# Curvature Regularized Surface Reconstruction from Point Cloud

arXiv: https://arxiv.org/abs/2001.07884 · HTML: https://mlsanity.com/paper/2001.07884/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2020.

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

- [PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks](https://mlsanity.com/paper/2307.09039/) (2023)
- [An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging](https://mlsanity.com/paper/2108.01914/) (2021)
- [p-Poisson surface reconstruction in curl-free flow from point clouds](https://mlsanity.com/paper/2310.20095/) (2023)
- [Double-well Net for Image Segmentation](https://mlsanity.com/paper/2401.00456/) (2023)
- [Elastica Models for Color Image Regularization](https://mlsanity.com/paper/2203.09995/) (2022)
- [CurvPnP: Plug-and-play Blind Image Restoration with Deep Curvature Denoiser](https://mlsanity.com/paper/2211.07286/) (2022)
- [Euler's Elastica Based Cartoon-Smooth-Texture Image Decomposition](https://mlsanity.com/paper/2407.02794/) (2024)
- [Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation](https://mlsanity.com/paper/2307.09052/) (2023)
- [Curvature regularization for Non-line-of-sight Imaging from Under-sampled Data](https://mlsanity.com/paper/2301.00406/) (2023)
- [Robust Estimation of Surface Curvature Information from Point Cloud Data](https://mlsanity.com/paper/2306.00299/) (2023)
- [Neural Shortest Path for Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2502.06047/) (2025)
- [A PCA Based Model for Surface Reconstruction from Incomplete Point Clouds](https://mlsanity.com/paper/2509.15675/) (2025)
- [Bayesian methods and Markov chain Monte Carlo algorithms for curve reconstruction and point cloud data analysis](https://mlsanity.com/paper/2608.26490/) (2026)

## Abstract (arXiv)

We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature term. Only the point location is used, without any local normal or curvature estimation at each point. With the added curvature constraint, the computation becomes particularly challenging. To enhance the computational efficiency, we solve the problem by a novel operator splitting scheme. It replaces the original high-order PDEs by a decoupled PDE system, which is solved by a semi-implicit method. We also discuss approach using an augmented Lagrangian method. The proposed method shows robustness against noise, and recovers concave features and sharp corners better compared to models without curvature constraint. Numerical experiments in two and three dimensional data sets, noisy and sparse data are presented to validate the model.