  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, a non-convex
non-smooth optimization framework is proposed to achieve diverse smoothing
natures where even contradictive smoothing behaviors can be achieved. To this
end, we first introduce the truncated Huber penalty function which has seldom
been used in image smoothing. A robust framework is then proposed. When
combined with the strong flexibility of the truncated Huber penalty function,
our framework is capable of a range of applications and can outperform the
state-of-the-art approaches in several tasks. In addition, an efficient
numerical solution is provided and its convergence is theoretically guaranteed
even the optimization framework is non-convex and non-smooth. The effectiveness
and superior performance of our approach are validated through comprehensive
experimental results in a range of applications.
