International Journal of Computer Vision

, Volume 118, Issue 3, pp 364–379

Bounding Multiple Gaussians Uncertainty with Application to Object Tracking

  • Baochang Zhang
  • Alessandro Perina
  • Zhigang Li
  • Vittorio Murino
  • Jianzhuang Liu
  • Rongrong Ji
Article

Abstract

This paper proves the uncertainty bound for the multiple Gaussian functions, termed multiple Gaussians Uncertainty (MGU), which significantly generalizes the uncertainty principle for the single Gaussian function. First, as a theoretical contribution, we prove that the momentum (velocity) and position for the sum of multiple Gaussians wave function are theoretically bounded. Second, as for a practical application, we show that the bound can be well exploited for object tracking to detect anomalies of local movement in an online learning framework. By integrating MGU with a given object tracker, we demonstrate that uncertainty principle can provide remarkable robustness in tracking. Extensive experiments are done to show that the proposed MGU can significantly help base trackers overcome the object drifting and reach state-of-the-art results.

Keywords

Uncertainty principle Object tracking MGU 

Supplementary material

11263_2016_880_MOESM1_ESM.pdf (151 kb)
Supplementary material 1 (pdf 151 KB)

References

  1. Adam, A., Rivlin, E., & Shimshoni, I. (2006). Robust fragments-based tracking using the integral histogram. CVPR.Google Scholar
  2. Ali, S., & Shah, M. (2008). Floor fields for tracking in high density crowd scenes. In Proceedings of ECCV.Google Scholar
  3. Avidan, S. (2004). Support vector tracking. IEEE Transactions on PAMI, 26(8), 1064–1072.CrossRefGoogle Scholar
  4. Babenko, B., Yang, M., & Belongie, S. (2011). Robust object tracking with online multiple instance learning. IEEE Trans. PAMI, 6.Google Scholar
  5. Betke, M., Hirsh, D., Bagchi, A., Hristov, N., Makris, N., & Kunz, T. (2007). Tracking large variable numbers of objects in clutter. In Proceedings of IEEE CVPR (pp. 1–8).Google Scholar
  6. Born & Jordan. (1926). In the relation between the quantum mechanics of Heisenberg. Analen der Physik(4), 79.Google Scholar
  7. Brostow, G., & Cipolla, R. (2006). Unsupervised bayesian detection of independent motion in crowds. In Proceedings of IEEE CVPR, (Vol. 1, pp. 594–601).Google Scholar
  8. Canny, J. (2009). A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence.Google Scholar
  9. Cehovin, L., Kristan, M., & Leonardis, A. (2013). Robust visual tracking using an adaptive coupled-layer visual model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(4), 941–953.CrossRefGoogle Scholar
  10. Chu, C.-T., Hwang, J.-N., Pai, H.-I., & Lan, K.-M. (2013). Tracking human under occlusion based on adaptive multiple kernels with projected gradients. IEEE Transactions on Multimedia, 15(7), 1602–1615.CrossRefGoogle Scholar
  11. de Broglie, L. (1929). The wave nature of the electron. Nobel Lecture, 12.Google Scholar
  12. Doulamis, A. D. (2009). Adaptable neural networks for objects’ tracking re-initialization. ICANN, 2, 715–724.Google Scholar
  13. Duffner, S., & Garcia, C. (2013). PixelTrack: A fast adaptive algorithm for tracking non-rigid objects. In Proceedings of ICCV.Google Scholar
  14. Felzenszwalb, P. F., Girshick, R. B., McAllester, D. A., & Ramanan, D. (2010). Object detection with discriminatively trained part-based models. IEEE Transactions on PAMI, 32(9), 1627–1645.CrossRefGoogle Scholar
  15. Gabor, D. (1946). Theory of communication. The Journal of the Institute of Electrical Engineers, 93(26), 429C457. pt. III.Google Scholar
  16. Gilbert, A., & Bowden, R. (2007). Multi person tracking within crowded scenes. In IEEE workshop on human motion (pp. 166–179).Google Scholar
