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Computational Visual Media

, Volume 4, Issue 3, pp 245–252 | Cite as

Component SPD matrices: A low-dimensional discriminative data descriptor for image set classification

  • Kai-Xuan Chen
  • Xiao-Jun Wu
Open Access
Research Article
  • 42 Downloads

Abstract

In pattern recognition, the task of image set classification has often been performed by representing data using symmetric positive definite (SPD) matrices, in conjunction with the metric of the resulting Riemannian manifold. In this paper, we propose a new data representation framework for image sets which we call component symmetric positive definite representation (CSPD). Firstly, we obtain sub-image sets by dividing the images in the set into square blocks of the same size, and use a traditional SPD model to describe them. Then, we use the Riemannian kernel to determine similarities of corresponding subimage sets. Finally, the CSPD matrix appears in the form of the kernel matrix for all the sub-image sets; its i, j-th entry measures the similarity between the i-th and j-th sub-image sets. The Riemannian kernel is shown to satisfy Mercer’s theorem, so the CSPD matrix is symmetric and positive definite, and also lies on a Riemannian manifold. Test on three benchmark datasets shows that CSPD is both lower-dimensional and more discriminative data descriptor than standard SPD for the task of image set classification.

Keywords

symmetric positive definite (SPD) matrices Riemannian kernel image classification Riemannian manifold 

References

  1. [1]
    Huang, Z.; Wang, R.; Shan, S.; Chen, X. Projection metric learning on Grassmann manifold with application to video based face recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 140–149, 2015.Google Scholar
  2. [2]
    Harandi, M.; Salzmann, M.; Hartley, R. Dimensionality reduction on SPD manifolds: The emergence of geometry-aware methods. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 40, No. 1, 48–62, 2017.CrossRefGoogle Scholar
  3. [3]
    Chang, F.-J.; Nevatia, R. Image set classification via template triplets and context-aware similarity embedding. In: Computer Vision–ACCV 2016. Lecture Notes in Computer Science, Vol. 10115. Lai, S. H.; Lepetit, V.; Nishino, K.; Sato, Y. Eds. Springer Cham, 231–247, 2016.Google Scholar
  4. [4]
    Huang, Z.; Wang, R.; Shan, S.; Li, X.; Chen, X. Log-Euclidean metric learning on symmetric positive definite manifold with application to image set classification. In: Proceedings of the 32nd International Conference on Machine Learning, Vol. 37, 720–729, 2015.Google Scholar
  5. [5]
    Faraki, M.; Harandi, M. T.; Porikli, F. Image set classification by symmetric positive semi-definite matrices. In: Proceedings of the IEEE Winter Conference on Applications of Computer Vision, 1–8, 2016.Google Scholar
  6. [6]
    Chen, Z.; Jiang, B.; Tang, J.; Luo, B. Image set representation and classification with attributed covariate-relation graph model and graph sparse representation classification. Neurocomputing Vol. 226, 262–268, 2017.CrossRefGoogle Scholar
  7. [7]
    Wang, R.; Guo, H.; Davis, L. S.; Dai, Q. Covariance discriminative learning: A natural and efficient approach to image set classification. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2496–2503, 2012.Google Scholar
  8. [8]
    Ren, J.; Wu, X. Bidirectional covariance matrices: A compact and efficient data descriptor for image set classification. In: Intelligence Science and Big Data Engineering. Image and Video Data Engineering. Lecture Notes in Computer Science, Vol. 9242. He, X. et al. Eds. Springer Cham, 186–195, 2015.Google Scholar
  9. [9]
    Cherian, A.; Sra, S. Riemannian dictionary learning and sparse coding for positive definite matrices. IEEE Transactions on Neural Networks and Learning Systems Vol. 28, No. 12, 2859–2871, 2017.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Harandi, M. T.; Hartley, R.; Lovell, B.; Sanderson, C. Sparse coding on symmetric positive definite manifolds using Bregman divergences. IEEE Transactions on Neural Networks and Learning Systems Vol. 27, No. 6, 1294–1306, 2016.CrossRefGoogle Scholar
  11. [11]
    Li, P.; Wang, Q.; Zuo, W.; Zhang, L. Log-Euclidean kernels for sparse representation and dictionary learning. In: Proceedings of the IEEE International Conference on Computer Vision, 1601–1608, 2013.Google Scholar
  12. [12]
    Wang, Q.; Li, P.; Zuo, W.; Zhang, L. RAID-G: Robust estimation of approximate infinite dimensional Gaussian with application to material recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 4433–4441, 2016.Google Scholar
  13. [13]
    Faraki, M.; Harandi, M. T.; Porikli, F. Approximate infinite-dimensional region covariance descriptors for image classification. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, 1364–1368, 2015.Google Scholar
  14. [14]
    Arandjelovic, O.; Shakhnarovich, G.; Fisher, J.; Cipolla, R.; Darrell, T. Face recognition with image sets using manifold density divergence. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 1, 581–588, 2005.Google Scholar
  15. [15]
    Tuzel, O.; Porikli, F.; Meer, P. Region covariance: A fast descriptor for detection and classification. In: Computer Vision–ECCV 2006. Lecture Notes in Computer Science, Vol. 3952. Leonardis, A.; Bischof, H.; Pinz, A. Eds. Springer Berlin Heidelberg, 589–600, 2006.Google Scholar
  16. [16]
    Moore, B. Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Transactions on Automatic Control Vol. 26, No. 1, 17–32, 1981.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Izenman, A. J. Linear discriminant analysis. In: Modern Multivariate Statistical Techniques. Springer Texts in Statistics. Springer New York, 237–280, 2013.CrossRefGoogle Scholar
  18. [18]
    Zhang, D.; Zhou, Z.-H. (2D)2PCA: Two-directional two-dimensional PCA for efficient face representation and recognition. Neurocomputing Vol. 69, Nos. 1–3, 224–231, 2005.CrossRefGoogle Scholar
  19. [19]
    Pennec, X.; Fillard, P.; Ayache, N. A Riemannian framework for tensor computing. International Journal of Computer Vision Vol. 66, No. 1, 41–66, 2006.CrossRefzbMATHGoogle Scholar
  20. [20]
    Harandi, M.; Salzmann, M. Riemannian coding and dictionary learning: Kernels to the rescue. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 3926–3935, 2015.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.School of IoT EngineeringJiangnan UniversityWuxiChina
  2. 2.Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational IntelligenceJiangnan UniversityWuxiChina

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