Advertisement

The VLDB Journal

, Volume 28, Issue 6, pp 897–921 | Cite as

One-pass trajectory simplification using the synchronous Euclidean distance

  • Xuelian Lin
  • Jiahao Jiang
  • Shuai MaEmail author
  • Yimeng Zuo
  • Chunming HuEmail author
Regular Paper
  • 33 Downloads

Abstract

Various mobile devices have been used to collect, store and transmit tremendous trajectory data, and it is known that raw trajectory data seriously wastes the storage, network bandwidth and computing resource. To attack this issue, one-pass line simplification (\(\textsf {LS} \)) algorithms have been developed, by compressing data points in a trajectory to a set of continuous line segments. However, these algorithms adopt the perpendicular Euclidean distance, and none of them uses the synchronous Euclidean distance (\(\textsf {SED} \)), and cannot support spatiotemporal queries. To do this, we develop two one-pass error bounded trajectory simplification algorithms (\(\textsf {CISED} \)-\(\textsf {S} \) and \(\textsf {CISED} \)-\(\textsf {W} \)) using \(\textsf {SED} \), based on a novel spatiotemporal cone intersection technique. Using four real-life trajectory datasets, we experimentally show that our approaches are both efficient and effective. In terms of running time, algorithms \(\textsf {CISED} \)-\(\textsf {S} \) and \(\textsf {CISED} \)-\(\textsf {W} \) are on average 3 times faster than \(\textsf {SQUISH} \)-\(\textsf {E} \) (the fastest existing \(\textsf {LS} \) algorithm using \(\textsf {SED} \)). In terms of compression ratios, \(\textsf {CISED} \)-\(\textsf {S} \) is close to and \(\textsf {CISED} \)-\(\textsf {W} \) is on average \(19.6\%\) better than \(\textsf {DPSED} \) (the existing sub-optimal \(\textsf {LS} \) algorithm using \(\textsf {SED} \) and having the best compression ratios), and they are \(21.1\%\) and \(42.4\%\) better than \(\textsf {SQUISH} \)-\(\textsf {E} \) on average, respectively.

Keywords

Trajectory simplification Synchronous Euclidean distance One-pass line simplification 

Notes

Acknowledgements

This work is supported in part by National Key R&D Program of China 2018YFB1700403, NSFC U1636210&61421003, Shenzhen Institute of Computing Sciences, and the Fundamental Research Funds for the Central Universities. Funding was provided by National Natural Science Foundation of China (Grant No. U1636210), 973 program (Grant No. 2014CB340300), Beijing Advanced Innovation Center for Big Data and Brain Computing.

