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.

翻译：平滑图像是应用计算机视觉和图形的基本程序。 平滑所需的特性可以是不同的, 甚至是不同任务之间的矛盾。 但是, 平滑操作器的内在平滑性质通常是固定的, 因而无法满足不同应用程序的各种要求。 在本文中, 我们首先引入了在不同的参数设置下表现出巨大灵活性的短线休伯特罚款功能。 然后提出了一个普遍框架, 并引入了短线枢纽处罚功能。 当我们的框架与其强大的灵活性相结合时, 我们的框架能够实现多样化的平滑性质, 甚至可以实现相互矛盾的平滑行为。 它还能够产生以往方法很少能够实现的平滑行为, 因而在具有挑战性的案件中能够实现优异性的表现。 这些共同使得我们的框架能够一系列的应用, 能够在不同的参数设置下表现出极大的灵活性。 然后提出一个普遍框架, 包括提高图像详细度, 清除剪裁工艺品, 引导深度地图的恢复, 清除图像纹理等。 此外, 我们提供了一个高效的数字解决方案, 并且理论上保证了整齐框架, 甚至优化框架是非隐化的, 在挑战性案例中可以实现优度- 测试方法。 将我们的常规方法 降低我们现有的常规方法, 。 以简单的测试方法 将降低我们现有的成本 。 。