Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of one smoothing operator is usually fixed and thus cannot meet the various requirements of different applications. In this paper, we first introduce the truncated Huber penalty function which shows strong flexibility under different parameter settings. A generalized framework is then proposed with the introduced truncated Huber penalty function. When combined with its strong flexibility, our framework is able to achieve diverse smoothing natures where contradictive smoothing behaviors can even be achieved. It can also yield the smoothing behavior that can seldom be achieved by previous methods, and superior performance is thus achieved in challenging cases. These together enable our framework capable of a range of applications and able to outperform the state-of-the-art approaches in several tasks, such as image detail enhancement, clip-art compression artifacts removal, guided depth map restoration, image texture removal, etc. In addition, an efficient numerical solution is provided and its convergence is theoretically guaranteed even the optimization framework is non-convex and non-smooth. A simple yet effective approach is further proposed to reduce the computational cost of our method while maintaining its performance. The effectiveness and superior performance of our approach are validated through comprehensive experiments in a range of applications. Our code is available at https://github.com/wliusjtu/Generalized-Smoothing-Framework.

中文翻译：

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边缘保留和结构保留图像平滑的通用框架

图像平滑是计算机视觉和图形应用中的基本过程。不同任务之间所需的平滑属性可能不同甚至相互矛盾。然而，一个平滑算子的固有平滑特性通常是固定的，因此不能满足不同应用的各种要求。在本文中，我们首先介绍了截断的 Huber 惩罚函数，它在不同的参数设置下表现出很强的灵活性。然后提出了一个通用框架，其中引入了截断的 Huber 惩罚函数。结合其强大的灵活性，我们的框架能够实现多样化的平滑特性，甚至可以实现相互矛盾的平滑行为。它还可以产生以前方法很少能实现的平滑行为，从而在具有挑战性的情况下实现卓越的性能。这些共同使我们的框架能够进行一系列应用，并能够在多项任务中超越最先进的方法，例如图像细节增强、剪贴画压缩伪影去除、引导深度图恢复、图像纹理去除、此外，提供了一个有效的数值解，即使优化框架是非凸和非光滑的，理论上也能保证其收敛性。进一步提出了一种简单而有效的方法来降低我们方法的计算成本，同时保持其性能。我们方法的有效性和卓越性能通过一系列应用中的综合实验得到验证。我们的代码可在 https://github 上找到。