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基于无监督聚类分析的鲁棒椭圆柱拟合

Robust Elliptic Cylinder Fitting Using Unsupervised Clustering Analysis

  • 摘要: 圆柱作为CAD模型中的基本几何基元,其鲁棒拟合方法已经被系统地研究,然而当CAD模型受外力发生形变时,圆柱通常演变为椭圆柱。针对点云数据中普遍存在的噪声、离群点和严重遮挡,进一步增加了椭圆柱拟合难度的问题,提出一种基于无监督聚类分析的椭圆柱拟合方法。首先将拟合问题重构为初始点云与表面内点之间的无监督聚类优化过程,并引入噪声聚类增强对离群点的鲁棒性;然后通过拉格朗日乘子法推导出优化模型的闭式解,有效提升了计算效率。在包含合成数据与真实CAD模型在内的多样化点云数据集上,将所提方法与多种经典几何拟合方法进行对比,并以拟合残差、角度偏差和轴线距离偏差作为评价指标,结果表明,该方法在噪声、离群点及严重遮挡条件下具有更高的拟合精度与鲁棒性。

     

    Abstract: As a fundamental geometric primitives in CADmodels, cylinders have been systematically studied in terms of robust fitting methods. However, when a CAD model undergoes deformation due to external forces, cyl-inders often evolve into elliptic cylinders. To date, systematic research on the robust estimation of elliptic cylinder shape parameters from scattered point clouds remains lacking. Moreover, the prevalence of noise, outliers, and severe occlusion in point cloud data further complicates the fitting of elliptic cylinders. To address this challenge, this paper proposes an elliptic cylinder fitting method based on unsupervised clus-tering. The proposed method reformulates the fitting problem as an unsupervised clustering optimization process between the initial point cloud and the inliers on the surface, while introducing a noise cluster to enhance robustness against outliers. A closed-form solution to the optimization model is derived using the Lagrange multiplier method, effectively improving computational efficiency. In the experiments, the pro-posed method is compared with several classical geometric fitting approaches using diverse point cloud data, including both synthetic data and real CAD models. The evaluation metrics include fitting residuals, angular deviation, and axis distance deviation. Quantitative results demonstrate that the proposed method achieves higher fitting accuracy and robustness under conditions of noise, outliers, and severe occlusion.

     

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