Visual Tracking Based on Log-Euclidean Riemannian Sparse Representation

  • Yi Wu
  • Haibin Ling
  • Erik Blasch
  • Li Bai
  • Genshe Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6938)


Recently, sparse representation has been utilized in many computer vision tasks and adapted for visual tracking. Sparsity-based visual tracking is formulated as searching candidates with minimal reconstruction errors from a template subspace with sparsity constraints in the approximation coefficients. However, an intensity template is easily corrupted by noise and not robust for target tracking under a dynamic environment. The recently proposed covariance region descriptor has been proven robust and versatile for a modest computational cost. Further, the covariance matrix enables efficient fusion of different types of features, where the spatial and statistical properties as well as their correlation are characterized, and its dimension is small. Although the covariance matrix lies on Riemannian manifolds, its log-transformation can be measured on a Euclidean subspace. Based on the covariance region descriptor and using the sparse representation, we propose a novel tracking approach on the Log-Euclidean Riemannian subspace. Specifically, the target region is characterized by a covariance matrix which is then log-transformed from the Riemannian manifold to the Euclidean subspace. After that, the target tracking problem is integrated under a sparse approximation framework, where the sparsity is achieved by solving an ℓ1-regularization problem. Then the candidate with the smallest approximation is taken as the tracked target. For target propagation, we use the Bayesian state inference framework, which propagates sample distributions over time using the particle filter algorithm. To evaluate our method, we have collected several video sequences and the experimental results show that our tracker can achieve robustly and reliably target tracking.


