用贝叶斯方法重建点云曲线并量化不确定性
Bayesian methods and Markov chain Monte Carlo algorithms for curve reconstruction and point cloud data analysis
- 将点云视为噪声扰动的隐含曲线点，用非参数先验正则化
- 在合成数据和真实LiDAR数据上实现高精度曲线重建
- 适合需要不确定性的3D重建与传感器数据分析场景
现代成像与传感技术捕获的点云数据提供了物体与环境的详细几何描述，但其分析受限于海量数据、定位噪声及信息缺失。现有重建流程通常仅输出单一最优结构，缺乏不确定性量化。本文提出一种完整的贝叶斯框架，用于表示点云数据并重构闭合曲线：观测点被建模为位于潜在曲线上的噪声扰动，该曲线受非参数先验正则化。通过针对点云特性的马尔可夫链蒙特卡洛采样器进行后验推断。数值实验（包括合成数据与真实LiDAR数据集）表明，该方法能实现精确重建，并对恢复曲线提供可靠的不确定性量化。
原文摘要 · Abstract (English)
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.
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