  17. Godec, M., Roth, P. M., & Bischof, H. (2013). Hough-based tracking of non-rigid objects. Computer Vision and Image Understanding, 117(10), 1245–1256.CrossRefGoogle Scholar
  18. Grabner, H., Grabner, M., & Bischof, H. (2008). Semi-supervised on-line boosting for robust tracking. In Proceedings of ECCV (pp. 234–247).Google Scholar
  19. Grabner, H., Grabner, M., & Bischof, H. (2006). Real-time tracking via on-line boosting. Proceedings of BMVC, 1, 47–56.Google Scholar
  20. Gustafson, F., Gunnison, F., & Nicolas, B. (2002). Particle filters for position, navigation, and tracking. IEEE Transactions on Signal Processing, 50(2), 425–437.CrossRefGoogle Scholar
  21. Han, Z., Jiao, J., Zhang, B., Ye, Q., & Liu, J. (2011). Visual object tracking via sample-based adaptive sparse representation. Pattern Recognition Journal.Google Scholar
  22. Hardy, G. H., Littlewood, J. E., & Pólya. (1967). Inequalities. Cambridge Mathematical Library.Google Scholar
  23. Hare, S., Saffari, A., & Torr, P. (2011). Struck: Structured output tracking with kernels. In Proceedings of IEEE ICCV (pp. 263-270).Google Scholar
  24. Hare, S., Saffari, A., & Torr,P. H. S. (2012). Efficient online structured output learning for keypoint-based object tracking. In Proceedings of CVPR (p. 1894)Google Scholar
  25. Hariharakrishnan, K., & Schonfeld, D. (2005). Fast object tracking using adaptive block matching. IEEE Transactions on Multimedia, 853–859.Google Scholar
  26. Hodge, V.J., & Austin, J. (2004). A survey of outlier detection methodologies. Artificial Intelligence Review.Google Scholar
  27. Hu, W., Li, X., Zhang, X., Shi, X., Maybank, S., & Zhang, Z. (2011). Incremental tensor subspace learning and its applications to foreground segmentation and tracking. International Journal of Computer Vision (IJCV), 91(3), 303–327.CrossRefMATHGoogle Scholar
  28. Jacobs, N., Dixon, M., & Pless, R. (2008). Location-specific transition distributions for tracking. In IEEE workshop on motion and video computing.Google Scholar
  29. Jepson, A., Fleet, D., & El-Maraghi, T. ( 2003). Robust online appearance models for visual tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1296–1311.Google Scholar
  30. Kalal, Z., Mikolajczyk, K., & Matas, J. (2010). Forward-backward error: automatic detection of tracking failures. In International conference on pattern recognition (pp. 23–26).Google Scholar
  31. Kalal, Z., Mikolajczyk, K., & Matas, J. (2010). Tracking-learning-detection. IEEE Transactions on PAMI, 6.Google Scholar
  32. Knutsson, H. (1994). Signal processing for computer vision. Springer: New York.Google Scholar
  33. Kristan et al. (2014). The visual object tracking VOT2014 challenge results. In ECCV visual object tracking challenge workshop.Google Scholar
  34. Kwon, J., & Lee, K. M. (2010). Visual tracking decomposition. In Proceedings of IEEE CVPR (pp. 1269–1276).Google Scholar
  35. Kwon, J., & Lee, K. M. (2013). Minimum uncertainty gap for robust visual tracking. In Proceedings of IEEE CVPR.Google Scholar
  36. Kwon, J., & Lee, K. Mu. (2014). Interval Tracker: Tracking by interval analysis. In Proceedings of IEEE CVPR.Google Scholar
  37. Li, S. (1999). Discrete multi-gabor expansions. IEEE Tranactions on Information theory, 45.Google Scholar
  38. Nestares, O., & Fleet, D. J. (2001). Probabilistic tracking of motion boundaries with spatiotemporal predictions. In Proceedings of IEEE CVPR (pp. 358–365).Google Scholar
  39. Peng, C., et al. (2009). Contextual mixture tracking. IEEE Transactions on Multimedia, 11.2, 333–341.CrossRefGoogle Scholar
  40. Purdy, T. P., Peterson, R. W., & Regal, C. A. (2013). Observation of radiation pressure shot noise on a macroscopic object. Science, 339(6121), 801–804.CrossRefGoogle Scholar