References

  1. 1.
    Cao, H., Wolfson, O., Trajcevski, G.: Spatio-temporal data reduction with deterministic error bounds. VLDBJ 15(3), 211–228 (2006)CrossRefGoogle Scholar
  2. 2.
    Chan, W., Chin, F.: Approximation of polygonal curves with minimum number of line segments or minimal error. Int. J. Comput. Geom. Appl. 6(1), 378–387 (1996)CrossRefGoogle Scholar
  3. 3.
    Chen, Y., Jiang, K., Zheng, Y., Li, C., Yu, N.: Trajectory simplification method for location-based social networking services. In: LBSN, pp. 33–40 (2009)Google Scholar
  4. 4.
    Chen, M., Xu, M., Fränti, P.: A fast multiresolution polygonal approximation algorithm for GPS trajectory simplification. IEEE Trans. Image Process. 21(5), 2770–2785 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Civilis, A., Jensen, C.S., Pakalnis, S.: Techniques for efficient road-network-based tracking of moving objects. TKDE 17(5), 698–712 (2005)Google Scholar
  6. 6.
    Douglas, D.H., Peucker, T.K.: Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Can. Cartogr. 10(2), 112–122 (1973)CrossRefGoogle Scholar
  7. 7.
    Dunham, J.G.: Piecewise linear approximation of planar curves. PAMI 8, 9–67 (1986)Google Scholar
  8. 8.
    Gotsman, R., Kanza, Y.: A dilution-matching-encoding compaction of trajectories over road networks. GeoInformatica 19(2), 331–3364 (2015)CrossRefGoogle Scholar
  9. 9.
    Han, Y., Sun, W., Zheng, B.: Compress: a comprehensive framework of trajectory compression in road networks. TODS 42(2), 11:1–11:9 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Heckbert, P.S., Garland, M.: Survey of polygonal surface simplification algorithms. In: SIGGRAPH (1997)Google Scholar
  11. 11.
    Hershberger, J., Snoeyink, J.: Speeding up the Douglas–Peucker line-simplification algorithm. Technical Report, University of British Columbia (1992)Google Scholar
  12. 12.
    Hung, C.C., Peng, W., Lee, W.: Clustering and aggregating clues of trajectories for mining trajectory patterns and routes. VLDBJ 24(2), 169–192 (2015)CrossRefGoogle Scholar
  13. 13.
    Imai, H., Iri, M.: Computational-geometric methods for polygonal approximations of a curve. Comput. Vis. Graph. Image Process. 36, 31–41 (1986)CrossRefGoogle Scholar
  14. 14.
    Lin, X., Ma, S., Zhang, H., Wo, T., Huai, J.: One-pass error bounded trajectory simplification. PVLDB 10(7), 841–852 (2017)Google Scholar
  15. 15.
    Liu, J., Zhao, K., Sommer, P., Shang, S., Kusy, B., Jurdak, R.: Bounded quadrant system: Error-bounded trajectory compression on the go. In: ICDE (2015)Google Scholar
  16. 16.
    Liu, J., Zhao, K., Sommer, P., Shang, S., Kusy, B., Lee, J.-G., Jurdak, R.: A novel framework for online amnesic trajectory compression in resource-constrained environments. IEEE Trans. Knowl. Data Eng. 28(11), 2827–2841 (2016)CrossRefGoogle Scholar
  17. 17.
    Long, C., Wong, R.C.-W., Jagadish, H.: Direction-preserving trajectory simplification. PVLDB 6(10), 949–960 (2013)Google Scholar
  18. 18.
    Melkman, A., O’Rourke, J.: On polygonal chain approximation. Mach. Intell. Pattern Recognit. 6, 87–95 (1988)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Meratnia, N., de By, R.A.: Spatiotemporal compression techniques for moving point objects. In: EDBT (2004)CrossRefGoogle Scholar
  20. 20.
    Metha, R., Mehta, V.K.: The Principles of Physics. S Chand, New Delhi (1999)Google Scholar
  21. 21.
    Mopsi routes 2014. http://cs.uef.fi/mopsi/routes/dataset/. Accessed 29 Nov 2017
  22. 22.
    Muckell, J., Hwang, J.-H., Lawson, C.T., Ravi, S.S.: Algorithms for compressing gps trajectory data: an empirical evaluation. In: ACM-GIS (2010)Google Scholar
  23. 23.
    Muckell, J., Olsen, P.W., Hwang, J.-H., Lawson, C.T., Ravi, S.S.: Compression of trajectory data: a comprehensive evaluation and new approach. GeoInformatica 18(3), 435–460 (2014)CrossRefGoogle Scholar
  24. 24.
    Nibali, A., He, Z.: Trajic: an effective compression system for trajectory data. TKDE 27(11), 3138–3151 (2015)Google Scholar
  25. 25.
    O’Rourke, J., Chien, C.B., Olson, T., Naddor, D.: A new linear algorithm for intersecting convex polygons. Comput. Graph. Image Process. 19(4), 384–391 (1982)CrossRefGoogle Scholar
  26. 26.
    Pavlidis, T., Horowitz, S.L.: Segmentation of plane curves. IEEE Trans. Comput. 23(8), 860–870 (1974)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Pfoser, D., Jensen, C.S.: Capturing the uncertainty of moving-object representations. In: SSD (1999)CrossRefGoogle Scholar
  28. 28.
    Popa, I.S., Zeitouni, K., Oria, V., Kharrat, A.: Spatio-temporal compression of trajectories in road networks. GeoInformatica 19(1), 117–145 (2014)CrossRefGoogle Scholar
  29. 29.
    Potamias, M., Patroumpas, K., Sellis, T.K.: Sampling trajectory streams with spatiotemporal criteria. In: SSDBM (2006)Google Scholar
  30. 30.
    Ramer, U.: An iterative procedure for the polygonal approximation of plane curves. Comput. Graph. Image Process. 1, 244–256 (1972)CrossRefGoogle Scholar
  31. 31.
    Reumann, K., Witkam, A.: Optimizing curve segmentation in computer graphics. In: International Computing Symposium (1974)Google Scholar
  32. 32.
    Richter, K.-F., Schmid, F., Laube, P.: Semantic trajectory compression: representing urban movement in a nutshell. J. Spat. Inf. Sci. 4(1), 3–30 (2012)Google Scholar
  33. 33.
    Schmid, F., Richter, K., Laube, P.: Semantic trajectory compression. In: SSTD, pp. 411–416 (2009)Google Scholar
  34. 34.
    Shamos, M.I., Dan, H.: Geometric intersection problems. In: Symposium on Foundations of Computer Science, pp. 208–215 (1976)Google Scholar
  35. 35.
    Shi, W., Cheung, C.: Performance evaluation of line simplification algorithms for vector generalization. Cartogr. J. 43(1), 27–44 (2006)CrossRefGoogle Scholar
  36. 36.
    Sklansky, J., Gonzalez, V.: Fast polygonal approximation of digitized curves. Pattern Recognit. 12, 327–331 (1980)CrossRefGoogle Scholar
  37. 37.
    Song, R., Sun, W., Zheng, B., Zheng, Y.: Press: a novel framework of trajectory compression in road networks. PVLDB 7(9), 661–672 (2014)Google Scholar
  38. 38.
    Toussaint, G.T.: On the complexity of approximating polygonal curves in the plane. In: International Symposium on Robotics and Automation (IASTED) (1985)Google Scholar
  39. 39.
    Trajcevski, G., Cao, H., Scheuermanny, P., Wolfsonz, O., Vaccaro, D.: On-line data reduction and the quality of history in moving objects databases. In: MobiDE (2006)Google Scholar
  40. 40.
    Williams, C.M.: An efficient algorithm for the piecewise linear approximation of planar curves. Comput. Graph. Image Process. 8, 286–293 (1978)CrossRefGoogle Scholar
  41. 41.
    Zhang, D., Ding, M., Yang, D., Liu, Y., Fan, J., Shen, H.T.: Trajectory simplification: an experimental study and quality analysis. PVLDB 9(11), 934–946 (2018)Google Scholar
  42. 42.
    Zhao, Z., Saalfeld, A.: Linear-time sleeve-fitting polyline simplification algorithms. In: Proceedings of AutoCarto, pp. 214–223 (1997)Google Scholar
  43. 43.
    Zheng, Y., Xie, X., Ma, W.: GeoLife: a collaborative social networking service among user, location and trajectory. IEEE Data Eng. Bull. 33(2), 32–39 (2010)Google Scholar
  44. 44.
    Züfle, A., Trajcevski, G., Pfoser, D., Renz, M., Rice, M.T., Leslie, T., Delamater, P.L., Emrich, T.: Handling uncertainty in geo-spatial data. In: ICDE (2017)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Beijing Advanced Innovation Center for Big Data and Brain Computing (BDBC)Beihang UniversityBeijingChina

Personalised recommendations