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  "contentMarkdown": "# PCL 移动最小二乘法：点云平滑与法线估计\n\n> [!note] 来源与许可\n> 旧稿是 2014 年 CSDN 文章转载，导出内容未保留明确转载许可，故原转载已移入私有来源归档。本文是依据 PCL 官方教程重新编写的独立摘要；示例接口以 PCL 当前文档为准。PCL 项目使用 BSD 许可证。\n\n## MLS 解决什么问题\n\n移动最小二乘法（Moving Least Squares, MLS）在每个采样点的局部邻域拟合平滑曲面，并把点投影到局部曲面上。它常用于：\n\n- 降低扫描噪声造成的局部起伏；\n- 对点云重采样；\n- 同时估计平滑后的法线；\n- 为后续三角化提供更一致的点和法线。\n\nMLS 输出的核心仍是点云（可包含法线），不会仅凭这一步生成三角网格。\n\n## 基本流程\n\n```cpp\n#include <pcl/point_types.h>\n#include <pcl/search/kdtree.h>\n#include <pcl/surface/mls.h>\n\nusing InputPoint = pcl::PointXYZ;\nusing OutputPoint = pcl::PointNormal;\n\npcl::PointCloud<InputPoint>::Ptr input(new pcl::PointCloud<InputPoint>);\npcl::PointCloud<OutputPoint> output;\n\npcl::search::KdTree<InputPoint>::Ptr tree(\n    new pcl::search::KdTree<InputPoint>);\n\npcl::MovingLeastSquares<InputPoint, OutputPoint> mls;\nmls.setInputCloud(input);\nmls.setSearchMethod(tree);\nmls.setSearchRadius(0.03);  // 应按点间距与几何尺度调参\nmls.setComputeNormals(true);\nmls.process(output);\n```\n\n具体接口会随 PCL 版本变化，编译时应核对当前头文件和官方示例。\n\n## 参数与边界\n\n- **搜索半径**过小：邻域点不足，拟合不稳定或出现空洞。\n- **搜索半径**过大：跨越尖锐边缘或薄壁两侧，细节被抹平。\n- **多项式阶数**越高不等于越准确，噪声、采样密度和计算成本都会影响结果。\n- 离群点会扭曲局部拟合，通常先进行统计或半径离群点过滤。\n- 点云密度变化剧烈、存在大孔洞或薄结构时，应分区调参并与原始数据对照。\n\n## 验证方式\n\n1. 记录点间距分布，以它为搜索半径的尺度依据。\n2. 在平面、曲面、尖锐边缘和稀疏区域分别抽样可视化。\n3. 比较点到原始数据/参考表面的距离，而不只看“更光滑”。\n4. 检查法线方向一致性及后续网格的孔洞、自交和错误连接。\n\n## 参考资料\n\n- [PCL 官方教程：Smoothing and normal estimation based on polynomial reconstruction](https://pointclouds.org/documentation/tutorials/resampling.html)\n- [PCL BSD License](https://github.com/PointCloudLibrary/pcl/blob/master/LICENSE.txt)\n"
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