Abstract
Video Surveillance is an active research topic in Computer Vision. Its applications include authentication in security sensitive areas, biometric-based specific person identification, overcrowding statistics and congestion control, strange situation detection and alarming, interactive surveillance using multiple cameras and so on. Video surveillance mainly involves modeling of background, detection of motion, classification of moving objects and object tracking. Background modeling is often used to detect moving object in video acquired by a fixed camera. Subspace learning method namely Principal Component Analysis (PCA) have been used to model the background to represent online data content while reducing dimension significantly. Detection and classification of the object of interest in the image captured by the camera is a vital step for automatic activity monitoring. Linear discriminant analysis (LDA) is a well-known classical statistical technique for dimension reduction and feature extraction for classification. This chapter gives an overview of the applications of Matrix Information Theory in video surveillance viz., background modeling by PCA, face recognition/object classification by LDA and finally object tracking using a covariance-based object description. The algorithms which are discussed in this paper are somewhat related to the broad area of Matrix Information Theory.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Szeliski, R.: Computer Vision: Algorithms and Applications. Springer, San Francisco (2010)
Robert, T.C., Lipton, A.J., Kanade, T.: Introduction to the special section on video surveillance. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 745–746 (2000)
Wang, L., Tan, T., Ning, H., Hu, W.: Silhouette analysis-based gait recognition for human identification. IEEE Trans. Pattern Anal. Mach. Intell. 25(12), 1505–1518 (2003)
Delac, K., Grgic, M., Grgic, S.: A comparative study of PCA, ICA and LDA. In: Proceedings of the \(5^{th}\) EURASIP Conference on Speech and Image Processing, Multimedia Communications and Services, pp. 99–106 (2005)
Austvoll, I., Kwolek, B.: Region covariance matrix-based object tracking with occlusions handling. In: International Conference on Computer Vision and Graphics, pp. 201–208 (2010)
Hu, W.M., Tan, T.N., Wang, L., Maybank, S.: A survey of visual surveillance of object motion and behaviors. IEEE Trans. Syst. Man Cybern. 34(3), 334–352 (2004)
Datla, S., Agarwal, A., Niyogi, R.: A novel algorithm for achieving a light-weight tracking system. In: International Conference on Contemporary, Computing, pp. 265–276 (2010)
Trucco, E., Plakas, K.: Video tracking: a concise survey. IEEE J. Oceanic Eng. 31(2), 520–529 (2006)
Bouwmans, T.: Subspace learning for background modeling: a survey. Recent Pat. Comput. Sci. 2(3), 223–234 (2009)
Jolliffe, I.: Principal Component Analysis. Springer, New York (2002)
Hyvarinen, A., Oja, E.: Independent component analysis: algorithms and applications. Neural Networks 13(4–5), 411–430 (2000)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process. Syst. 13, 556–562 (2001)
Tang, F., Tao, H.: Fast linear discriminant analysis using binary bases. Int. Conf. Pattern Recogn. 28(16), 2209–2218 (2007)
Hardoon, D.R., Szedmak, S.R., Taylor, J.R.S.: Canonical correlation analysis: An overview with application to learning methods. Neural Comput. 16(12), 2639–2664 (2004)
Kemsley, E.K.: Discriminant Analysis and Class Modeling of Spectroscopic Data. Wiley, Chichester (1998)
Zheng, N., Xue, J.: Statistical Learning and Pattern Analysis for Image and Video Processing. Springer, New York (2009)
Biswas, S., Sil, J., Sengupta, N.: Background modeling and implementation using discrete wavelet transform: a review. ICGST J. Graph. Vis. Image Process. 11(1), 29–42 (2011)
Elhabian, S.Y., El-Sayed, K.M., Ahmed, S.H.: Moving object detection in spatial domain using background removal techniques—state-of-art. Recent Pat. Comput. Sci. 1(1), 32–34 (2008)
