Spectral Reflectance Reconstruction With Color Constancy

Given the tristimulus value of an object, its reflectance reconstruction has important applications in the field of cross-media color reproduction. Common algorithms for reconstruction reflectance, including the basis vector method, Wiener estimation method, weighted pseudo-inverse method, etc., are derived based on the reconstructed reflectance and the original reflectance as the reconstruction and evaluation objective. All algorithms map low dimensional tristimulus value or RGB to high dimensional spectral reflectance. Hence most of these algorithms need to be trained using a training dataset. However, in many application areas, color constancy or color inconstancy index (CII) should be considered in product design to ensure that the object is perceived as the same color under different lighting conditions. Object' s spectral reflectance determines the color constancy property of the object. Takahama and Nyatani developed a linear programming method for reconstructing reflectance based on the given tristimulus values so that the reconstructed reflectance has a better color constancy. However, test results showed that the reflectance reconstructed by this method has stair-like shape, which is much different from the real object reflectance. After that, Berns et al. further improved the Takahama and Nyatani method by introducing further constraints. It was found that the reflectance reconstructed by the improved method is smooth but heavily oscillated. Li and Luo proposed a smoothing constrained quadratic programming algorithm. The reconstructed reflectance is s smooth and close to the reflectance of real object color. In this paper, a new algorithm or more exactly, a new constrained nonlinear optimization algorithm is proposed to reconstruct reflectance based on the given tristimulus values so that the reconstructed reflectance is smooth and has a better color constancy property. The proposed method is tested using the reflectance dataset measured from 1 560 Munsell chips from Munsell Color System and compared with other methods. The comparison results show that our method is not only better than Takahama and Nyatani method, Berns et al. method and Li and Luo method in terms of color constancy index, but also better or similar to other methods in terms of root mean square error (RMSE) and good fitting coefficient (GEC). Therefore, the proposed method has important application in many industries with color constancy requirements for designing products.