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Bidirectional Covariance Matrices: A Compact and Efficient Data Descriptor for Image Set Classification

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Intelligence Science and Big Data Engineering. Image and Video Data Engineering (IScIDE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9242))

Abstract

Symmetric Positive Definite (SPD) matrices have been widely used in many computer vision tasks. Recently, there are growing interests in applying covariance matrices to image set classification due to their benefit of encoding image features as a data descriptor. Since SPD matrices follow a non-linear Riemannian geometry, exploiting an appropriate Riemannian metric is the key to successful classification. Adopting Riemannian metrics to classify covariance matrices of image sets is nontrivial, since such matrices are usually singular matrices. Besides, the computational complexity is intolerable while dealing with high dimensional covariance matrices. This paper proposes to use bidirectional covariance matrices instead of covariance matrices as a data descriptor. We model image sets both from the row and column directions of images and these bidirectional covariance matrices are proved to be compact and efficient. Improved accuracy and efficiency are obtained through experiments on standard datasets for comparing bidirectional covariance matrices with covariance matrices.

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References

  1. 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)

    Chapter  Google Scholar 

  2. Pang, Y., Yuan, Y., Li, X.: Gabor-based region covariance matrices for face recognition. IEEE Trans. Circ. Syst. Video Technol. 18, 989–993 (2008)

    Article  Google Scholar 

  3. Sivalingam, R., Boley, D., Morellas, V., Papanikolopoulos, N.: Tensor sparse coding for region covariances. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part IV. LNCS, vol. 6314, pp. 589–600. Springer, Heidelberg (2010)

    Google Scholar 

  4. Cherian, A., Morellas, V., Papanikolopoulos, N., Bedros, S.J.: Dirichlet process mixture models on symmetric positive definite matrices for appearance clustering in video surveillance applications. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 3417–3424. IEEE (2011)

    Google Scholar 

  5. Porikli, F., Tuzel, O., Meer, P.: Covariance tracking using model update based on lie algebra. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 728–735. IEEE (2006)

    Google Scholar 

  6. Ma, B., Wu, Y., Sun, F.: Affine object tracking using kernel-based region covariance descriptors. In: Wang, Y., Li, T. (eds.) Foundations of Intelligent Systems, pp. 613–623. Springer, Heidelberg (2012)

    Google Scholar 

  7. Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 29, 328–347 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Xie, Y., Vemuri, B.C., Ho, J.: Statistical analysis of tensor fields. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010, Part I. LNCS, vol. 6361, pp. 682–689. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Shakhnarovich, G., Fisher III, J.W., Darrell, T.: Face recognition from long-term observations. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part III. LNCS, vol. 2352, pp. 851–865. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Arandjelovic, O., Shakhnarovich, G., Fisher, J., Cipolla, R., Darrell, T.: Face recognition with image sets using manifold density divergence. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 581–588. IEEE (2005)

    Google Scholar 

  11. Hamm, J., Lee, D.D.: Grassmann discriminant analysis: a unifying view on subspace-based learning. In: 25th International Conference on Machine Learning, pp. 376–383. ACM (2008)

    Google Scholar 

  12. Hu, Y., Mian, A.S., Owens, R.: Sparse approximated nearest points for image set classification. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 121–128. IEEE (2011)

    Google Scholar 

  13. Wang, R., Guo, H., Davis, L.S., Dai, Q.: Covariance discriminative learning: a natural and efficient approach to image set classification. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 2496–2503. IEEE (2012)

    Google Scholar 

  14. Uzair, M., Mahmood, A., Mian, A., McDonald, C.: A compact discriminative representation for efficient image-set classification with application to biometric recognition. In: International Conference on Biometrics, pp. 1–8. IEEE (2013)

    Google Scholar 

  15. Huang, Z., Wang, R., Shan, S., Chen, X.: Hybrid Euclidean-and-Riemannian metric learning for image set classification. In: Cremers, D., Reid, I., Saito, H., Yang, M.-H. (eds.) ACCV 2014. LNCS, vol. 9005, pp. 562–577. Springer, Heidelberg (2015)

