Abstract: In this paper a framework is built for differential quantity calculation on spatial curves of point cloud and a new matching method for given point curves is proposed.The differential quantities（including Frenet frame，curvature and torsion） are used that are computed directly from point cloud to get a rough and global alignment.With the help of kinematics，a model is developed that minimizes a metric of the tangent distance error to obtain the optimal matching.Experiments indicate that this algorithm is insensitive to noise and reaches accurate results.

Key words: spatial curve of point cloud, differential quantities, matching

摘要： 建立了点云几何分析的相关理论框架，即定义和计算点云潜在曲线的几何微分量，包括Frenet标架、曲率、挠率等；在此基础上提出一种新的点云空间曲线匹配方法。直接在点云上计算微分量来获取相应曲线的特征信息，从而构建全局粗匹配方案，并进一步建立基于空间动力学的精细匹配优化模型。数值实验表明，微分信息计算和匹配方法能很好地适用于带噪音的点云数据，有效地实现点云空间曲线的高精度匹配。

关键词: 点云空间曲线, 微分信息, 匹配