# A Generalized Framework for Edge-preserving and Structure-preserving Image Smoothing

## TL;DR

This paper introduces a versatile, non-convex optimization framework utilizing a truncated Huber penalty for diverse image smoothing tasks, outperforming existing methods with guaranteed convergence.

## Contribution

It presents a novel non-convex, non-smooth optimization framework with a truncated Huber penalty for flexible, structure-preserving image smoothing, along with an efficient, convergent numerical solution.

## Key findings

- Outperforms state-of-the-art smoothing methods in various tasks
- Capable of achieving contradictory smoothing behaviors
- Provides a theoretically guaranteed convergence proof

## Abstract

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.