# Weighted Mean Curvature

arXiv: https://arxiv.org/abs/1903.07189 · HTML: https://mlsanity.com/paper/1903.07189/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2019.

## Built on by (most cited first, 15 of 15)

- [A Discrete Scheme for Computing Image's Weighted Gaussian Curvature](https://mlsanity.com/paper/2101.07927/) (2021)
- [Quarter Laplacian Filter for Edge Aware Image Processing](https://mlsanity.com/paper/2101.07933/) (2021)
- [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)
- [Fast Multi-grid Methods for Minimizing Curvature Energy](https://mlsanity.com/paper/2204.07921/) (2022)
- [Isotropic Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2403.14244/) (2024)
- [TSSR: A Truncated and Signed Square Root Activation Function for Neural Networks](https://mlsanity.com/paper/2308.04832/) (2023)
- [One-Sided Box Filter for Edge Preserving Image Smoothing](https://mlsanity.com/paper/2108.05021/) (2021)
- [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)
- [Shared-kernel Wavelet Neural Networks for Poisson Image Reconstruction](https://mlsanity.com/paper/2604.24000/) (2026)
- [LEGS: Laplacian-Enhanced Gaussian Splatting with a Nonlinear Weighted Loss](https://mlsanity.com/paper/2606.07932/) (2026)

## Abstract (arXiv)

In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature.