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Sparse Coding for Symmetric Positive Definite Matrices with Application to 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))

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Abstract

Modelling videos or images with Symmetric Positive Definite (SPD) matrices and utilizing the intrinsic geometry of the Riemannian manifold has proven helpful for many computer vision tasks. Inspired by the significant success of sparse coding for vector data, recent researches show great interests in studying sparse coding for SPD matrices. However, the space of SPD matrices is a well-known Riemannian manifold so that existing sparse coding approaches for vector data cannot be directly extended. In this paper, we propose to use the Log-Euclidean Distance on the Riemannian manifold, which naturally derives a Riemannian kernel function to solve the sparse coding problem. The proposed method can be easily applied to image set classification by representing image sets with nonsingular covariance matrices. We compare our method with other sparse coding techniques for SPD matrices and demonstrate its benefits in image set classification on several standard datasets.

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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, Wuxi, 214122, China

    Jieyi Ren

  2. School of IOT Engineering, Jiangnan University, Wuxi, 214122, 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). Sparse Coding for Symmetric Positive Definite Matrices with Application to 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_64

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  • DOI: https://doi.org/10.1007/978-3-319-23989-7_64

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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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