Xu, L., Qi, F., Jiang, R., Wu, G.: Shadow detection and removal in real images: A survey. Shanghai Jiao Tong University, Technical report (2006)
Bishop, C.M.: Pattern Recognition and Machine Learning Information Science and Statistics. Springer, New York (2006)
Oliver, N., Rosario, B., Pentland, A.: A Bayesian computer vision system for modeling human interactions. In: International Conference on vision Systems, pp. 255–272 (1999)
Xu, Z., Shi, P., Gu, I.: An eigenbackground subtraction method using recursive error compensation, PCM, pp. 779–787 (2006)
Kawabata, S., Hiura, S., Sato, K.: Real-time detection of anomalous objects in dynamic scene. In: International Conference on Pattern Recognition, vol. 3, pp. 1171–1174 (2006)
Hall, P.M., Marshall, A.D., Martin, R.R.: Incremental eigen analysis for classification. In: British Machine Vision Conference, pp. 286–295 (1998)
Leonardis, A., Bischof, H.: Robust recognition using eigen images. Comput. Vis. Image Underst. 78(1), 99–118 (2000)
Storer, M., Roth, P.M., Urschler, M., Bischof, H.: Fast-robust PCA. In: Proceedings of the 16th Scandinavian Conference on Image Analysis, pp. 430–439 (2009)
Li, Y., Xu, L., Morphett, J., Jacobs, R.: An integrated algorithm of incremental and robust PCA. IEEE International Conference on Image Processing, pp. 245–248 (2003)
Li, Y.: On incremental and robust subspace learning. Pattern Recogn. 37(7), 1509–1518 (2004)
Skocaj, D., Leonardis, A.: Weighted and robust incremental method for subspace learning. In: International Conference on Computer Vision, pp. 1494–1501 (2003)
Skocaj, D., Leonardis, A.: Incremental and robust learning of subspace representations. Image Vis. Comput. 26(1), 27–38 (2008)
Zhang, J., Zhuang, Y.: Adaptive weight selection for incremental eigenbackground modeling. IEEE International Conference on Multimedia and Expo, pp. 851–854 (2007)
La, X., Zhao, G., Meng, H.: A new method for selecting gradient weight in incremental eigenbackground modeling. In: International Conference on Information and Automation, pp. 801–805 (2009)
Wang, L., Wang, L., Zhuo, Q., Xiao, H., Wang, W.: Adaptive eigenbackground for dynamic background modeling. Intelligent Computing in Signal Processing and Pattern Recognition, Lecture Notes in Control and Information Sciences, vol. 345, pp. 670–675 (2006)
Wang, L., Wang, L., Wen, M., Zhuo, Q., Wang, W.: Background subtraction using incremental subspace learning. In: International Conference on Image Processing, pp. 45–48 (2007)
Zhang, J., Yang, Y., Zhu, C.: Robust foreground segmentation using subspace based background model. In: Asia-Pacific Conference on Information Processing, pp. 214–217 (2009)
Li, R., Chen, Y., Zhang, X.: Fast robust eigenbackground updating for foreground detection. In: International Conference on Image Processing, pp. 1833–1836 (2006)
Han, B., Jain, R.: Real-time subspace based background modeling using multi-channel data, \(8^{th}\) International Symposium on Visual, Computing, (2007) 162–172.
Zhao, Y., Gong, H., Lin, L., Jia, Y.: Spatio-temporal patches for night background modeling by subspace learning. In: International Conference on Pattern Recognition, pp. 1–4 (2008)
Weng, J., Zhang, Y., Hwang, W.: Candid covariance free incremental principal components analysis. IEEE Trans. Pattern Anal. Mach. Intell. 25, 1034–1040 (2003)
Wu, X., Wang, Y., Li, J.: Video background segmentation using adaptive background models. International Conference on Image Analysis and Processing, pp. 623–632 (2009)
Wu, X., Yang, L., Yang, C.: Real-time foreground segmentation based on a fused background model. International Conference on Computer and Automation Engineering, pp. 585–588 (2010)
Dong, Y., DeSouza, G.N.: Adaptive learning of multi-subspace for foreground detection under illumination changes. J. Comput. Vis. Image Underst. 115(1), 31–49 (2011)
Quivy, C., Kumazawa, I.: Background images generation based on the Nelder-Mead simplex algorithm using the eigenbackground model. In: International Conference on Image Analysis and Recognition, pp. 21–29 (2011)
