Describing Local Reference Frames for 3-D Motion Trajectory Recognition

Motion trajectories tracked from the points of interest can provide the key relevant features for characterizing the motion patterns in video. As the increasing number of 3-D vision sensors rises, the 3-D motion trajectories that serve as motion representations have been applied successfully to video retrieval and analysis, scene understanding, motion recognition, and so on, in existing works. Most of these works use raw data of motion trajectories directly or draw simple geometric quantities to describe the motion trajectories, whereas these simple descriptions are not intrinsically complete as they cannot feature the orientation changes of moving points along the 3-D motion trajectories. In principle, orientation changes of a single moving point in 3-D space have to been obtained by resorting to high-order derivatives, but the high-order derivatives would result in high sensitivity to noise. This paper tackles the problem by describing the local reference frames along 3-D motion trajectories, while we consider a motion trajectory as a temporal sequence of local reference frames. The maximal blurred segment of the noisy discrete curves is employed to estimate the local reference frames without high-order derivatives involved, and the local reference frame contains complete information of positions and orientations in the 3-D Euclidean space. To describe such local reference frames, we use the rotations and local square root velocities of local reference frames as the proposed descriptor to characterize the position and orientation changes of the moving points along the motion trajectories. In the experiments, we evaluate the effectiveness of the proposed descriptor by applying it to the gesture recognition on two large benchmark data sets that contain hand motion trajectories. The results show that our proposed descriptor can achieve superior performance compared to the existing descriptors and state-of-the-art methods in the 3-D motion trajectory recognition.