Abstract
In many computer vision tasks, images or image sets can be modeled as a Gaussian distribution to capture the underlying data distribution. The challenge of using Gaussians to model the vision data is that the space of Gaussians is not a linear space. From the perspective of information geometry, the Gaussians lie on a specific Riemannian Manifold. In this paper, we present a joint metric learning (JML) model on Riemannian Manifold of Gaussian distributions. The distance between two Gaussians is defined as the sum of the Mahalanobis distance between the mean vectors and the log-Euclidean distance (LED) between the covariance matrices. We formulate the multi-metric learning model by jointly learning the Mahalanobis distance and the log-Euclidean distance with pairwise constraints. Sample pair weights are embedded to select the most informative pairs to learn the discriminative distance metric. Experiments on video based face recognition, object recognition and material classification show that JML is superior to the state-of-the-art metric learning algorithms for Gaussians.
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References
Calvo, M., Oller, J.M.: A distance between multivariate normal distributions based in an embedding into the Siegel group (1990). https://doi.org/10.1016/0047-259X(90)90026-E
Cevikalp, H., Triggs, B.: Face recognition based on image sets. In: CVPR, pp. 2567–2573 (2010). https://doi.org/10.1109/CVPR.2010.5539965
Gong, L., Wang, T., Liu, F.: Shape of Gaussians as feature descriptors. In: CVPR, pp. 2366–2371 (2009). https://doi.org/10.1109/CVPR.2009.5206506
Harandi, M., Salzmann, M., Hartley, R.: Dimensionality reduction on spd manifolds: the emergence of geometry-aware methods. TPAMI (2017). https://doi.org/10.1109/TPAMI.2017.2655048
Harandi, M.T., Sanderson, C., Hartley, R., Lovell, B.C.: Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012. LNCS, pp. 216–229. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33709-3_16
Huang, Z., Wang, R., Shan, S., Chen, X.: Projection metric learning on Grassmann manifold with application to video based face recognition. In: CVPR, pp. 140–149 (2015). https://doi.org/10.1109/CVPR.2015.7298609
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: ICML, pp. 720–729 (2015)
Jegou, H., Perronnin, F., Douze, M., Sánchez, J., Perez, P., Schmid, C.: Aggregating local image descriptors into compact codes. TPAMI 34(9), 1704–1716 (2012). https://doi.org/10.1109/tpami.2011.235
Kim, M., Kumar, S., Pavlovic, V., Rowley, H.: Face tracking and recognition with visual constraints in real-world videos. In: CVPR, pp. 1–8 (2008). https://doi.org/10.1109/CVPR.2008.4587572
Leibe, B., Schiele, B.: Analyzing appearance and contour based methods for object categorization. In: CVPR, vol. 2, pp. 402–409 (2003). https://doi.org/10.1109/CVPR.2003.1211497
Li, P., Wang, Q., Zeng, H., Zhang, L.: Local log-Euclidean multivariate Gaussian descriptor and its application to image classification. TPAMI 39(4), 803–817 (2017). https://doi.org/10.1109/TPAMI.2016.2560816
Li, P., Wang, Q., Zhang, L.: A novel earth mover’s distance methodology for image matching with Gaussian mixture models. In: ICCV, pp. 1689–1696 (2013). https://doi.org/10.1109/ICCV.2013.212
Li, P., Zeng, H., Wang, Q., Shiu, S.C., Zhang, L.: High-order local pooling and encoding Gaussians over a dictionary of Gaussians. TIP 26(7), 3372–3384 (2017). https://doi.org/10.1109/TIP.2017.2695884
Liao, Z., Rock, J., Wang, Y., Forsyth, D.: Non-parametric filtering for geometric detail extraction and material representation. In: CVPR, June 2013. https://doi.org/10.1109/CVPR.2013.129
