Bayesian methods and Markov chain Monte Carlo algorithms for curve reconstruction and point cloud data analysis
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Computer Science > Machine Learning
Title:Bayesian methods and Markov chain Monte Carlo algorithms for curve reconstruction and point cloud data analysis
Abstract: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.
| Comments: | 32 pages and 12 figures |
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| MSC classes: | 62F15 (Primary), 62-08, 65C40 (Secondary) |
| Cite as: | arXiv:2608.26490 [cs.LG] |
| (or arXiv:2608.26490v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.26490
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Asir Intesar Tushar [view email][v1] Thu, 27 Aug 2026 00:26:00 UTC (3,598 KB)
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