    Google Scholar 

  16. Jayasumana, S., Hartley, R., Salzmann, M., Li, H., Harandi, M.: Kernel methods on the Riemannian manifold of symmetric positive definite matrices. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 73–80. IEEE (2013)

    Google Scholar 

  17. Förstner, W., Moonen, B.: A metric for covariance matrices. In: Grafarend, E.W., Krumm, F.W., Schwarze, V.S. (eds.) Geodesy-The Challenge of the 3rd Millennium, pp. 299–309. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Yang, J., Zhang, D., Frangi, A.F., Yang, J.Y.: Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans. Pattern Anal. Mach. Intell. 26, 131–137 (2004)

    Article  Google Scholar 

  19. Zhang, D., Zhou, Z.H.: (2D) 2PCA: two-directional two-dimensional PCA for efficient face representation and recognition. Neurocomputing 69, 224–231 (2005)

    Article  Google Scholar 

  20. Baudat, G., Anouar, F.: Generalized discriminant analysis using a kernel approach. Neural Comput. 12, 2385–2404 (2000)

    Article  Google Scholar 

  21. Lee, K.C., Ho, J., Yang, M.H., Kriegman, D.: Video-based face recognition using probabilistic appearance manifolds. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 313–320. IEEE (2003)

    Google Scholar 

  22. Kim, M., Kumar, S., Pavlovic, V., Rowley, H.: Face tracking and recognition with visual constraints in real-world videos. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8. IEEE (2008)

    Google Scholar 

  23. Leibe, B., Schiele, B.: Analyzing appearance and contour based methods for object categorization. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. II-409-15. IEEE (2003)

    Google Scholar 

  24. Lazebnik, S., Schmid, C., Ponce, J.: Beyond bags of features: spatial pyramid matching for recognizing natural scene categories. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 2169–2178. IEEE (2006)

    Google Scholar 

  25. Viola, P., Jones, M.J.: Robust real-time face detection. Int. J. Comput. Vision 57, 137–154 (2004)

    Article  Google Scholar 

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Acknowledgments

This work was supported in part by the project of NSFC (No. 61373055) and the Research Project on Surveying and Mapping of Jiangsu Province (No. JSCHKY201109).

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Authors and Affiliations

  1. School of Digital Media, Jiangnan University, 214122, Wuxi, China

    Jieyi Ren

  2. School of IOT Engineering, Jiangnan University, 214122, Wuxi, China

    Xiaojun Wu

Authors
  1. Jieyi Ren
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  2. Xiaojun Wu
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Corresponding author

Correspondence to Xiaojun Wu .

Editor information

Editors and Affiliations

  1. Zhejiang University, Hangzhou, China

    Xiaofei He

  2. Xidian University, Xi'an, China

    Xinbo Gao

  3. Northwestern Polytechnical University, Shaanxi, China

    Yanning Zhang

  4. Nanjing University, Nanjing, China

    Zhi-Hua Zhou

  5. Chinese Academy of Sciences, Beijing, China

    Zhi-Yong Liu

  6. Suzhou University of Science and Technology, Suzhou, China

    Baochuan Fu

  7. Suzhou University of Science and Technology, Jiangsu, China

    Fuyuan Hu

  8. Suzhou University of Science and Technology, Jiangsu, China

    Zhancheng Zhang

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Ren, J., Wu, X. (2015). Bidirectional Covariance Matrices: A Compact and Efficient Data Descriptor for Image Set Classification. In: He, X., et al. Intelligence Science and Big Data Engineering. Image and Video Data Engineering. IScIDE 2015. Lecture Notes in Computer Science(), vol 9242. Springer, Cham. https://doi.org/10.1007/978-3-319-23989-7_20

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  • DOI: https://doi.org/10.1007/978-3-319-23989-7_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23987-3

  • Online ISBN: 978-3-319-23989-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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