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

arXiv: https://arxiv.org/abs/1907.09642 · HTML: https://mlsanity.com/paper/1907.09642/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2019.

## Built on by (most cited first, 13 of 13)

- [Guided Depth Map Super-resolution: A Survey](https://mlsanity.com/paper/2302.09598/) (2023)
- [Contrastive Semantic-Guided Image Smoothing Network](https://mlsanity.com/paper/2209.00977/) (2022)
- [Hierarchical Image Peeling: A Flexible Scale-space Filtering Framework](https://mlsanity.com/paper/2104.01534/) (2021)
- [Metropolis Theorem and Its Applications in Single Image Detail Enhancement](https://mlsanity.com/paper/2302.09762/) (2023)
- [Pyramid Texture Filtering](https://mlsanity.com/paper/2305.06525/) (2023)
- [When A Conventional Filter Meets Deep Learning: Basis Composition Learning on Image Filters](https://mlsanity.com/paper/2203.00258/) (2022)
- [Improved Real-time Image Smoothing with Weak Structures Preserved and High-contrast Details Removed](https://mlsanity.com/paper/2307.06298/) (2023)
- [Enhanced Edge-Perceptual Guided Image Filtering](https://mlsanity.com/paper/2310.10387/) (2023)
- [Edge-guided Low-light Image Enhancement with Inertial Bregman Alternating Linearized Minimization](https://mlsanity.com/paper/2403.01142/) (2024)
- [Gaussian highpass guided image filtering](https://mlsanity.com/paper/2503.03284/) (2025)
- [Real-World Depth Recovery via Structure Uncertainty Modeling and Inaccurate GT Depth Fitting](https://mlsanity.com/paper/2504.11820/) (2025)
- [Deep Image Prior with L0 Gradient Regularizer for Image Smoothing](https://mlsanity.com/paper/2601.13400/) (2026)
- [Generative Texture Filtering](https://mlsanity.com/paper/2604.19039/) (2026)

## Abstract (arXiv)

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.