ABSTRACT ix
LIST OF FIGURE xxviii
LIST OF TABLE xxxi
ABBREVIATION xxxii
1. Introduction 1
1.1. Motivation 2
1.2. Application 3
1.3. Challenge 4
1.4. Review of the background initialization method 5
1.4.1. Method based on pixel 5
1.4.2. Method based on iterative model completion 6
1.4.3. Method based on low-rank/ sparse data separation 7
1.4.4. Method based on neural network 8
1.5. Background/ foreground separation problem 9
1.6. Contribution 10
1.7. Dissertation organization 10
1.8. Publication 11
2. Data preparation 13
2.1. Scene background initialization database 13
2.2. Spatio-temporal data 25
2.3. Storing a video as spatio-temporal data 26
2.4. Evaluation metric 28
2.4.1. Average gray-level error 30
2.4.2. Percentage of error pixels 30
2.4.3. Peak signal-to-noise ratio 30
2.4.4. Structural similarity index 31
2.4.5. Feature similarity index for image quality assessment 31
3. Background initialization based on singular value decomposition 33
3.1. Introduction 33
3.2. Mathematical background on singular value decomposition 34
3.3. Proposed method 36
3.4. Experiment result and discussion 42
3.5. Conclusion 51
4. Background initialization based on higher-order singular value decomposition 52
4.1. Introduction 52
4.2. Mathematical background on higher-order singular value decomposition 53
4.3. Proposed method 54
4.4. Experiment result and discussion 57
4.5. Conclusion 63
5. Background initialization based on singular spectrum analysis 65
5.1. Introduction 65
5.2. Mathematical background on singular spectrum analysis 66
5.3. Proposed method 69
5.4. Experiment result and discussion 74
5.5. Conclusion 82
6. Conclusion and future work 84
REFERENCE 86
BIOGRAPHY 94

[1]L. Maddalena and A. Petrosino, "The 3dSOBS+ algorithm for moving object detection," Computer Vision and Image Understanding, vol. 122, pp. 65-73, 2014.
[2]F. De la Torre and M. J. Black, "Robust principal component analysis for computer vision," in Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, 2001, vol. 1, pp. 362-369: IEEE.
[3]J. Grosek and J. N. Kutz, "Dynamic mode decomposition for real-time background/foreground separation in video," arXiv preprint arXiv:1404.7592, 2014.
[4]Y. Xu, W. Yin, Z. Wen, and Y. Zhang, "An alternating direction algorithm for matrix completion with nonnegative factors," Frontiers of Mathematics in China, vol. 7, no. 2, pp. 365-384, 2012.
[5]M. De Gregorio and M. Giordano, "Background estimation by weightless neural networks," Pattern Recognition Letters, vol. 96, pp. 55-65, 2017.
[6]L. Maddalena and A. Petrosino, "Towards benchmarking scene background initialization," in International conference on image analysis and processing, 2015, pp. 469-476: Springer.
[7]C.-C. Chiu, M.-Y. Ku, and L.-W. Liang, "A robust object segmentation system using a probability-based background extraction algorithm," IEEE Transactions on circuits and systems for video technology, vol. 20, no. 4, pp. 518-528, 2009.
[8]M. Paul, "Efficient video coding using optimal compression plane and background modelling," IET Image Processing, vol. 6, no. 9, pp. 1311-1318, 2012.
[9]M. Granados, H.-P. Seidel, and H. P. Lensch, "Background estimation from non-time sequence images," in Proceedings of graphics interface 2008, 2008, pp. 33-40.
[10]T. Bouwmans, "Traditional and recent approaches in background modeling for foreground detection: An overview," Computer science review, vol. 11, pp. 31-66, 2014.
[11]L. Maddalena, A. Petrosino, and F. Russo, "People counting by learning their appearance in a multi-view camera environment," Pattern Recognition Letters, vol. 36, pp. 125-134, 2014.
[12]X. Li, "Background-foreground information based bit allocation algorithm for surveillance video on high efficiency video coding (HEVC)," in 2016 Visual Communications and Image Processing (VCIP), 2016, pp. 1-4: IEEE.
