  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.
