International Journal of Computer Vision

, Volume 118, Issue 3, pp 364–379 | Cite as

Bounding Multiple Gaussians Uncertainty with Application to Object Tracking

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


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.


Uncertainty principle Object tracking MGU 



This work was supported in the part by Natural Science Foundation of China, under Contracts 61272052 and 61473086, and by the Program for New Century Excellent Talents University of Ministry of Education of China, and the National Basic Research Program of China (2015CB352501). The work of R. Ji is supported by the Special Fund for Earthquake Research in the Public Interest No. 201508025, the Open Projects Program of National Laboratory of Pattern Recognition, and the Nature Science Foundation of China (Nos. 61422210 and 61373076). Thanks for the suggestions from Alessio Del Bue and Wanquan Liu to improve the paper. Alessandro Perina and Zhigang Li have the same contribution to the paper.

Supplementary material

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


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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

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