A modulus iteration method for retinex problem

Abstract

SummaryRetinex theory was proposed by Land and McCann, which manifests that the perception of object colors by human eyes is only dependent on the reflectance of the object and unrelated to the illumination amount on the object. Image intensity recorded by digital cameras is the product of reflectance and illumination. The main purpose of the retinex problem is to recover the reflectance from the recorded image just like the human vision system. In this paper, we propose a variational minimization model with physical constraints imposed on reflectance values. We show that the proposed model is equivalent to a linear complementarity problem, and a modulus iteration method is applied to solve it. A large sparse linear system of equations arises in the modulus iteration method. By utilizing the special structure of the coefficient matrix, the solution of the linear system is obtained by solving a smaller linear system of only half of the unknowns. The convergence of the modulus iteration method for solving the linear complementarity problem for the proposed model is also demonstrated. The experiments show that the convergence of the proposed method is much faster than the existing efficient methods for the retinex problem, and the proposed method is also competitive to the existing methods for the retinex problem when considering recovered reflectance quality.