Riemannian Manifold Sparse Representation Target Tracking Visual Tracking Covariance Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Isard, M., Blake, A.: Condensation-Conditional Density Propagation for Visual Tracking. Int’l Journal of Computer Vision 29, 5–28 (1998)CrossRefGoogle Scholar
  2. 2.
    Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online Learning for Matrix Factorization and Sparse Coding. J. Machine Learning Research 11, 19–60 (2010)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Mei, X., Ling, H.: Robust Visual Tracking using ℓ1 Minimization. In: ICCV (2009)Google Scholar
  4. 4.
    Pérez, P., Hue, C., Vermaak, J., Gangnet, M.: Color-Based Probabilistic Tracking. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 661–675. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Wright, J., Yang, A., Ganesh, A., Sastry, S., Ma, Y.: Robust Face Recognition via Sparse Representation. IEEE T. Pattern Analysis and Machine Intelligence 31(1), 210–227 (2009)CrossRefGoogle Scholar
  6. 6.
    Wu, Y., Wu, B., Liu, J., Lu, H.Q.: Probabilistic Tracking on Riemannian Manifolds. In: ICPR (2008)Google Scholar
  7. 7.
    Wu, Y., Wang, J.Q., Lu, H.Q.: Robust Bayesian tracking on Riemannian manifolds via fragments-based representation. In: ICASSP (2009)Google Scholar
  8. 8.
    Wu, Y., Cheng, J., Wang, J., Lu, H.: Real-time Visual Tracking via Incremental Covariance Tensor Learning. In: ICCV (2009)Google Scholar
  9. 9.
    Yilmaz, A., Javed, O., Shah, M.: Object tracking: A survey. ACM Computing Surveys 38(4) (2006)Google Scholar
  10. 10.
    Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM J. on Matrix Analysis and Applications 29(1) (2008)Google Scholar
  11. 11.
    Li, X., Hu, W., Zhang, Z., Zhang, X., Zhu, M., Cheng, J.: Visual tracking via incremental Log-Euclidean Riemannian subspace learning. In: CVPR (2008)Google Scholar
  12. 12.
    Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. Int’l Journal of Computer Vision 66(1), 41–66 (2006)CrossRefzbMATHGoogle Scholar
  13. 13.
    Tuzel, O., Porikli, F., Meer, P.: Region covariance: A fast descriptor for detection and classification. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952, pp. 589–600. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Porikli, F., Tuzel, O., Meer, P.: Covariance tracking using model update based on Lie Algebra. In: CVPR, pp. 728–735 (2006)Google Scholar
  15. 15.
    Donoho, D.: Compressed sensing. IEEE T. Information Theory 52(4), 1289–1306 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Ling, H., Wu, Y., Blasch, E., Chen, G., Lang, H., Bai, L.: Evaluation of Visual Tracking in Extremely Low Frame Rate Wide Area Motion Imagery. Fusion (2011)Google Scholar
  17. 17.
    Chen, M., Pang, S.K., Cham, T.J., Goh, A.: Visual Tracking with Generative Template Model based on Riemannian Manifold of Covariances. Fusion (2011)Google Scholar
  18. 18.
    Liu, B., Yang, L., Huang, J., Meer, P., Gong, L., Kulikowski, C.: Robust and fast collaborative tracking with two stage sparse optimization. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6314, pp. 624–637. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Mei, X., Ling, H., Wu, Y., Blasch, E., Bai, L.: Minimum Error Bounded Efficient ℓ1 Tracker with Occlusion Detection. In: CVPR (2011)Google Scholar
  20. 20.
    Hong, X., Chang, H., Shan, S., Chen, X., Gao, W.: Sigma set: A small second order statistical region descriptor. In: CVPR, pp. 1802–1809 (2009)Google Scholar
  21. 21.
    Tosato, D., Farenzena, M., Spera, M., Murino, V., Cristani, M.: Multi-class classification on Riemannian manifolds for video surveillance. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6312, pp. 378–391. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  22. 22.
    Tuzel, O., Porikli, F., Meer, P.: Human detection via classification on Riemannian manifolds. In: CVPR (2007)Google Scholar
  23. 23.
    Paisitkriangkrai, S., Shen, C., Zhang, J.: Fast pedestrian detection using a cascade of boosted covariance features. IEEE T. Circuits & Systems for Video Technology 18(8), 1140–1151 (2008)CrossRefGoogle Scholar
  24. 24.
    Pang, Y., Yuan, Y., Li, X.: Gabor-based region covariance matrices for face recognition. IEEE T. Circuits & Systems for Video Technology 18(7), 989–993 (2008)CrossRefGoogle Scholar
  25. 25.
    Guo, K., Ishwar, P., Konrad, J.: Action change detection in video by covariance matching of silhouette tunnels. In: ICASSP, pp. 1110–1113 (2010)Google Scholar
  26. 26.
    Candès, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. on Pure and Applied Mathematics 59(8), 1207–1223 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Baker, S., Matthews, I.: Lucas-kanade 20 years on: A unifying framework. Int’l Journal of Computer Vision 56, 221–255 (2004)CrossRefGoogle Scholar
  28. 28.
    Comaniciu, D., Ramesh, V., Meer, P.: Kernel-based object tracking. IEEE T. Pattern Analysis and Machine Intelligence 25, 564–577 (2003)CrossRefGoogle Scholar
  29. 29.
    Hager, G., Belhumeur, P.: Real-time tracking of image regions with changes in geometry and illumination. In: CVPR, pp. 403–410 (1996)Google Scholar
  30. 30.
    Wu, Y., Blasch, E., Chen, G., Bai, L., Ling, H.: Multiple Source Data Fusion via Sparse Representation for Robust Visual Tracking. Fusion (2011)Google Scholar
  31. 31.
    Zhou, S.K., Chellappa, R., Moghaddam, B.: Visual tracking and recognition using appearance-adaptive models in particle filters. IEEE T. Image Processing 11, 1491–1506 (2004)CrossRefGoogle Scholar
  32. 32.

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yi Wu
    • 1
  • Haibin Ling
    • 1
  • Erik Blasch
    • 2
  • Li Bai
    • 3
  • Genshe Chen
    • 1
  1. 1.Center for Data Analytics and Biomedical Informatics, Computer and Information Science DepartmentTemple UniversityPhiladelphiaUSA
  2. 2.Air Force Research Lab/SNAAUSA
  3. 3.Electrical and Computer Engineering DepartmentTemple UniversityPhiladelphiaUSA

Personalised recommendations