  41. Qu, W., et al. (2007). Real-time distributed multiobject tracking using multiple interactive trackers and a magnetic-inertia potential model. IEEE Transactions on Multimedia, 9(3), 511–519.CrossRefGoogle Scholar
  42. Ramakrishna, V., Sheikh, Y., & Kanade, T. (2013). Tracking human pose by tracking symmetric parts. In Proceedings of IEEE CVPR.Google Scholar
  43. Rodriguez, M., Ali, S., & Kanade, T. (2009). Tracking in unstructured crowded scenes. In Proceedings of IEEE ICCV.Google Scholar
  44. Ross, D. A., Lim, J., Lin, R.-S., & Yang, M.-H. (2008). Incremental learning for robust visual tracking. International Journal Computer Vision, 77, 125–141.CrossRefGoogle Scholar
  45. Shinde, S., & Gadre, V. M. (2001). An uncertainty principle for real signals in the fractional Fourier transform domain. IEEE Transactions on Signal Processing, 49(11).Google Scholar
  46. Stauder, J., & Ostermann, J. (1999). Detection of moving cast shadows for object segmentation. IEEE Transactions on Multimedia, 65–76.Google Scholar
  47. Stauffer, C., & Grimson, W.E.L. (1999). Adaptive background mixture models for real-time tracking. In Proceedings of IEEE CVPR, 2, 246–252.Google Scholar
  48. Wang, X., Hua, G., & Han, T. X. (2010). Discriminative tracking by metric learning. In Proceedings of ECCV (pp. 200–214).Google Scholar
  49. Wilson, R., & Granlund, G. (1984). The uncertainty principle in image processing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6.Google Scholar
  50. Wilson, R., & Goesta, H. (1984). Granlund the uncertainty principle in image processing. IEEE Transactions on PAMI, 6(6), 758–767.CrossRefGoogle Scholar
  51. Wu, Yi., Jongwoo L., & Ming-Hsuan Y. (2013). Online object tracking: A benchmark. In Proc. of CVPR (pp. 2411–2418).Google Scholar
  52. Wu, B., & Nevatia, R. (2006). Tracking of multiple, partially occluded humans based on static body part detection. In Proceedings of IEEE CVPR (pp. 951–958).Google Scholar
  53. Yao, R., Shi, Q., Shen, C., Zhang, Y., & Hengel, A. V. (2013). Part-based visual tracking with online latent structural learning. In Proceedings of IEEE CVPR (pp. 25–27).Google Scholar
  54. Zhang, B., & Li, Z. (2016). Alessandro Perina, Alessio Del Bue, Vittorio Murino, Jianzhuang Liu. IEEE Transactions on CSVT: Adaptive Local Movement Modeling (ALMM) for Object Tracking.Google Scholar
  55. Zhang, K., Zhang, L., Yang, M., Zhang, D. (2014). Fast tracking via spatio-temporal context learning. ECCV.Google Scholar
  56. Zhang, B., Gao, Y., Zhao, S., & Zhong, B. (2011). Kernel Similarity modeling of texture pattern flow for motion detection in complex background. IEEE Transactions on CSVT, 21(1), 29–38.Google Scholar
  57. Zhang, K., Zhang, L., & Yang, M. H. (2014). Real-time compressive tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(10), 2002–2015.CrossRefGoogle Scholar
  58. Zhuang, B., Lu, H., Xiao, Z., & Wang, D. (2014). Visual tracking via discriminative sparse similarity map. IEEE Transactions on Image Processing, 23(4), 1872–1881.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Baochang Zhang
    • 1
  • Alessandro Perina
    • 3
  • Zhigang Li
    • 1
  • Vittorio Murino
    • 3
  • Jianzhuang Liu
    • 4
  • Rongrong Ji
    • 2
  1. 1.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina
  2. 2.Fujian Key Laboratory of Sensing and Computing for Smart City, School of Information Science and EngineeringXiamen UniversityXiamenChina
  3. 3.Pattern Analysis and Computer Vision (PAVIS)Istituto Italiano di Tecnologia (IIT)GenovaItaly
  4. 4.Media LaboratoryHuawei Technologies Company Ltd.ShenzhenChina

Personalised recommendations