基于主成分分析法和二阶多项式回归的多光谱降维算法研究

Research on Multispectral Dimensionality Reduction Based on Second Order Polynomial Regression Combined with Principal Component Analysis

针对主成分多光谱降维算法得到的低维空间没有色度意义、不能很好地与目前主流的色彩管理系统兼容的问题,本研究提出根据色度学公式将高维光谱降维到三维XYZ空间,利用二阶多项式回归结合主成分分析法(PR-PCA)实现三维XYZ空间到高维光谱的转换。并以自然颜色系统(NCS)、孟塞尔颜色系统(Munsell)和2张多光谱图像作为测试样本比较PR-PCA和经典PCA的性能。实验结果表明,相对于经典PCA,基于PR-PCA的多光谱降维方法在牺牲少量光谱重建精度的条件下,色度重建精度得到很大提高,这对光谱颜色复制非常重要,同时该方法得到的低维空间是色度空间,具有色度意义。

In view of the principal component multispectral dimension reduction algorithm without chroma significance and not very compatible with the mainstream color management system,reducing the high dimensional spectrum dimension to three dimensional XYZ space according to chromatid formula,and using the second order polynomial regression combined with principal component analysis(PR-PCA)were proposed to realize transforming the three dimensional XYZ space to high dimensional spectrum,in this study.The performance of PR-PCA was compared with classical PCA by taking NCS,Munsell and two multispectral images as test samples.The results showed that comparing with the classical PCA,the multispectral dimension reduction algorithm of PR-PCA greatly improves the chromaticity reconstruction accuracy when sacrificing a small amount of spectral reconstruction accuracy,which is very important for spectral color replication.Meanwhile,the low-dimensional space obtained by the multispectral dimension reduction algorithm of this study is the chromatic space,which has chromaticity significance.