨大的光谱数据在存储、数据处理及传递等方面造成巨大的负担,花费太多的计算时间。如果高维光谱可以通过数学变换方法映射到低维空间,并确保低维空间能够更好地表示原始光谱所覆盖的信息,可以有效地压缩多光谱数据,提高基于光谱的颜色复制的处理效率。针对主成分分析法平等地对待可见光范围的所有波长,重建光谱仅仅是对原始光谱的数学逼近,由于波长对颜色的重要性不同,经常会导致光谱重建误差较小而色度误差较大的问题,提出了一种基于光谱色差权重函数的多光谱降维算法。使用主成分分析法将孟塞尔颜色系统Munsell维度降低到1维,再恢复重建到31维,Munsell的原始光谱和重建光谱的平均光谱色差作为权重函数。以NCS为训练样本,分别以NCS、Munsell和3张多光谱图像为测试样本,分析和比较本文推荐的权重主成分分析法与主成分分析法以及另外4种权重主成分的性能。以D65/2°和A/2°照明观察条件下的CIELAB色差和均方根误差(RMSE)分别评价测试样本的原始光谱和重建光谱之间的色度重建精度和光谱重建精度。实验统计结果表明:相对于主成分分析法,无论测试样本是多光谱数据还是多光谱图像,推荐的方法在牺牲一定光谱重建精度的情况下,在D65/2°和在A/2°两种照明观察条件下的色度重建精度得到显著的提高,而色度重建精度提高对于目前广受关注的基于光谱的颜色复制研究具有非常重要意义。实验统计结果也表明本文推荐的方法的色度重建精度优于目前已经存在的另外4种权重主成分分析法。The reflectance spectrum has a high dimension and has nothing to do with illumination and observation.It can truly and objectively describe the color information of an object.The characteristics of the object itself determine it,so it is called the"fingerprint"of the object.However,the amount of reflectance spectra data is more than ten times that of the traditional three-color system,and these huge spectral data cause huge burdens in terms of storage,data processing,and data transfer,and they spend too much computing time.Suppose the high-dimensional spectrum can be mapped to the low-dimensional space through mathematical transformation methods,and ensure that the low-dimensional space data can better represent the information covered by the original spectrum.In that case,the multi-spectral data can be effectively compressed and the processing efficiency of spectrum-based color reproduction can be improved.PCA treats all wavelengths in the visible range equally,and the reconstructed spectrum is only a mathematical approximation to the original spectrum,which often leads to the problem of small spectral reconstruction error and significant colorimetric reconstruction error.A multispectral dimension reduction algorithm based on the weight function of spectral color difference is proposed in this paper.The dimensionality of Munsell was reduced to one dimension by PCA and then restored to 31 dimensions,and the average spectral color difference between Munsell s original spectrum and its reconstructed spectrum was used as a weight function.Taking NCS as the training sample and NCS,Munsell and 3 multispectral images as the test samples respectively,the performance of the proposed method of this paper and the classical PCA and the other four weighted PCA are analyzed and compared.CIELAB color difference under the conditions of multiple Lighting and viewing(D65/2°and A/2°)and root mean square error(RMSE)evaluate the colorimetric and spectral reconstruction accuracy between the original spectra and the reconstructed sp

关 键 词：多光谱降维 多光谱压缩 主成分分析法 权重函数 光谱色差 

分 类 号：O432.3[机械工程—光学工程]