Spectral decomposition of black coated fabrics to optimal feasible primaries

In this paper, the reflectance spectra of a series of black coated fabrics were decomposed to a limited number of feasible spectra that could be collected as optimal primaries. In fact, the possibility of finding the optimal feasible vectors with the capability of matching the spectral space of black samples was investigated. In this way, the application of non-negative matrix factorization (NNMF) method was examined on spectral dataset of 363 black coated fabrics to derive the non-negative basis functions. The extracted primaries were then employed for spectral matching of black samples where, one to three non-negative spectra were employed as optimal colorants. Results showed that both the spectral and colorimetric reconstruction errors decreased by increasing the number of primaries while applying of 3 non-negative feasible bases could mimic the spectral behaviors of black samples well. Besides, the role of chromatic primaries in two and three bases system was found very important due to better replication of reflectance spectra that matches the tint effect of blacks.