Lovri, M., Min-Oo, M., Ruh, E.A.: Multivariate normal distributions parametrized as a riemannian symmetric space. JMVA 74(1), 36–48 (2000). https://doi.org/10.1006/jmva.1999.1853
Matsukawa, T., Okabe, T., Suzuki, E., Sato, Y.: Hierarchical Gaussian descriptor for person re-identification. In: CVPR, pp. 1363–1372 (2016). https://doi.org/10.1109/CVPR.2016.152
Nakayama, H., Harada, T., Kuniyoshi, Y.: Global Gaussian approach for scene categorization using information geometry. In: CVPR, pp. 2336–2343 (2010). https://doi.org/10.1109/CVPR.2010.5539921
Nchez, J., Perronnin, F., Mensink, T., Verbeek, J.: Image classification with the fisher vector: theory and practice. IJCV 105(3), 222–245 (2013). https://doi.org/10.1007/s11263-013-0636-x
Niesen, U., Shah, D., Wornell, G.W.: Adaptive alternating minimization algorithms. TIT 55(3), 1423–1429 (2008). https://doi.org/10.1109/tit.2008.2011442
Serra, G., Grana, C., Manfredi, M., Cucchiara, R.: Gold: Gaussians of local descriptors for image representation. CVIU 134, 22–32 (2015). https://doi.org/10.1016/j.cviu.2015.01.005
Sharan, L., Rosenholtz, R., Adelson, E.H.: Material perception: what can you see in a brief glance? J. Vis. 9(8), 784 (2009)
Wang, J., Yang, J., Yu, K., Lv, F., Huang, T., Gong, Y.: Locality-constrained linear coding for image classification. In: CVPR, pp. 3360–3367 (2010). https://doi.org/10.1109/CVPR.2010.5540018
Wang, Q., Li, P., Zhang, L., Zuo, W.: Towards effective codebookless model for image classification. PR 59(C), 63–71 (2016). https://doi.org/10.1016/j.patcog.2016.03.004
Wang, R., Chen, X.: Manifold discriminant analysis. In: CVPR, pp. 429–436 (2009). https://doi.org/10.1109/CVPRW.2009.5206850
Wang, W., Wang, R., Huang, Z., Shan, S., Chen, X.: Discriminant analysis on Riemannian Manifold of Gaussian distributions for face recognition with image sets. TIP 27(1), 151–163 (2018). https://doi.org/10.1109/TIP.2017.2746993
Wang, W., Wang, R., Huang, Z., Shan, S., Chen, X.: Discriminant analysis on Riemannian Manifold of Gaussian distributions for face recognition with image sets. In: CVPR, pp. 2048–2057 (2015). https://doi.org/10.1109/CVPR.2015.7298816
Wang, W., Wang, R., Shan, S., Chen, X.: Discriminative covariance oriented representation learning for face recognition with image sets. In: CVPR, pp. 5599–5608 (2017). https://doi.org/10.1109/CVPR.2017.609
Zadeh, P.H., Hosseini, R., Sra, S.: Geometric mean metric learning. In: ICML, pp. 2464–2471 (2016)
Zhou, X., Cui, N., Li, Z., Liang, F., Huang, T.S.: Hierarchical Gaussianization for image classification. In: ICCV, pp. 1971–1977 (2009). https://doi.org/10.1109/ICCV.2009.5459435
Zhou, X., Yu, K., Zhang, T., Huang, T.S.: Image classification using super-vector coding of local image descriptors. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6315, pp. 141–154. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15555-0_11
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grants 61502332, 61876127 and 61732011, Natural Science Foundation of Tianjin Under Grants 17JCZDJC30800, Key Scientific and Technological Support Projects of Tianjin Key R&D Program 18YFZCGX00390 and 18YFZCGX00680.
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Nie, Q., Zhou, B., Zhu, P., Hu, Q., Cheng, H. (2019). Joint Metric Learning on Riemannian Manifold of Global Gaussian Distributions. In: Tetko, I., Kůrková, V., Karpov, P., Theis, F. (eds) Artificial Neural Networks and Machine Learning – ICANN 2019: Deep Learning. ICANN 2019. Lecture Notes in Computer Science(), vol 11728. Springer, Cham. https://doi.org/10.1007/978-3-030-30484-3_43
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