Illuminant dependence of PCA, NMF and NTF in spectral color imaging

Abstract

In this study principal component analysis (PCA), non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) are applied as dimension reduction methods in color spectrum domain. The effect of light sources to the quality of the reconstructed spectrum is investigated. Due to the orthogonality, the corresponding bases vectors from PCA usually contain negative coefficients and are difficult to implement optically. NTF and NMF find non-negative basis for color spectrum space and are more suitable for optical implementation. Also the energy of NMF and NTF bases is more concentrated than PCA one. They should be more suitable for peaky light sources (i.e. Poly lux or LED) Five reflectance spectra sets from the different sources were used in tests. Four light source spectrums with the various shapes were applied for light source simulation. We evaluate reconstruction spectrum by quality and error measures including AE, GFC and PSNR.