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

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Abstract

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.

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Funding

Fang Chen and Yu Zhu were supported by the National Natural Science Foundation (No. 11501038) and the Science and Technology Planning Projects of Beijing Municipal Education Commission (No. KM201911232010 and No. KM202011232019), P.R. China. Galina V. Muratova was supported by The Grant of the Government of the Russian Federation (No. 075-15-2019-1928).

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Fang Chen & Yu Zhu

  2. Laboratory of Computational Mechanics, I.I. Vorovich Institute of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don, 344090, Russia

    Galina V. Muratova

Authors
  1. Fang Chen
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  2. Yu Zhu
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  3. Galina V. Muratova
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Correspondence to Fang Chen.

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Chen, F., Zhu, Y. & Muratova, G.V. Two-step modulus-based matrix splitting iteration methods for retinex problem. Numer Algor 88, 1989–2005 (2021). https://doi.org/10.1007/s11075-021-01103-y

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