IEEE Trans Image Process. 2015 Sep;24(9):2889-904. doi: 10.1109/TIP.2015.2423615.
This paper presents a novel gradient correlation similarity (Gcs) measure-based decolorization model for faithfully preserving the appearance of the original color image. Contrary to the conventional data-fidelity term consisting of gradient error-norm-based measures, the newly defined Gcs measure calculates the summation of the gradient correlation between each channel of the color image and the transformed grayscale image. Two efficient algorithms are developed to solve the proposed model. On one hand, due to the highly nonlinear nature of Gcs measure, a solver consisting of the augmented Lagrangian and alternating direction method is adopted to deal with its approximated linear parametric model. The presented algorithm exhibits excellent iterative convergence and attains superior performance. On the other hand, a discrete searching solver is proposed by determining the solution with the minimum function value from the linear parametric model-induced candidate images. The non-iterative solver has advantages in simplicity and speed with only several simple arithmetic operations, leading to real-time computational speed. In addition, it is very robust with respect to the parameter and candidates. Extensive experiments under a variety of test images and a comprehensive evaluation against existing state-of-the-art methods consistently demonstrate the potential of the proposed model and algorithms.
本文提出了一种新颖的基于梯度相关相似度（Gcs）度量的去色模型，用于真实地保留原始彩色图像的外观。与传统的数据保真项不同，它由基于梯度误差范数的度量组成，新定义的 Gcs 度量计算了彩色图像每个通道与变换后的灰度图像之间的梯度相关性的总和。本文开发了两种有效的算法来解决所提出的模型。一方面，由于 Gcs 度量具有高度的非线性性质，因此采用了包含增广拉格朗日和交替方向法的求解器来处理其近似线性参数模型。所提出的算法具有出色的迭代收敛性，并取得了优异的性能。另一方面，通过从线性参数模型诱导的候选图像中确定具有最小函数值的解，提出了一种离散搜索求解器。非迭代求解器具有简单和快速的优点，仅需进行几次简单的算术运算，实现实时计算速度。此外，它对参数和候选图像具有很强的鲁棒性。在各种测试图像下进行的广泛实验以及与现有最先进方法的综合评估一致证明了所提出的模型和算法的潜力。
