# Quarter Laplacian Filter for Edge Aware Image Processing

arXiv: https://arxiv.org/abs/2101.07933 · HTML: https://mlsanity.com/paper/2101.07933/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 20 Jan 2021.

## Builds on (most cited first, 4 of 4)

- [Deep Bilateral Learning for Real-Time Image Enhancement](https://mlsanity.com/paper/1707.02880/) (2017)
- [Fast Image Processing with Fully-Convolutional Networks](https://mlsanity.com/paper/1709.00643/) (2017)
- [Side Window Filtering](https://mlsanity.com/paper/1905.07177/) (2019)
- [Weighted Mean Curvature](https://mlsanity.com/paper/1903.07189/) (2019)

## Built on by (most cited first, 9 of 9)

- [EGGS: Edge Guided Gaussian Splatting for Radiance Fields](https://mlsanity.com/paper/2404.09105/) (2024)
- [Dynamic Large Language Models on Blockchains](https://mlsanity.com/paper/2307.10549/) (2023)
- [Multilevel Large Language Models for Everyone](https://mlsanity.com/paper/2307.13221/) (2023)
- [Gradient Domain Diffusion Models for Image Synthesis](https://mlsanity.com/paper/2309.01875/) (2023)
- [TSSR: A Truncated and Signed Square Root Activation Function for Neural Networks](https://mlsanity.com/paper/2308.04832/) (2023)
- [Language identification as improvement for lip-based biometric visual systems](https://mlsanity.com/paper/2302.13902/) (2023)
- [STL: A Signed and Truncated Logarithm Activation Function for Neural Networks](https://mlsanity.com/paper/2307.16389/) (2023)
- [PLMM: Personal Large Language Models on Mobile Devices](https://mlsanity.com/paper/2309.14726/) (2023)
- [GDGS: Gradient Domain Gaussian Splatting for Sparse Representation of Radiance Fields](https://mlsanity.com/paper/2405.05446/) (2024)

## Abstract (arXiv)

This paper presents a quarter Laplacian filter that can preserve corners and edges during image smoothing. Its support region is 2×2, which is smaller than the 3×3 support region of Laplacian filter. Thus, it is more local. Moreover, this filter can be implemented via the classical box filter, leading to high performance for real time applications. Finally, we show its edge preserving property in several image processing tasks, including image smoothing, texture enhancement, and low-light image enhancement. The proposed filter can be adopted in a wide range of image processing applications.