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International Journal of Computer Vision

Erschienen in:

01.02.2013

Euler Principal Component Analysis

verfasst von: Stephan Liwicki, Georgios Tzimiropoulos, Stefanos Zafeiriou, Maja Pantic

Erschienen in: International Journal of Computer Vision | Ausgabe 3/2013

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Abstract

Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the ℓ ₂-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA, which we call Euler-PCA (e-PCA). In particular, our algorithm utilizes a robust dissimilarity measure based on the Euler representation of complex numbers. We show that Euler-PCA retains PCA’s desirable properties while suppressing outliers. Moreover, we formulate Euler-PCA in an incremental learning framework which allows for efficient computation. In our experiments we apply Euler-PCA to three different computer vision applications for which our method performs comparably with other state-of-the-art approaches.

Vorheriger Artikel Using Segmented 3D Point Clouds for Accurate Likelihood Approximation in Human Pose Tracking

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Without loss of generality we assume zero mean.

We set α=1.9, as will be discussed later, in Sect. 4.

The fingerspelling alphabet is a subset of sign language which is utilized for spelling names. Examples can be found at http://asl.ms/.

The Matlab implementation is publicly available at http://www.cs.toronto.edu/~dross/ivt/.

The Matlab implementation of the IKPCA was kindly provided by the authors of the paper.

The implementation is publicly available at http://www.ist.temple.edu/~hbling/code_data.htm.

The implementation (only for translation motion model) is publicly available at http://vision.ucsd.edu/~bbabenko/project_miltrack.shtml, we carefully modified it in order to support an affine motion model in a particle filter framework.

Videos V ₄ and V ₅ are available at http://vision.ucsd.edu/~bbabenko/project_miltrack.shtml and the remaining videos are published at http://www.cs.toronto.edu/~dross/ivt/.

MATLAB implementations on a desktop computer with Intel Core i7 870 at 2.93 GHz and 8 GB RAM.

Avidan, S. (2004). Support vector tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1064–1072. doi:10.1109/TPAMI.2004.53.

Babenko, B., Yang, M., & Belongie, S. (2009). Visual tracking with online multiple instance learning. In CVPR’09 (pp. 983–990).

Babenko, B., Yang, M., & Belongie, S. (2011). Robust object tracking with online multiple instance learning. IEEE Transactions on Pattern Analysis and Machine Intelligence. doi:10.1109/TPAMI.2010.226.

Candés, E., Li, X., Ma, Y., & Wright, J. (2009). Robust principal component analysis? Available at: http://arxiv.org/abs/0912.3599v1.

Chin, T. J., & Suter, D. (2007). Incremental kernel principal component analysis. IEEE Transactions on Image Processing, 1662–1674. doi:10.1109/TIP.2007.896668.

Chin, T., Schindler, K., & Suter, D. (2006). Incremental kernel SVD for face recognition with image sets. In FG’06 (pp. 461–466).

Cohn, J., Zlochower, A., Lien, J., & Kanade, T. (1999). Automated face analysis by feature point tracking has high concurrent validity with manual FACS coding. Psychophysiology, 35–43. doi:10.1017/S0048577299971184.

Collins, R., Lipton, J., Fujiyoshi, H., & Kanade, T. (2001). Algorithms for cooperative multisensor surveillance. In The IEEE (p. 89). doi:10.1109/5.959341.

Comaniciu, D., Ramesh, V., & Meer, P. (2003). Kernel-based object tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence, 564–577. doi:10.1109/TPAMI.2003.1195991.

de la Torre, F., & Black, M. (2003). A framework for robust subspace learning. International Journal of Computer Vision, 117–142. doi:10.1023/A:1023709501986.

Ding, D., Zhou, D., He, X., & Zha, H. (2006). R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. In ACM (pp. 281–288). doi:10.1145/1143844.1143880.

Fitch, A., Kadyrov, A., Christmas, W., & Kittler, J. (2005). Fast robust correlation. IEEE Transactions on Image Processing, 1063–1073. doi:10.1109/TIP.2005.849767.

Fraundorfer, F., Engels, C., & Nistér, D. (2007). Topological mapping, localization and navigation using image collections. In Intell. robots and systems (pp. 3872–3877).

Gunawan, H., Neswan, O., & Budhi, W. (2005). A formula for angles between subspaces of inner product spaces. Contributions to Algebra and Geometry, 46(2), 311–320. MathSciNetMATH

Gunes, H., & Pantic, M. (2010). Automatic, dimensional and continuous emotion recognition. International Journal of Synthetic Emotion, 68–99. doi:10.4018/jse.2010101605.

Handmann, U., Kalinke, T., & Tzomakas, C. (1998). Computer vision for driver assistance systems. Proc. SPIE, 136–147. doi:10.1117/12.317463.

Haritaoglu, I., Harwood, D., & Davis, L. (2000). W4: real-time surveillance of people and their activities. IEEE Transactions on Pattern Analysis and Machine Intelligence, 809–830. doi:10.1109/34.868683.

Hashima, M., Hasegawa, F., Kanda, S., Maruyama, T., & Uchiyama, T. (1997). Localization and obstacle detection for a robot for carrying food trays. In Intell. robots and systems (pp. 345–351).

He, R., Hu, B., Zheng, W., & Kong, X. (2011). Robust principal component analysis based on maximum correntropy criterion. IEEE Transactions on Image Processing, 1485–1494. doi:10.1109/TIP.2010.2103949.

