Constrained nonlinear optimization approaches to color-signal separation

Separating a color signal into illumination and surface reflectance components is a fundamental issue in color reproduction and constancy. This can be carried out by minimizing the error in the least squares (LS) fit of the product of the illumination and the surface spectral reflectance to the actual color signal. When taking in account the physical realizability constraints on the surface reflectance and illumination, the feasible solutions to the nonlinear LS problem should satisfy a number of linear inequalities. Four distinct novel optimization algorithms are presented to employ these constraints to minimize the nonlinear LS fitting error. The first approach, which is based on Ritter's superlinear convergent method (Luengerger, 1980), provides a computationally superior algorithm to find the minimum solution to the nonlinear LS error problem subject to linear inequality constraints. Unfortunately, this gradient-like algorithm may sometimes be trapped at a local minimum or become unstable when the parameters involved in the algorithm are not tuned properly. The remaining three methods are based on the stable and promising global minimizer called simulated annealing. The annealing algorithm can always find the global minimum solution with probability one, but its convergence is slow. To tackle this, a cost-effective variable-separable formulation based on the concept of Golub and Pereyra (1973) is adopted to reduce the nonlinear LS problem to be a small-scale nonlinear LS problem. The computational efficiency can be further improved when the original Boltzman generating distribution of the classical annealing is replaced by the Cauchy distribution.