Abstract: The trajectory similarity measure that is invariant to Rotation, Scaling and Translation（RST） operations is crucial to applications such as precise sign language recognition, similar trajectory index etc. However, traditional similarity measures do not meet this requirements, especially the rotation invariant. This paper proposes an RST invariant measure. This method begins by filtering, normalizing and resampling the trajectory, which is followed by an optimal estimation of rotation matrix between any two trajectories. After that, the interference of uncertain rotation is reliably removed. The proposed method has time complexity of [ON] and applies to both 2D and 3D trajectories. Compared with invariants like curvature and torsion, this method is quite insensitive to noises.

Key words: trajectory data, distance measure, Rotation, Scaling and Translation（RST） invariant, optimal rotation matrix

摘要： 具有旋转、缩放、平移不变性的轨迹相似性度量是实现精准手语识别、相似轨迹检索等的关键环节，常规的相似性度量往往不满足这一要求，特别是不具备旋转不变性。提出一种具有旋转、缩放、平移不变性的轨迹相似性度量方法，该方法首先对轨迹进行滤波、归一化、等间距重采样等预处理操作，然后对任意两条待比较的轨迹估计最优旋转矩阵，从而消除旋转对距离度量的干扰。该方法对二维、三维轨迹数据均适用，计算复杂度为[ON]，与曲率、挠率等不变量相比，该方法对轨迹噪声不敏感。

关键词: 轨迹数据, 距离度量, 旋转、缩放、平移（RST）不变性, 最优旋转矩阵