IEEE Trans Image Process. 2018 Mar;27(3):1214-1229. doi: 10.1109/TIP.2017.2779601. Epub 2017 Dec 4.
This paper discusses a novel conceptual formulation of the fractional-order variational framework for retinex, which is a fractional-order partial differential equation (FPDE) formulation of retinex for the multi-scale nonlocal contrast enhancement with texture preserving. The well-known shortcomings of traditional integer-order computation-based contrast-enhancement algorithms, such as ringing artefacts and staircase effects, are still in great need of special research attention. Fractional calculus has potentially received prominence in applications in the domain of signal processing and image processing mainly because of its strengths like long-term memory, nonlocality, and weak singularity, and because of the ability of a fractional differential to enhance the complex textural details of an image in a nonlinear manner. Therefore, in an attempt to address the aforementioned problems associated with traditional integer-order computation-based contrast-enhancement algorithms, we have studied here, as an interesting theoretical problem, whether it will be possible to hybridize the capabilities of preserving the edges and the textural details of fractional calculus with texture image multi-scale nonlocal contrast enhancement. Motivated by this need, in this paper, we introduce a novel conceptual formulation of the fractional-order variational framework for retinex. First, we implement the FPDE by means of the fractional-order steepest descent method. Second, we discuss the implementation of the restrictive fractional-order optimization algorithm and the fractional-order Courant-Friedrichs-Lewy condition. Third, we perform experiments to analyze the capability of the FPDE to preserve edges and textural details, while enhancing the contrast. The capability of the FPDE to preserve edges and textural details is a fundamental important advantage, which makes our proposed algorithm superior to the traditional integer-order computation-based contrast enhancement algorithms, especially for images rich in textural details.
本文讨论了一种新的分数阶变分框架理论，用于提出一种分数阶偏微分方程（FPDE）形式的 Retinex 模型，以实现多尺度非局部对比度增强和纹理保持。传统的整数阶计算对比度增强算法存在明显的缺点，例如振铃伪影和阶梯效应，仍然需要特别的研究关注。分数阶微积分在信号处理和图像处理领域的应用中具有潜在的优势，主要是因为它具有长期记忆、非局部性和弱奇异性等特点，以及分数微分能够以非线性方式增强图像的复杂纹理细节。因此，为了解决传统整数阶计算对比度增强算法存在的上述问题，我们研究了是否可以将分数阶微积分的保持边缘和纹理细节的能力与纹理图像多尺度非局部对比度增强相结合。受此需求的启发，本文提出了一种新的分数阶 Retinex 变分框架理论。首先，我们采用分数阶最陡下降法实现 FPDE。其次，我们讨论了限制性分数阶优化算法和分数阶柯西-弗里德里希斯-莱维条件的实现。最后，我们进行了实验，分析 FPDE 增强对比度的同时保持边缘和纹理细节的能力。FPDE 保持边缘和纹理细节的能力是一个基本的重要优势，这使得我们提出的算法优于传统的整数阶计算对比度增强算法，特别是对于富含纹理细节的图像。
