Due to the inherent nonlinear nature of data, traditional linear methods have some limitations in finding the intrinsic dimensions of motion capture (Mo‐cap) data. Mo‐cap data are more in line with the characteristics of the manifold. Assuming that the data are initially a low‐dimensional manifold and uniformly sampled in high‐dimensional Euclidean space, manifold learning recovers low‐dimensional manifold structures from high‐dimensional sampled data. This paper proposes an automatic segmentation method based on geodesics by introducing a Riemannian manifold. We convert Mo‐cap data from Euler angles into quaternions, calculate the intrinsic mean of the motion sequence, hemispherize quaternions, and use logarithmic and exponential mapping to calculate geodesic distances instead of quaternions. The experimental results show that the algorithms can achieve automatic segmentation and have a better segmentation effect.

中文翻译：

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使用黎曼流形学习进行运动捕捉数据分割

由于数据固有的非线性特性，传统的线性方法在寻找运动捕捉 (Mo-cap) 数据的内在维度方面存在一些局限性。Mo-cap 数据更符合流形的特征。假设数据最初是低维流形并在高维欧几里德空间中均匀采样，流形学习从高维采样数据中恢复低维流形结构。本文通过引入黎曼流形，提出了一种基于测地线的自动分割方法。我们将 Mo-cap 数据从欧拉角转换为四元数，计算运动序列的内在平均值，将四元数半球化，并使用对数和指数映射来计算测地距离而不是四元数。