Goce Trajcevski
Roberto Tamassia
ABSTRACT
This work addresses the problem of obtaining the degree of similarity between trajectories of moving objects. Typically, a Moving Objects Database (MOD) contains sequences of (location, time) points describing the motion of individual objects, however, they also implicitly storethe velocity -- an important attribute describing the dynamics the motion. Our main goal is to extend the MOD capability with reasoning about how similar are the trajectories of objects, possibly moving along geographically different routes. We use a distance function which balances the lack of temporal-awareness of the Hausdorff distance with the generality (and complexity of calculation) of the Fréchet distance. Based on the observation that in practice the individual segments of trajectories are assumed to have constant speed, we provide efficient algorithms for: (1) optimal matching between trajectories; and (2) approximate matching between trajectories, both under translations and rotations, where the approximate algorithm guarantees a bounded error with respect to the optimal one.
- Rakesh Agrawal, Christos Faloutsos, and Arun N. Swami. Efficient similarity search in sequence databases. In FODO, 1993. Google Scholar
Digital Library
- A. Alt, C. Knauer, and C. Wenk. Comparison of distance measures for planar curves. Algorithmica, 38, 2004. Google ScholarDigital Library
- H. Alt, O. Aicholzer, and G. Rote. Matching shapes with a reference point. In Symp. Computational Geometry, 1994. Google ScholarDigital Library
- H. Alt, A. Efrat, G. Rote, and C. Wenk. Matching plannar graphs. Journal of Algorithms, 49, 2003. Google ScholarDigital Library
- H. Alt and L. Guibas. Discrete geometric shapes: Matching, interpolation, and approximation. In Handbook of Computational Geometry, 1999.Google Scholar
- H. Alt, C. Knauer, and C. Wenk. Matching polygonal curves with respect to the fréchet distance. In STACS, 2001. Google ScholarDigital Library
- B. Aronov, S. Har-Peled, C. Knauer, Y. Wang, and C. Wenk. Fréchet distance for curves, revisited. In ESA, 2006. Google ScholarDigital Library
- F. Aurenhammer. Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Comput. Surv., 23(3), 1991. Google ScholarDigital Library
- P. Bakalov, M. Hadjielefteriou, and V. Tsotras. Time relaxed spatiotemporal trajectory joins. In GIS, 2005. Google ScholarDigital Library
- Thomas Brinkhoff. A framework for generating network-based moving objects. GeoInformatica, 6(2), 2002. Google ScholarDigital Library
- H. Cao, O. Wolfson, and G. Trajcevski. Spatio-temporal data reduction with deterministic error bounds. VLDB Journal, 15(3), 2006. Google ScholarDigital Library
- M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational geometry: algorithms and applications. Springer-Verlag New York, Inc., 1997. Google ScholarDigital Library
- S. E. Dreyfus. An appraisal of some shortest -- path algorithms. Operations Research, 17(3), 1969.Google Scholar
- C. du Mouza and R. Rigaux. Multi-scale classification of moving objects trajectories. In SSDBM, 2004. Google ScholarDigital Library
- A. Efrat, Q. Fan, and S. Venkatasubramanian. Curve matching, time warping, and light fields: New algorithms for computing similarity between curves. J. Mathematic Imaging and Vision, 2007. to appear. Google ScholarDigital Library
- T. Eiter and H. Mannila. Distance measures for point sets and their computation. Acta Inf., 34(2), 1997.Google Scholar
- M. T. Goodrich, J. S. B. Mitchell, and M. W. Orletsky. Approximate geometric pattern matching under rigid motions. IEEE Trans. Pattern Anal. Mach. Intell., 21(4), 1999. Google ScholarDigital Library
- R. H. Güting, V. T. de Almeida, and Z. Ding. Modeling and querying moving objects in networks. VLDB J., 15(2), 2006. Google ScholarDigital Library
- R. H. Güting and M. Schneider. Moving Objects Databases. Morgan Kaufmann, 2005.Google Scholar
- M. Hadjielefteriou, G. Kollios, P. Bakalov, and V. Tsotras. Complex spatio-temporal pattern queries. In VLDB, 2005. Google ScholarDigital Library
- P. J. Heffernan and S. Schirra. Approximate decision algorithms for point set congruence. In Symp. Computational Geometry, 1992. Google ScholarDigital Library
- K. Imai, S. Sumino, and H. Imai. Minimax geometric fitting of two corresponding sets of points and dynamic furthest voronoi diagrams. IEICE Trans. Inf. and Syst., E81-D(11), 1998.Google Scholar
- Forbes Online Issue http://www.forbes.com/home, April 2006.Google Scholar
- F. P. Preparata and M. I. Shamos. Computational Geometry: an introduction. Springer Verlag, 1985. Google ScholarDigital Library
- J. Schiller and A. Voisard. Location-based Services. Morgan Kaufmann Publishers, 2004. Google ScholarDigital Library
- M. Sharir and P. K. Agarwal. Davenport-Schinzel Sequences and Their Geometric Applications. Cambridge University Press, 1995. Google ScholarDigital Library
- G. Trajcevski, O. Wolfson, K. Hinrichs, and S. Chamberlain. Managing uncertainty in moving objects databases. ACM TODS, 29(3), 2004. Google ScholarDigital Library
- M. Vlachos, M. Hadjielefteriou, D. Gunopulos, and E. Keogh. Indexing multidimensional time-series. VLDB Journal, 15(1), 2006. Google ScholarDigital Library
- M. Vlachos, G. Kollios, and D. Gunopulos. Elastic translation invariant matching of trajectories. Machine Learning, 58, 2005. Google ScholarDigital Library
- C. Wenk, R. Salas, and D. Pfoser. Addressing the need for map-matching speed: Localizing global curve-matching algorithms. In SSDBM, 2006. Google ScholarDigital Library
Index Terms
- Dynamics-aware similarity of moving objects trajectories
Recommendations
Indexing the Trajectories of Moving Objects in Networks*
The management of moving objects has been intensively studied in recent years. A wide and increasing range of database applications has to deal with spatial objects whose position changes continuously over time, called moving objects. The main interest ...
Indexing frequently updated trajectories of network-constrained moving objects
DEXA'11: Proceedings of the 22nd international conference on Database and expert systems applications - Volume Part IIIndex is a key technique in improving the query processing performance of moving objects databases. However, current index methods for moving object trajectories take trajectory units as the basic index records and frequent index updates are needed when ...
Similarity measurement of moving object trajectories
IWGS '12: Proceedings of the 3rd ACM SIGSPATIAL International Workshop on GeoStreamingTo study the similarity between moving object trajectories is important in many applications, e.g., to find the clusters of moving objects which share the same moving pattern, and infer the future locations of a moving object from its similar ...
Comments