A Variational Model with Barrier Functionals for Retinex

Abstract

This paper proposes a variational model with barriers for Retinex, borrowing the ideas of barrier methods. We first present an energy functional and then deduce a new energy functional from it by adding two barriers. The proposed model is defined as a constrained optimization problem associated with the deduced energy functional. Next, an alternating minimization scheme is used to solve the proposed model. Some theoretic analyses are given for the proposed model and algorithm. Finally, numerical examples are presented to show the effectiveness of the proposed model with its algorithm.

A modulus iteration method for retinex problem

“…We apply the proposed method to restore the reflectances from the images. The proposed method is denoted as “MODULUS.” We also report numerical results of retinex problem for these six images by using some state‐of‐the‐art methods for the retinex problem such as “TV” in the work of Ng et al, “HOTVL1” in the work of Liang et al, and “WH” in the work of Wang et al for comparisons. Because the original reflectance is unknown, we adopt the blind image quality analyzer “natural image quality evaluator” (NIQE) proposed in the work of Mittal et al to judge the quality of the recovered reflectance.…”

“…Because of monotonicity of the logarithm operation, it easily follows that r ≤ 0 and s ≤ l . By introducing variables u , v such that the logarithmic illumination l and the logarithmic reflectance r can be reformulated as Usually, the logarithmic reflectance r = − u is close to the difference between the logarithmic observed image s and the logarithmic illumination l ; see, for instance, the work of Wang et al By assuming that both the logarithmic reflectance r and the logarithmic illumination l are spatially smooth (see, for instance, the works of Wang et al and Kimmel et al), the following constrained optimization model is proposed: where β , ω , μ , ν are positive regularization parameters and ‖·‖ 2 denotes the Euclidean norm. In addition, is the fidelity term, the regularization terms and concur with the smoothness assumption on both r and l .…”

“…In this paper, we present a novel variational model for the retinex problem under the assumptions that both the reflectance and the illumination are spatially smooth. Such assumptions are the same as the ones in the works of Kimmel et al and Wang et al The proposed model can be particularly described as a linear complementarity problem (LCP) and the constraint 0 < R ≤ 1 can be automatically achieved. A modulus iteration method is applied to solve the LCP.…”

Mission-critical monitoring based on surround suppression variational Retinex enhancement for non-uniform illumination images

“…To overcome this problem, many modified Retinex theories have been proposed. Retinex algorithms are basically categorized into path-based methods [12][13][14], center-/ surround-based methods [15][16][17][18], recursive methods [19][20][21], PDE-based methods [22][23][24], and variational methods [11,[25][26][27][28][29][30]. Path-based Retinex methods are the simplest, but they usually necessitate high computational complexity.…”

“…In 2014, L. Wang et al [11] proposed variational bayesian model for Retinex by combining the variational Retinex and Beyesian theory. Due to the shortage of the traditional variational method on limiting the scope of reflectance and illumination components, Wei Wang [30] proposed a variational model with barrier functionals for Retinex. They built a new energy function by adding two barriers for getting a better output.…”