Optimized basis function for spectral reflectance recovery from tristimulus values

Spectral reflectance is a significant physical property of materials. It plays an important role in color constancy, illumination modeling, and color reproduction. Spectral reflectance basis functions are the most important impact factors for spectral reflectance recovery. Previous methods mainly calculated basis functions for the reflectance spectra data sets by employing the principle component analysis (PCA) and its improved methods. In this paper, we present a new method to solve this problem. Specifically, we propose a new cost function and some constraint conditions to convert the problem into an optimization problem by minimizing the cost function. Unlike the PCA method which yields the orthogonal basis functions for approximating the reflectance spectra, our method yields the nonorthogonal basis functions for better approximating the reflectance spectra. Experimental results show that our derived basis functions are better than those obtained by the PCA method for reflectance spectra recovery.