# A Discrete Scheme for Computing Image's Weighted Gaussian Curvature

arXiv: https://arxiv.org/abs/2101.07927 · HTML: https://mlsanity.com/paper/2101.07927/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 20 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [Weighted Mean Curvature](https://mlsanity.com/paper/1903.07189/) (2019)
- [An End-to-End Deep Learning Histochemical Scoring System for Breast Cancer Tissue Microarray](https://mlsanity.com/paper/1801.06288/) (2018)
- [Speeding Up the Bilateral Filter: A Joint Acceleration Way](https://mlsanity.com/paper/1803.00004/) (2018)

## Built on by (most cited first, 10 of 10)

- [An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging](https://mlsanity.com/paper/2108.01914/) (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)
- [TSSR: A Truncated and Signed Square Root Activation Function for Neural Networks](https://mlsanity.com/paper/2308.04832/) (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)
- [Shared-kernel Wavelet Neural Networks for Poisson Image Reconstruction](https://mlsanity.com/paper/2604.24000/) (2026)

## Abstract (arXiv)

Weighted Gaussian Curvature is an important measurement for images. However, its conventional computation scheme has low performance, low accuracy and requires that the input image must be second order differentiable. To tackle these three issues, we propose a novel discrete computation scheme for the weighted Gaussian curvature. Our scheme does not require the second order differentiability. Moreover, our scheme is more accurate, has smaller support region and computationally more efficient than the conventional schemes. Therefore, our scheme holds promise for a large range of applications where the weighted Gaussian curvature is needed, for example, image smoothing, cartoon texture decomposition, optical flow estimation, etc.