Hu, Z., Wang, Y., Tian, Y., Huang, T.: Selective eigenbackgrounds method for background subtraction in crowed scenes. In: International Conference on Image Processing, pp. 3277–3280 (2011)
Kawanishi, Y., Mitsugami, I., Mukunoki, M., Minoh, M.: Background image generation preserving lighting condition of outdoor scenes. Procedia Soc. Behav. Sci. 2(1), 137–142 (2010)
Candes, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58(1), 1–37 (2009)
Wright, J., Peng, Y., Ma, Y., Ganesh, A., Roa, S.: Robust principal component analysis: exact recovery of corrupted low-rank matrices by convex optimization, Neural Inf. Process. Syst. 2080–2088 (2009)
Xu, H., Caramanis, C., Sanghavi, S.: Robust PCA via outlier pursuit. Adv. Neural Inf. Pro. Syst. 23, 2496–2504 (2010)
Zhou, T., Tao, D.: GoDec: Randomized low-rank and sparse matrix decomposition in noisy case. In: International Conference on Machine Learning, pp. 33–40 (2011)
Ding, X., He, L., Carin, L.: Bayesian robust principal component analysis. IEEE Trans. Image Process. 20(12), 3419–3430 (2011)
Mateos, G., Giannakis, G.: Sparsity control for robust principal component analysis. International Conference on Signals Systems and Computers, pp. 1925–1929 (2010)
Torre, F.D.L., Black, M.J.: A framework for robust subspace learning. Int. J. Comput. Vision 54(1–3), 183–209 (2003)
Mu, Y., Dong, J., Yuan, X., Yan, S.: Accelerated low-rank visual recovery by random projection. International Conference on Computer Vision, pp. 2609–2616 (2011)
Anderson, M., Ballard, J., Keutzer, K.: Communication-Avoiding QR decomposition for GPUs. In: IEEE International Symposium on Parallel and Distributed Processing, pp. 48–58 (2011)
Qiu, C., Vaswani, N.: Real-time robust principal components pursuit. In: International Conference on Communication Control and Computing (2010)
Qiu, C., Vaswani, N.: Support predicted modified-CS for recursive robust principal components pursuit. In: Proceedings of the IEEE International Symposium on Information Theory, pp. 668–672 (2011)
Zhao, C., Wang, X., Cham, W.: Background Subtraction via Robust Dictionary Learning, EURASIP J. Image Video Process. 2011, 1–12 (2011)
Yamazaki, M., Xu, G., Chen, Y.: Detection of moving objects by independent component analysis. In: 7th Asian Conference on Computer Vision, pp. 467–478 (2006)
Tsai, D., Lai, C.: Independent component analysis-based background subtraction for indoor surveillance. IEEE Trans Image Process. 18(1), 158–167 (2009)
Yu, H., Yang, J.: A direct LDA algorithm for high-dimensional data with application to face recognition. Pattern Recogn. 34, 2067–2070 (2001)
Song, F., Zhang, D., Wang, J., Liu, H., Tao, Q.: A parameterized direct LDA and its application to face recognition. Neurocomputing 71, 191–196 (2007)
Loog, M., Duin, R.P.W., Haeb-Umbach, R.: Multiclass linear dimension reduction by weighted pairwise Fisher criteria. IEEE Trans. Pattern Anal. Mach. Intell. 23, 762–766 (2001)
Zhou, D., Yang, X.: Face recognition using direct-weighted LDA. 8th Pacific Rim International Conference on Artificial Intelligence, pp. 760–768 (2004)
Chen, L.F., Liao, H.Y.M., Lin, J.C., Ko, M.T., Yu, G.J.: A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recogn. 33(10), 1713–1726 (2000)
Liu, W., Wang, Y., Li, Z., Tan, T.: Null Space Approach of Fisher Discriminant Analysis for Face Recognition, Biometric Authentication. Springer, Berlin (2004)
Wang, X., Tang, X.: Dual-space linear discriminant analysis for face recognition. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, pp. 564–569 (2004)
Zheng, W., Tang, X.: Fast algorithm for updating the discriminant vectors of dual-space LDA. IEEE Trans. Inf. Forensics Secur. 4(3), 418–427 (2009)
Pima. I., Aladjem, M.: Regularized discriminant analysis for face recognition. Pattern Recogn. 37(9), 1945–1948 (2004)
Howland, P., Park, H.: Generalized discriminant analysis using the generalized singular value decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 26, 995–1006 (2004)
