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Cartoon and texture decomposition for color image in opponent color space
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2021-09-27 , DOI: 10.1016/j.amc.2021.126654
You-Wei Wen 1, 2 , Mingchao Zhao 1 , Michael Ng 3
Affiliation  

The Meyer model has been successfully applied to decompose cartoon component and texture component for the gray scale image, where the total variation (TV) norm and the G-norm are respectively modeled to capture the cartoon component and the texture component in an energy minimization method. In this paper, we extend this model to the color image in the opponent color space, which is closer to human perception than the RGB space. It is important to extend the TV norm and the G-norm correspondingly because the color image is viewed as a vector-valued vector. We introduce the definition of the L1 norm and L norm for the vector-valued vector and accordingly define the TV norm and the G-norm for the color image. In order to handle the numerical difficulty caused by the non-differentiability of the TV norm and G-norm, the dual formulations are used to represent these norm. Then the decomposition problem is reformulated into a minimax problem. A first-order primal-dual algorithm is readily applied to compute the saddle point of the minimax problem. Numerical results are shown the performance of the proposed model.



中文翻译:

对立色彩空间中彩色图像的卡通与纹理分解

Meyer模型已成功应用于分解灰度图像的卡通成分和纹理成分,其中分别建模总变异(TV)范数和G-范数,以能量最小化方法捕获卡通成分和纹理成分. 在本文中,我们将此模型扩展到对手色彩空间中的彩色图像,它比 RGB 空间更接近人类的感知。相应地扩展 TV 范数和 G 范数很重要,因为彩色图像被视为向量值向量。我们引入定义1 规范和 向量值向量的范数,并相应地定义彩色图像的 TV 范数和 G 范数。为了处理由 TV 范数和 G 范数的不可微性引起的数值困难,使用对偶公式来表示这些范数。然后分解问题被重新表述为一个极小极大问题。一阶原始对偶算法很容易用于计算极大极小问题的鞍点。数值结果显示了所提出模型的性能。

更新日期:2021-09-28
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