[13]M. De Gregorio and M. Giordano, "Background modeling by weightless neural networks," in International Conference on Image Analysis and Processing, 2015, pp. 493-501: Springer.
[14]T. Zhang, S. Liu, N. Ahuja, M.-H. Yang, and B. Ghanem, "Robust visual tracking via consistent low-rank sparse learning," International Journal of Computer Vision, vol. 111, no. 2, pp. 171-190, 2015.
[15]A. J. Schofield, P. Mehta, and T. J. Stonham, "A system for counting people in video images using neural networks to identify the background scene," Pattern Recognition, vol. 29, no. 8, pp. 1421-1428, 1996.
[16]A. Flores and S. Belongie, "Removing pedestrians from google street view images," in 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition-Workshops, 2010, pp. 53-58: IEEE.
[17]P.-M. Jodoin, L. Maddalena, A. Petrosino, and Y. Wang, "Extensive benchmark and survey of modeling methods for scene background initialization," IEEE Transactions on Image Processing, vol. 26, no. 11, pp. 5244-5256, 2017.
[18]C. Stauffer and W. E. L. Grimson, "Adaptive background mixture models for real-time tracking," in Proceedings. 1999 IEEE computer society conference on computer vision and pattern recognition (Cat. No PR00149), 1999, vol. 2, pp. 246-252: IEEE.
[19]B. Laugraud, S. Piérard, and M. Van Droogenbroeck, "LaBGen: A method based on motion detection for generating the background of a scene," Pattern Recognition Letters, vol. 96, pp. 12-21, 2017.
[20]L. Tian, H. Wang, Y. Zhou, and C. Peng, "Video big data in smart city: Background construction and optimization for surveillance video processing," Future Generation Computer Systems, vol. 86, pp. 1371-1382, 2018.
[21]A. H. Lai and N. H. Yung, "A fast and accurate scoreboard algorithm for estimating stationary backgrounds in an image sequence," in 1998 IEEE international symposium on circuits and systems (ISCAS), 1998, vol. 4, pp. 241-244: IEEE.
[22]W. Liu, Y. Cai, M. Zhang, H. Li, and H. Gu, "Scene background estimation based on temporal median filter with Gaussian filtering," in 2016 23rd International Conference on Pattern Recognition (ICPR), 2016, pp. 132-136: IEEE.
[23]H.-H. Hsiao and J.-J. Leou, "Background initialization and foreground segmentation for bootstrapping video sequences," EURASIP Journal on Image and Video Processing, vol. 2013, no. 1, pp. 1-19, 2013.
[24]G. Reitberger and T. Sauer, "Background Subtraction using Adaptive Singular Value Decomposition," Journal of Mathematical Imaging and Vision, vol. 62, pp. 1159-1172, 2020.
[25]Z. Chen, R. Wang, Z. Zhang, H. Wang, and L. Xu, "Background–foreground interaction for moving object detection in dynamic scenes," Information Sciences, vol. 483, pp. 65-81, 2019.
[26]A. Colombari, M. Cristani, V. Murino, and A. Fusiello, "Exemplar-based background model initialization," in Proceedings of the third ACM international workshop on Video surveillance & sensor networks, 2005, pp. 29-36.
[27]Y.-C. Chung, J.-M. Wang, and S.-W. Chen, "Progressive background images generation," in Proc. of 15th IPPR Conf. on Computer Vision, Graphics and Image Processing, 2002, pp. 858-865.
[28]E. J. Candès, X. Li, Y. Ma, and J. Wright, "Robust principal component analysis?," Journal of the ACM (JACM), vol. 58, no. 3, pp. 1-37, 2011.
[29]S. Javed, A. Mahmood, T. Bouwmans, and S. K. Jung, "Spatiotemporal low-rank modeling for complex scene background initialization," IEEE Transactions on Circuits and Systems for Video Technology, vol. 28, no. 6, pp. 1315-1329, 2016.
[30]X. Zhou, C. Yang, and W. Yu, "Moving object detection by detecting contiguous outliers in the low-rank representation," IEEE transactions on pattern analysis and machine intelligence, vol. 35, no. 3, pp. 597-610, 2012.
