IEEE Trans Cybern. 2016 Feb;46(2):511-23. doi: 10.1109/TCYB.2015.2404828. Epub 2015 Mar 3.
Motion trajectories tracked from the motions of human, robots, and moving objects can provide an important clue for motion analysis, classification, and recognition. This paper defines some new integral invariants for a 3-D motion trajectory. Based on two typical kernel functions, we design two integral invariants, the distance and area integral invariants. The area integral invariants are estimated based on the blurred segment of noisy discrete curve to avoid the computation of high-order derivatives. Such integral invariants for a motion trajectory enjoy some desirable properties, such as computational locality, uniqueness of representation, and noise insensitivity. Moreover, our formulation allows the analysis of motion trajectories at a range of scales by varying the scale of kernel function. The features of motion trajectories can thus be perceived at multiscale levels in a coarse-to-fine manner. Finally, we define a distance function to measure the trajectory similarity to find similar trajectories. Through the experiments, we examine the robustness and effectiveness of the proposed integral invariants and find that they can capture the motion cues in trajectory matching and sign recognition satisfactorily.
从人体、机器人和移动物体的运动轨迹中跟踪到的运动轨迹可以为运动分析、分类和识别提供重要线索。本文为三维运动轨迹定义了一些新的积分不变量。基于两个典型的核函数，我们设计了两个积分不变量，即距离积分不变量和面积积分不变量。基于模糊离散曲线的段，设计面积积分不变量可以避免计算高阶导数。这样的运动轨迹积分不变量具有一些理想的性质，例如计算局部性、表示唯一性和对噪声不敏感性。此外，我们的公式允许通过改变核函数的尺度来分析不同尺度的运动轨迹。因此，可以以粗到细的方式在多尺度级别上感知运动轨迹的特征。最后，我们定义了一个距离函数来测量轨迹相似度，以找到相似的轨迹。通过实验，我们检验了所提出的积分不变量的鲁棒性和有效性，并发现它们可以在轨迹匹配和符号识别中很好地捕捉运动线索。
