# Bayesian methods and Markov chain Monte Carlo algorithms for curve reconstruction and point cloud data analysis

arXiv: https://arxiv.org/abs/2608.26490 · HTML: https://mlsanity.com/paper/2608.26490/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 41 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Deep Learning for LiDAR Point Clouds in Autonomous Driving: A Review](https://mlsanity.com/paper/2005.09830/) (2020)
- [A comprehensive overview of deep learning techniques for 3D point cloud classification and semantic segmentation](https://mlsanity.com/paper/2405.11903/) (2024)
- [Curvature Regularized Surface Reconstruction from Point Cloud](https://mlsanity.com/paper/2001.07884/) (2020)
- [An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging](https://mlsanity.com/paper/2108.01914/) (2021)
- [Ground vehicle mapping of fields using LiDAR to enable prediction of crop biomass](https://mlsanity.com/paper/1805.01426/) (2018)
- [StretchDenoise: Parametric Curve Reconstruction with Guarantees by Separating Connectivity from Residual Uncertainty of Samples](https://mlsanity.com/paper/1808.07778/) (2018)
- [2D Points Curve Reconstruction Survey and Benchmark](https://mlsanity.com/paper/2103.09583/) (2021)

## Abstract (arXiv)

Point-cloud data routinely captured by modern imaging and sensor technologies provide detailed geometric descriptions of objects and environments, but their analysis is hindered by large data volumes, localization noise, and missing information. In addition, existing point-cloud reconstruction pipelines typically return a single best-fit structure without uncertainty quantification. We introduce a fully Bayesian framework for representing point-cloud data and reconstructing closed curves, in which observed points are modeled as noisy perturbations of latent locations constrained to lie on the underlying curve that is regularized by a non-parametric prior. Posterior inference in our framework is carried out using a series of Markov chain Monte Carlo samplers tailored to point-cloud characteristics. Numerical experiments, including synthetic examples and real-world LiDAR datasets, show accurate reconstructions and quantified uncertainty over the recovered curves.