[31]X. Ye, J. Yang, X. Sun, K. Li, C. Hou, and Y. Wang, "Foreground–background separation from video clips via motion-assisted matrix restoration," IEEE Transactions on Circuits and Systems for Video Technology, vol. 25, no. 11, pp. 1721-1734, 2015.
[32]I. Kajo, N. Kamel, Y. Ruichek, and A. S. Malik, "SVD-based tensor-completion technique for background initialization," IEEE Transactions on Image Processing, vol. 27, no. 6, pp. 3114-3126, 2018.
[33]J. A. Ramirez-Quintana and M. I. Chacon-Murguia, "Self-adaptive SOM-CNN neural system for dynamic object detection in normal and complex scenarios," Pattern Recognition, vol. 48, no. 4, pp. 1137-1149, 2015.
[34]Z. Zhao, X. Zhang, and Y. Fang, "Stacked multilayer self-organizing map for background modeling," IEEE Transactions on Image Processing, vol. 24, no. 9, pp. 2841-2850, 2015.
[35]I. Halfaoui, F. Bouzaraa, and O. Urfalioglu, "CNN-based initial background estimation," in 2016 23rd International Conference on Pattern Recognition (ICPR), 2016, pp. 101-106: IEEE.
[36]L. Yang, J. Li, Y. Luo, Y. Zhao, H. Cheng, and J. Li, "Deep background modeling using fully convolutional network," IEEE Transactions on Intelligent Transportation Systems, vol. 19, no. 1, pp. 254-262, 2017.
[37]L. Zhang, Z. Chen, M. Zheng, and X. He, "Robust non-negative matrix factorization," Frontiers of Electrical and Electronic Engineering in China, vol. 6, no. 2, pp. 192-200, 2011.
[38]C. G. Gonzalez, O. Absil, P.-A. Absil, M. Van Droogenbroeck, D. Mawet, and J. Surdej, "Low-rank plus sparse decomposition for exoplanet detection in direct-imaging adi sequences-the llsg algorithm," Astronomy & Astrophysics, vol. 589, p. A54, 2016.
[39]J. Han, J. Pei, and M. Kamber, Data mining: concepts and techniques. Elsevier, 2011.
[40]T. T. Torku, "Takens Theorem with Singular Spectrum Analysis Applied to Noisy Time Series," East Tennessee State University, 2016.
[41]Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: from error visibility to structural similarity," IEEE transactions on image processing, vol. 13, no. 4, pp. 600-612, 2004.
[42]L. Zhang, L. Zhang, X. Mou, and D. Zhang, "FSIM: A feature similarity index for image quality assessment," IEEE transactions on Image Processing, vol. 20, no. 8, pp. 2378-2386, 2011.
[43]R. C. Gonzalez and R. E. Woods, "Digital image processing," ed: Prentice hall Upper Saddle River, NJ, 2002.
[44]P. C. Hansen, Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion. SIAM, 1998.
[45]E. F. Deprettere, SVD and signal processing: algorithms, applications and architectures. North-Holland Publishing Co., 1989.
[46]J.-W. Wang, N. T. Le, J.-S. Lee, and C.-C. Wang, "Illumination compensation for face recognition using adaptive singular value decomposition in the wavelet domain," Information Sciences, vol. 435, pp. 69-93, 2018.
[47]N. T. Le, D. H. Le, J.-W. Wang, and C.-C. Wang, "Entropy-Based Clustering Algorithm for Fingerprint Singular Point Detection," Entropy, vol. 21, no. 8, p. 786, 2019.
[48]X. Ma, X. Xie, K.-M. Lam, J. Hu, and Y. Zhong, "Saliency detection based on singular value decomposition," Journal of Visual Communication and Image Representation, vol. 32, pp. 95-106, 2015.
[49]Q. Guo, C. Zhang, Y. Zhang, and H. Liu, "An efficient SVD-based method for image denoising," IEEE transactions on Circuits and Systems for Video Technology, vol. 26, no. 5, pp. 868-880, 2015.
[50]C. Hu, X. Lu, M. Ye, and W. Zeng, "Singular value decomposition and local near neighbors for face recognition under varying illumination," Pattern Recognition, vol. 64, pp. 60-83, 2017.
[51]H. Andrews and C. Patterson, "Singular value decompositions and digital image processing," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 24, no. 1, pp. 26-53, 1976.
[52]W. Hackbusch, Tensor spaces and numerical tensor calculus. Springer, 2012.
[53]T. G. Kolda and B. W. Bader, "Tensor decompositions and applications," SIAM review, vol. 51, no. 3, pp. 455-500, 2009.
[54]L. R. Tucker, "Some mathematical notes on three-mode factor analysis," Psychometrika, vol. 31, no. 3, pp. 279-311, 1966.
[55]L. De Lathauwer, B. De Moor, and J. Vandewalle, "A multilinear singular value decomposition," SIAM journal on Matrix Analysis and Applications, vol. 21, no. 4, pp. 1253-1278, 2000.
[56]T. N. Le, D. B. Giap, J.-W. Wang, and C.-C. Wang, "Tensor-Compensated Color Face Recognition," IEEE Transactions on Information Forensics and Security, vol. 16, pp. 3339-3354, 2021.
[57]Y. He and S. Chen, "Person-Independent Facial Expression Recognition Based on Improved Local Binary Pattern and Higher-Order Singular Value Decomposition," IEEE Access, vol. 8, pp. 190184-190193, 2020.
[58]N. D. Sidiropoulos, L. De Lathauwer, X. Fu, K. Huang, E. E. Papalexakis, and C. Faloutsos, "Tensor decomposition for signal processing and machine learning," IEEE Transactions on Signal Processing, vol. 65, no. 13, pp. 3551-3582, 2017.
[59]N. Golyandina, "Particularities and commonalities of singular spectrum analysis as a method of time series analysis and signal processing," Wiley Interdisciplinary Reviews: Computational Statistics, vol. 12, no. 4, p. e1487, 2020.
[60]P. Ormerod and M. Campbell, "Predictability and economic time series," System Dynamics in Economic and Financial Models, New York: John Wiley, 1997.
[61]K. Fraedrich, "Estimating the dimensions of weather and climate attractors," Journal of Atmospheric Sciences, vol. 43, no. 5, pp. 419-432, 1986.
[62]D. S. Broomhead and G. P. King, "Extracting qualitative dynamics from experimental data," Physica D: Nonlinear Phenomena, vol. 20, no. 2-3, pp. 217-236, 1986.
[63]R. Vautard and M. Ghil, "Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series," Physica D: Nonlinear Phenomena, vol. 35, no. 3, pp. 395-424, 1989.
[64]M. Ghodsi, H. Hassani, S. Sanei, and Y. Hicks, "The use of noise information for detection of temporomandibular disorder," Biomedical Signal Processing and Control, vol. 4, no. 2, pp. 79-85, 2009.
[65]A. Yurova, L. P. Bobylev, Y. Zhu, R. Davy, and A. Y. Korzhikov, "Atmospheric heat advection in the Kara Sea region under main synoptic processes," International Journal of Climatology, vol. 39, no. 1, pp. 361-374, 2019.
[66]R. Vautard, P. Yiou, and M. Ghil, "Singular-spectrum analysis: A toolkit for short, noisy chaotic signals," Physica D: Nonlinear Phenomena, vol. 58, no. 1-4, pp. 95-126, 1992.
[67]J. Arteche and J. García-Enríquez, "Singular Spectrum Analysis for signal extraction in Stochastic Volatility models," Econometrics and statistics, vol. 1, pp. 85-98, 2017.
[68]S. Lahmiri, "Minute-ahead stock price forecasting based on singular spectrum analysis and support vector regression," Applied Mathematics and Computation, vol. 320, pp. 444-451, 2018.
[69]J. B. Elsner and A. A. Tsonis, Singular spectrum analysis: a new tool in time series analysis. Springer Science & Business Media, 1996.
[70]N. Golyandina, V. Nekrutkin, and A. A. Zhigljavsky, Analysis of time series structure: SSA and related techniques. CRC press, 2001.