A modulus iteration method for retinex problem

Abstract

Summary Retinex 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.

A class of two-step modulus-based matrix splitting iteration methods for quasi-complementarity problems

“…In another direction, the MMS iteration methods have been extended to solve other types of complementarity problems, including the NCP (Xia and Li 2015;Xie et al 2016;Zheng and Liu 2018), the ICP (Hong and Li 2016;Wang et al 2018Wang et al , 2019aCao and Wang 2019), the QCP (Wu and Guo 2018) and so on. Other significant developments include finding better convergence wide (Zhang and Ren 2013;Ke and Ma 2014;Cvetković et al 2016;Li and Yin 2018), constructing efficient preconditioners Dai et al 2019) and testing their performance in actual applications Yang et al 2018) often with excellent results.…”