Ye, J., Janardan, R., Park, C.H., Park, H.: An optimization criterion for generalized discriminant analysis on undersampled problems. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 982–994 (2004)
Lu, J.W., Plataniotis, K.N., Venetsanopoulos, A.N.: Face recognition using LDA based algorithms. IEEE Trans. Neural Networks 14, 195–200 (2003)
Lu, J.W., Plataniotis, K.N., Venetsanopoulos, A.N.: Boosting linear discriminant analysis for face recognition. In: Proceedings of the IEEE International Conference on Image Processing, pp. 657–660 (2003)
Yang, Q., Ding, Q.X.: Discriminant local feature analysis of facial images. In: IEEE International Conference on Image Processing, pp. 863–866 (2003)
Hwang, W., Kim, J., Kee, S.: Face recognition using local features based on two-layer block model. In: Proceedings of the International Association for Pattern Recognition Conference on Machine Vision Applications, pp. 104–107 (2005)
Liu, Q., Huang, R., Lu, H., Ma, S.: Face recognition using kernel based Fisher discriminant analysis. In: 5th IEEE International Conference on Automatic Face and Gesture Recognition, pp. 197–201 (2002)
Liu, Q., Tang, X., Lu, H., Ma, S.: Kernel scatter-difference based discriminant analysis for face recognition. In: Proceedings of the IEEE International Conference on Pattern Recognition, pp. 419–422 (2004)
Li, M., Yuan, B.: 2D-LDA: a statistical linear discriminant analysis for image matrix. Pattern Recogn. Lett. 26, 527–532 (2005)
Jing, X.Y., Tang, Y.Y., Zhang, D.: A fourier-LDA approach for image recognition. Pattern Recogn. 38, 453–457 (2005)
Pang, Y.W., Zhang, L., Li, M.J., Liu, Z.K., Ma, W.Y.: A novel Gabor-LDA based face recognition method. Adv. Multimedia Inf. Process. PCM 2004(3331), 352–358 (2004)
Nhat, V.D.M., Lee, S.: Block LDA for Face Recognition, Computational Intelligence and Bioinspired Systems, vol. 3512, pp. 899–905. Springer, Berlin (2005)
Zhou, D., Yang, X.: Face recognition using enhanced Fisher linear discriminant model with facial combined feature. In: 8th Pacific Rim International Conference on Artifical Intelligence: Trends in Artificial Intelligence, vol. 3157, pp. 769–777, Springer, Berlin (2004)
Zhang, W.C., Shan, S.G., Gao, W., Chang, Y.Z., Cao, B.: Component based cascade linear discriminant analysis for face recognition. Adv. Biometric Pers. Authentication 3338, 288–295 (2004)
Zhao, H., Yuen, P.C.: Incremental linear discriminant analysis for face recognition. IEEE Trans. Syst. Man Cybern. 38, 210–221 (2008)
Jafri, R., Arabnia, H.R.: A survey of face recognition techniques. J. Inf. Process. Syst. 5(2), 41–68 (2009)
Yilmaz, A., Javed, O., Shah, M.: Object tracking: a survey. ACM Comput. Surv. 38(4), 1–45 (2006)
Fu, Z., Han, Y.: Centroid weighted Kalman filter for visual object tracking. J. Int. Meas. Confederation 45(4), 650–655 (2012)
Li X., Wang, K., Wang, W., Li X.: A multiple object tracking method using Kalman filter. In: IEEE International Conference on Information and Automation, pp. 1862–1866 (2010)
Arulampalam, S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50, 174–188 (2001)
Smith, A.F.M., Gelfand, A.E.: Bayesian statistics without tears: a sampling-resampling perspective. The Am. Statistician 46(2), 84–88 (1992)
Snoussi, H., Richard, C.: Monte Carlo tracking on the Riemannian manifold of multivariate normal distributions. In: IEEE Digital Signal Processing, pp. 280–285 (2009)
Porikli, F., Tuzel, O., Meer, P.: Covariance tracking using model update based on Lie algebra. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 728–735 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bhuyan, M.K., T, M. (2013). Review of the Application of Matrix Information Theory in Video Surveillance. In: Nielsen, F., Bhatia, R. (eds) Matrix Information Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30232-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-30232-9_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30231-2
Online ISBN: 978-3-642-30232-9
eBook Packages: EngineeringEngineering (R0)