用PCA估计法向量，修复缺失点云的表面结构。
A PCA Based Model for Surface Reconstruction from Incomplete Point Clouds
- 基于PCA估算点云法向量，作为重建约束。
- 在缺失区域成功推断出表面形状，效果优于现有方法。
- 适合处理扫描不完整数据的几何重建任务。
点云数据是数学建模中的关键信息，从点云中进行表面重建在多个领域具有重要意义。然而，由于高吸光率和遮挡等因素，扫描过程中常导致点云覆盖不全，形成数据缺失。如何推断缺失区域的表面结构并完成准确重建是一大挑战。本文提出一种基于主成分分析（PCA）的表面重建模型。首先利用PCA从已有点云数据中估计底层表面的法向信息，该法向信息作为正则项引入模型，引导重建过程，尤其在数据缺失区域提供有效指导。此外，采用算子分裂方法高效求解所提模型。通过系统实验验证，该方法能有效推断缺失区域的表面结构，实现高质量表面重建，性能优于现有方法。
原文摘要 · Abstract (English)
Point cloud data represents a crucial category of information for mathematical modeling, and surface reconstruction from such data is an important task across various disciplines. However, during the scanning process, the collected point cloud data may fail to cover the entire surface due to factors such as high light-absorption rate and occlusions, resulting in incomplete datasets. Inferring surface structures in data-missing regions and successfully reconstructing the surface poses a challenge. In this paper, we present a Principal Component Analysis (PCA) based model for surface reconstruction from incomplete point cloud data. Initially, we employ PCA to estimate the normal information of the underlying surface from the available point cloud data. This estimated normal information serves as a regularizer in our model, guiding the reconstruction of the surface, particularly in areas with missing data. Additionally, we introduce an operator-splitting method to effectively solve the proposed model. Through systematic experimentation, we demonstrate that our model successfully infers surface structures in data-missing regions and well reconstructs the underlying surfaces, outperforming existing methodologies.
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