Two-step modulus-based matrix splitting iteration methods for retinex problem

Retinex theory was proposed by Land in the 1970s. Its theoretical basis is that the color of an object is determined by the reflection ability of the object to the light of long wave, medium wave, and short wave, rather than by the absolute value of the reflected light intensity. There is color sense consistency in Retinex theory. The main purpose of Retinex problem is to recover the reflection properties of objects from the images obtained under a certain illumination intensity, so as to obtain the real colors of objects. There are many methods for solving the Retinex problem. In this paper, based on a variational minimization model with physical constraints of reflectance value, we first transform the Retinex problem into a linear complementarity problem, and then propose a class of two-step modulus-based matrix splitting iteration methods to solve this problem. We also prove the convergence of the two-step modulus-based matrix splitting iteration methods for solving the linear complementarity problem. The experimental results show that the convergence speeds of the proposed methods are much faster than the existing methods for solving the Retinex problem, and that the advantages of the new methods over the existing ones could be significant in the quality of the reflectance recovery.

Automated summary

The Retinex theory proposes that an object's color is determined by its reflection ability to different wavelengths of light, rather than the intensity of the reflected light. The main goal of Retinex theory is to recover the true colors of objects from images. A new two-step modulus-based matrix splitting iteration method is proposed in this study to solve the Retinex problem, showing faster convergence speeds and significant improvement in reflectance recovery quality compared to existing methods.