Abstract Retinex theory shows that the color of a scene perceived by human visual system is only dependent on the intrinsic reflectance and unrelated to the illumination. For images recorded by digital cameras, the intensities are the product of the scene reflectance and illumination. Image intensities are different when taken under different illuminations. The aim of image retinex problem is to decompose the reflectance from the image intensities. In this paper, we propose a variational model for image retinex problem. The model can be reduced to a linear complementarity problem and a modulus-based multigrid method is applied to solve it. A pointwise coupled modulus-based Gauss-Seidel iteration scheme is used as a smoother of the multigrid method. The smoothing factor of the smoother is analyzed by using the local Fourier analysis. Both theoretical analyses and numerical results show the efficiency of the proposed method for image retinex problem.

中文翻译：

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一种基于模数的图像 Retinex 多重网格方法

摘要 Retinex 理论表明，人类视觉系统感知的场景颜色仅依赖于内在反射率，与光照无关。对于数码相机记录的图像，强度是场景反射率和照度的乘积。在不同光照下拍摄的图像强度是不同的。图像视网膜问题的目的是从图像强度中分解反射率。在本文中，我们为图像视网膜问题提出了一个变分模型。该模型可以简化为线性互补问题，并应用基于模数的多重网格方法来解决它。基于点耦合模量的 Gauss-Seidel 迭代方案被用作多重网格方法的平滑器。使用局部傅立叶分析来分析平滑器的平滑因子。