Honeine, P., & Richard, C. (2011). Preimage problem in kernel-based machine learning. IEEE Signal Processing Magazine, 28(2), 77–88. CrossRef

Hsieh, J., Yu, S., Chen, Y., & Hu, W. (2006). Automatic traffic surveillance system for vehicle tracking and classification. IEEE Transactions on Intelligent Transportation Systems, 175–187. doi:10.1109/TITS.2006.874722.

Jolliffe, T. (2002). Principal component analysis (2nd edn.). Berlin: Springer. MATH

Kamijo, S., Matsushita, Y., Ikeuchi, K., & Sakauchi, M. (2000). Traffic monitoring and accident detection at intersections. IEEE Transactions on Intelligent Transportation Systems, 108–118. doi:10.1109/6979.880968.

Ke, Q., & Kanade, T. (2003). Robust subspace computation using L1 norm (Tech. Rep. CMU-CS-03-172). Computer Science Department, Carnegie Mellon University.

Ke, Q., & Kanade, T. (2005). Robust L1 norm factorization in the presence of outliers and missing data by alternative convex programming. In CVPR’05 (pp. 739–746).

Krzanowski, W. (1979). Between-groups comparison of principal components. Journal of the American Statistical Association, 703–707. doi:10.1080/01621459.1979.10481674.

Kwak, N. (2008). Principal component analysis based on L1-norm maximization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1672–1680. doi:10.1109/TPAMI.2008.114.

Kwok, J., & Tsang, I. (2004). The pre-image problem in kernel methods. IEEE Transactions on Neural Networks, 15(6), 1517–1525. CrossRef

Levy, A., & Lindenbaum, M. (2000). Sequential Karhunen-Loeve basis extraction and its application to images. IEEE Transactions on Image Processing, 1371–1374. doi:10.1109/83.855432.

Li, Y. (2004). On incremental and robust subspace learning. Pattern Recognition, 1509–1518. doi:10.1016/j.patcog.2003.11.010.

Li, L., Huang, W., Gu, I., & Tian, Q. (2004). Statistical modeling of complex backgrounds for foreground object detection. IEEE Transactions on Image Processing, 13(11), 1459–1472. CrossRef

Liu, W., Pokharel, P., & Principe, J. (2007). Correntropy: properties and applications in non-Gaussian signal processing. IEEE Transactions on Signal Processing, 5286–5298. doi:10.1109/TSP.2007.896065.

Liwicki, S., & Everingham, M. (2009). Automatic recognition of fingerspelled words in British sign language. In CVPR4HB’09, in conj. with CVPR’09 (pp. 50–57).

Liwicki, S., et al. (2012). doi:10.1109/TNNLS.2012.2208654.

Luo, Y., Wu, T., & Hwang, J. (2003). Object-based analysis and interpretation of human motion in sports video sequences by dynamic Bayesian networks. Computer Vision and Image Understanding, 196–216. doi:10.1016/j.cviu.2003.08.001.

Maddalena, L., & Petrosino, A. (2008). A self-organizing approach to background subtraction for visual surveillance applications. IEEE Transactions on Image Processing, 1168–1177. doi:10.1109/TIP.2008.924285.

Martinez, A., & Benavente, R. (1998). The AR face database (Tech. Rep. #24). The Ohio State University.

Mei, X., & Ling, H. (2009). Robust visual tracking using L1 minimization. In ICCV’09.

Mika, S., Schölkopf, B., Smola, A., Müller, K., Scholz, M., & Rätsch, G. (1999). Kernel pca and de-noising in feature spaces. Advances in Neural Information Processing Systems, 11(1), 536–542.

Nguyen, M., & de la Torre, F. (2009). Robust kernel principal component analysis. In Advances in NIPS (pp. 1185–1192).

Oliver, N., Rosario, B., & Pentland, A. (2000). A Bayesian computer vision system for modeling human interactions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 831–843. doi:10.1109/34.868684.

Paulsen, V. (2009). An introduction to the theory of reproducing kernel Hilbert spaces. Available at: http://www.math.uh.edu/~vern/rkhs.pdf.

Ross, D., Lim, J., Lin, R., & Yang, M. (2008). Incremental learning for robust visual tracking. International Journal of Computer Vision, 125–141. doi:10.1007/s11263-007-0075-7.

Tzimiropoulos, G. (2010). IEEE Transactions on Pattern Analysis and Machine Intelligence. doi:10.1109/TPAMI.2010.107.

Tzimiropoulos, G. (2012). IEEE Transactions on Pattern Analysis and Machine Intelligence. doi:10.1109/TPAMI.2012.40.

Turk, M., & Pentland, A. (1991). Eigenfaces for recognition. Journal of Cognitive Neuroscience, 71–86. doi:10.1162/jocn.1991.3.1.71.

Wren, C., Azarbayejani, A., Darrel, T., & Pentland, A. (1997). Pfinder: real-time tracking of the human body. IEEE Transactions on Pattern Analysis and Machine Intelligence, 780–785. doi:10.1109/34.598236.

Titel: Euler Principal Component Analysis
verfasst von: Stephan Liwicki
Georgios Tzimiropoulos
Stefanos Zafeiriou
Maja Pantic
Publikationsdatum: 01.02.2013
Verlag: Springer US
Erschienen in: International Journal of Computer Vision / Ausgabe 3/2013
Print ISSN: 0920-5691
Elektronische ISSN: 1573-1405
DOI: https://doi.org/10.1007/s11263-012-0558-z

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