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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 613939, 29 pages
Research Article

Mixed Signature: An Invariant Descriptor for 3D Motion Trajectory Perception and Recognition

1Department of MEEM, City University of Hong Kong, Hong Kong
2Department of PMPI, University of Science and Technology of China, Hefei 230027, China
3Department of MEEM, USTC-CityU Joint Advanced Research Centre, Suzhou 215123, China
4Department of CS, University of Science and Technology of China, Hefei 230027, China
5Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy
6Department of Mathematics, Sapienza University of Rome, P.le A. Moro 2, 00185 Rome, Italy

Received 30 March 2011; Accepted 27 April 2011

Academic Editor: Shengyong Chen

Copyright © 2012 Jianyu Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Motion trajectory contains plentiful motion information of moving objects, for example, human gestures and robot actions. Motion perception and recognition via trajectory are useful for characterizing them and a flexible descriptor of motion trajectory plays important role in motion analysis. However, in the existing tasks, trajectories were mostly used in raw data and effective descriptor is lacking. In this paper, we present a mixed invariant signature descriptor with global invariants for motion perception and recognition. The mixed signature is viewpoint invariant for local and global features. A reliable approximation of the mixed signature is proposed to reduce the noise in high-order derivatives. We use this descriptor for motion trajectory description and explore the motion perception with DTW algorithm for salient motion features. To achieve better accuracy, we modified the CDTW algorithm for trajectory matching in motion recognition. Furthermore, a controllable weight parameter is introduced to adjust the global features for tasks in different circumstances. The conducted experiments validated the proposed method.