Skip to main content
SpringerLink
Log in

Background and Literature Review

  • Chapter
  • First Online:
Robust Subspace Estimation Using Low-Rank Optimization

Part of the book series: The International Series in Video Computing ((VICO,volume 12))

  • 1001 Accesses

Abstract

In this chapter, we first review the problem of linear subspace estimation and present example problems where the conventional method (PCA) is typically used. Consequently, we discuss the most prominent advances in low-rank optimization, which is the main theoretical topic of this book. Since the various low-rank formulations discussed in this book fall into several computer vision domains, we additionally review the latest techniques in each domain, including video denosing, turbulence mitigation, background subtraction, and activity recognition.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Agarwal, S. Neghaban, M. Wainwright, Noisy matrix decomposition: optimal rates in high dimensions (2012), arXiv:1102.4807v3

    Google Scholar 

  2. A. Agrawal, Y. Xu, R. Raskar, “Invertible motion blur in video.” ACM Transactions on Graphics (TOG). 28(3), in ACM, 2009

    Google Scholar 

  3. S. Ali, M. Shah, Human action recognition in videos using kinematic features and multiple instance learning, in PAMI, 2010

    Google Scholar 

  4. S. Ali, A. Basharat, M. Shah, Chaotic invariants for human action recognition, in ICCV (Rio de Janeiro, Brazil, 2007)

    Google Scholar 

  5. S. Baker, K.M. Cheung, T. Kanade, Shape-from-silhouette of articulated objects and its use for human body kinematics estimation and motion capture, in CVPR (Madison, Wisconsin, 2003)

    Google Scholar 

  6. M. Blank, L. Gorelick, E. Shechtman, M. Irani, R. Basri, Actions as space-time shapes, in ICCV (Beijing, China, 2005)

    Google Scholar 

  7. A.F. Bobick, J. Davis, The recognition of human movement using temporal templates, in PAMI, 2001

    Google Scholar 

  8. A. Buades, B. Coll, J.M. Morel, A non-local algorithm for image denoising, in CVPR (San Diego, CA, 2005)

    Google Scholar 

  9. E.J. Candes, X. Li, Y. Ma, J. Wright, Robust principal component analysis? in IEEE Sensor Array and Multichannel Signal Processing Workshop (Hoboken, NJ, 2009)

    Google Scholar 

  10. E.J. Candes, X. Li, Y. Ma, J. Wright, Robust principal component analysis? (2009, arXiv:0912.3599v1)

    Google Scholar 

  11. G. Carhat, M. Aubailly, M. Vorontsov, M. Valley, Automated video enhancement from a stream of atmospherically-distorted images: the lucky-region fusion approach, in SPIE (San Diego, CA, 2009)

    Google Scholar 

  12. S.H. Chan, R. Khoshabeh, K.B. Gibson, P.E. Gill, T.Q. Nguyen. An augmented Lagrangian method for total variation video restoration. Image Processing, IEEE Transactions on 20.11 (2011): 3097–3111

    Article  MathSciNet  Google Scholar 

  13. C. Chen, C. Wei, Y. Wang, Low-rank matrix recovery with structural incoherence for robust face recognition, in CVPR (Providence, Rhode Island, 2012)

    Google Scholar 

  14. M. Collins, S. Dasgupta, R.E. Schapire, A generalization of principal component analysis to the exponential family, in Advances in Neural Information Processing Systems, ed. by M.I. Jordan, Y. LeCun, S.A. Solla (MIT, Cambridge, 2001)

    Google Scholar 

  15. G. Cottrell, P. Dollar, V. Rabaud, S. Belongie, Behavior recognition via sparse spatio-temporal features, in IEEE VS-PETS (Beijing, China, 2005)

    Google Scholar 

  16. M. Cristani, M. Farenzena, D. Bloisi, V. Murino, Background subtraction for automated multisensor surveillance: a comprehensive review. EURASIP J. Adv. Signal Process. 2010, 43 (2010)

    Google Scholar 

  17. R. Cucchiara, C. Grana, M. Piccardi, A. Prati, Detecting moving objectss, ghosts and shadows in video streams, in PAMI, 2003

    Google Scholar 

  18. T. Darrell, A. Pentland, Classifying hand gestures with a view-based distributed representation, in NIPS (Denver, CO, 1993)

    Google Scholar 

  19. P. Dollar, V. Rabaud, V. Cottrell, S. Belongie, Behavior recognition via sparse spatio-temporal features, in VS-PETS (Beijing, China, 2005)

    Google Scholar 

  20. A. Donate, E. Ribeiro, Improved reconstruction of images distorted by waterwaves, in VISAPP (Setúbal, Portugal, 2006)

    Google Scholar 

  21. A. Donate, G. Dahme, E. Ribeiro, Classification of textures distorted by waterwaves, in ICPR (Hong Kong, 2006)

    Google Scholar 

  22. A. Efros, V. Isler, J. Shi, M. Visontai, Seeing through water, in NIPS (Vancouver, Canada, 2004)

    Google Scholar 

  23. A. Elgammal, D. Harwood, L.S. Davis, Non-parametric model for background subtraction, in ICCV (Kerkyra, Greece, 1999)

    Google Scholar 

  24. S.Y. Elhabian, K.M. El-Sayed, S.H. Ahmed, Moving object detection in spatial domain using background removal techniques-state-of-art. Recent Pat. Comput. Sci. 1(1), 32–54 (2008)

    Article  Google Scholar 

  25. A. Farhadi, I. Endres, D. Hoiem, D. Forsyth, Describing objects by their attributes, in CVPR (Miami, Florida, 2009)

    Google Scholar 

  26. D. Gabay, B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl. 2, 17–40 (1976)

    Article  MATH  Google Scholar 

  27. B. Ghanem, T. Zhang, N. Ahuja, Low-rank sparse learning for robust visual tracking, in ECCV (Firenze, Italy, 2012)

    Google Scholar 

  28. R. Glowinski, A. Marroco, Sur l’approximation, par elements finis d’ordre un, et la resolution, par penalisation-dualite, d’une classe de problemes de dirichlet non lineaires, in Revue Francaise d’Automatique, Informatique et RechercheOperationelle, 1975

    Google Scholar 

  29. D. Goldfarb, S. Ma, Fast multiple splitting algorithms for convex optimization, 2009, arXiv:0912.4570v2

    Google Scholar 

  30. S. Gong, A. Psarrou, M. Walter, Recognition of human gestures and behaviour based on motion trajectories. Image Vis. Comput. 20, 349–358 (2002)

    Article  Google Scholar 

  31. J. Goodman, Statistical Optics (Wiley, New York, 2000)

    Google Scholar 

  32. J. Goodman, Introduction to Fourier Optics (Roberts and Company, Greenwood Village, Colorado, 2004)

    Google Scholar 

  33. H. Hassanpour, M. Sedighi, A.R. Manashty, Video frame’s background modeling: reviewing the techniques. J. Signal Inf. Process. 2(2), 72–78 (2011)

    Article  Google Scholar 

  34. B. He, M. Tao, X. Yuan. Alternating direction method with Gaussian back substitution for separable convex programming. SIAM Journal on Optimization 22(2):313–340 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  35. M. Hebert, P. Matikainen, R. Sukthankar, Trajectons: action recognition through the motion analysis of tracked features, in ICCV (Kyoto, Japan, 2009)

    Google Scholar 

  36. H. Hoffmann, Kernel PCA for novelty detection. Pattern Recognit. 40, 863–874 (2007)

    Article  MATH  Google Scholar 

  37. H. Izadinia, M. Shah, Recognizing complex events using large margin joint low-level event model, in ECCV (Firenze, Italy, 2012)

    Google Scholar 

  38. O. Javed, A. Yilmaz, M. Shah, Object tracking: a survey. ACM J. Comput. Surv. 38, 1–45 (2006)

    Article  Google Scholar 

  39. H. Ji, C. Liu, Y. Xu, Z. Shen, Robust video denoising using low rank matrix completion, in CVPR (San Fransisco, CA, 2010)

    Google Scholar 

  40. N. Johnson, D. Hogg, Learning the distribution of object trajectories for event recognition, in BMVC (Birmingham, UK, 1995)

    Google Scholar 

  41. N. Joshi, M. Cohen, Lucky imaging for multi-image denoising, sharpening, and haze removal, in ICCP (Cambridge MA, 2010)

    Google Scholar 

  42. N. Joshiy, C. Lawrence Zitnicky, R. Szeliskiy, D.J. Kriegman, Image deblurring and denoising using color priors, in CVPR (Miami, FL, 2009)

    Google Scholar 

  43. M.B. Kaaniche, F. Bremond, Bremond, gesture recognition by learning local motion signatures, in CVPR (San Fransisco, CA, 2010)

    Google Scholar 

  44. I. Laptev, T. Lindeberg, Space-time interest points, in ICCV (Nice, France, 2003)

    Google Scholar 

  45. I. Laptev, C. Schuldt, B. Caputo, Recognizing human actions: a local SVM approach, in ICPR (Cambridge, England, UK, 2004)

    Google Scholar 

  46. Q.V. Le, J. Ngiam, Z. Chen, D. Chia, P.W. Koh, A.Y. Ng, Tiled convolutional neural networks, in Advances in Neural Information Processing Systems (Vancouver, British Columbia, Canada, 2010)

    Google Scholar 

  47. I.M. Levin, V.V. Savchenko, V.J. Osadchy, Correction of an image distorted by a wavy water surface: laboratory experiment. Appl. Opt. 47, 6650–6655 (2008)

    Article  Google Scholar 

  48. Y. Li, S. Kang, N. Joshi, S. Seitz, D. Huttenlocher, Generating sharp panoramas from motion-blurred videos, in CVPR (San Fransisco, CA, 2010)

    Google Scholar 

  49. C. Liangliang, M. Yadong, N. Apostol, S.F. Chang, G. Hua, J.R. Smith, Scene aligned pooling for complex video recognition, in ECCV (Firenze, Italy, 2012)

    Google Scholar 

  50. Z. Lin, M. Chen, L. Wu, Y. Ma, The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices, UIUC technical report, 2009

    Google Scholar 

  51. Z. Lin, A. Ganesh, J. Wright, L. Wu, M. Chen, Y. Ma, Fast Convex Optimization Algorithms for Exact Recovery of a Corrupted Low-Rank Matrix, UIUC technical report, 2009

    Google Scholar 

  52. Z. Lin, G. Liu, Y. Yu, Robust subspace segmentation by low-rank representation, in International Conference on Machine Learning (Haifa, Israel, 2010)

    Google Scholar 

  53. C. Liu, W. Freeman, A high-quality video denoising algorithm based on reliable motion estimation, in ECCV (Crete, Greece, 2010)

    Google Scholar 

  54. X. Liu, B. Huet, Automatic concept detector refinement for large-scale video semantic annotation, in IEEE Fourth International Conference on Semantic Computing (ICSC, Pittsburgh, PA, 2010)

    Google Scholar 

  55. J. Liu, J. Luo, M. Shah, Recognizing realistic actions from videos “in the wild”, in CVPR (Miami, FL, 2009)

    Google Scholar 

  56. A. Loui, J. Luo, S. Chang, D. Ellis, W. Jiang, L. Kennedy, K. Lee, A. Yanagawa, Kodak’s consumer video benchmark data set: concept definition and annotation, in Multimedia Information Retrieval (Augsburg, Germany, 2007)

    Google Scholar 

  57. D.G. Lowe, Distinctive image features from scale-invariant keypoints, in IJCV, 2004

    Google Scholar 

  58. Y. Ma, R. Vidal, S. Sastry, Generalized principal component analysis, in PAMI, 2005

    Google Scholar 

  59. Y. Ma, J. Wright, A.Y. Yang, Sparse representation and low-rank representation in computer vision, in ECCV Short Course (Firenze, Italy, 2012)

    Google Scholar 

  60. A.M. McIvor, Background subtraction techniques. Proc. Image Vis. Comput. 1(3), 155–163 (2000)

    Google Scholar 

  61. S. Mika, B. Schölkopf, A.J. Smola, K.-R. Müller, M. Scholz, G. Rätsch, Kernel PCA and de-noising in feature spaces, in NIPS (Denver, CO, 1998)

    Google Scholar 

  62. J. Min, R. Kasturi, Activity recognition based on multiple motion trajectories, in ICPR (Cambridge, UK, 2004)

    Google Scholar 

  63. N.M. Oliver, B. Rosario, A.P. Pentland, A Bayesian computer vision system for modeling human interactions, in PAMI, 2000

    Google Scholar 

  64. C. Pal, R. Messing, H. Kautz, Activity recognition using the velocity histories of tracked keypoints, in ICCV (Kyoto, Japan, 2009)

    Google Scholar 

  65. V. Parameswaran, R. Chellappa, View invariance for human action recognition, in IJCV, 2006

    Google Scholar 

  66. Y. Peng, A. Ganesh, J. Wright, W. Xu, Y. Ma, Rasl: robust alignment by sparse and low-rank decomposition for linearly correlated images, in PAMI, 2010

    Google Scholar 

  67. M. Piccardi, Background subtraction techniques: a review. IEEE Int. Conf. Syst. Man Cybern. 4, 3099–3104 (2004). IEEE

    Google Scholar 

  68. J. Psl, D. Meyer, H. Niemann, Gait classification with hmms for trajectories of body parts extracted by mixture densities, in BMVC (Southampton, UK, 1998)

    Google Scholar 

  69. M. Roggemann, B. Welsh, Imaging Through Turbulence (CRC, Boca Raton, 1996)

    Google Scholar 

  70. B. Scholkopf, A. Smola, K.-R. Müller, Kernel principal component analysis, in Advances in Kernel Methods – Support Vector Learning, ed. by B. Schölkopf, C.J.C. Burges, A.J. Smola (MIT, Cambridge, 1999), pp. 327–352

    Google Scholar 

  71. C. Schuldt, I. Laptev, B. Caputo, Recognizing human actions: a local SVM approach, in ICPR (Cambridge, England, UK, 2004)

    Google Scholar 

  72. S.C. Sen-Ching, C. Kamath, Robust techniques for background subtraction in urban traffic video, in Electronic Imaging 2004 (International Society for Optics and Photonics, Glasgow, Scotland), pp. 881–892

    Google Scholar 

  73. E. Shechtman, M. Irani, M. Blank, L. Gorelick, R. Basri, Actions as space-time shapes, in ICCV (Beijing, China, 2005)

    Google Scholar 

  74. Y. Sheikh, M. Shah, Bayesian modeling of dynamic scenes for object detection, in PAMI, 2005

    Google Scholar 

  75. X. Shen, Y. Wu, A unified approach to salient object detection via low rank matrix recovery, in CVPR (Providence, Rhode Island, 2012)

    Google Scholar 

  76. Z. Shen, H. Ji, C. Liu, Y. Xu, Robust subspace segmentation by low-rank representation, in CVPR, 2010

    Google Scholar 

  77. M. Shimizu, S. Yoshimura, M. Tanaka, M. Okutomi, Super-resolution from image sequence under influence of hot-air optical turbulence, in CVPR, 2008

    Google Scholar 

  78. B. Siddiquie, R. Feris, L. Davis, Image ranking and retrieval based on multiattribute queries, in CVPR (Colorado Springs, CA, 2011)

    Google Scholar 

  79. C. Stauffer, W.E.L. Grimson, Adaptive background mixture models for real-time tracking, in CVPR (Ft. Collins, CO, 1999)

    Google Scholar 

  80. R. Sukthankar, Y. Ke, M. Hebert, Efficient visual event detection using volumetric features, in ICCV (Beijing, China, 2005)

    Google Scholar 

  81. A. Tamrakar, S. Ali, Q. Yu, J. Liu, O. Javed, A. Divakaran, H. Cheng, H. Sawhney, Evaluation of low-level features and their combinations for complex event detection in open source videos, in CVPR (Providence, Rhode Island, 2012)

    Google Scholar 

  82. M. Tao, X. Yuan, Recovering low-rank and sparse components of matrices from incomplete and noisy observations. SIAM J. Optim. 21, 57–81 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  83. Y.D. Tian, S.G. Narasimhan, Seeing through water: image restoration using model-based tracking, in ICCV (Kyoto, Japan, 2009)

    Google Scholar 

  84. Y. Tian, S. Narasimhan, A globally optimal data-driven approach for image distortion estimation, in CVPR (San Fransisco, CA, 2010)

    Google Scholar 

  85. M.E. Tipping, C.M. Bishop, Probabilistic principal component analysis. J. R. Stat. Soc. B 61, 611–622 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  86. C. Tomasi, J. Shi, Good features to track, in CVPR (Seattle, WA, 1994)

    Google Scholar 

  87. M. Turk, A. Pentland, Face recognition using eigenfaces, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Maui, HI, 1991)

    Google Scholar 

  88. H. Wang, M. Ullah, A. Klaser, I. Laptev, C. Schmid, Evaluation of local spatio-temporal features for action recognition, in BMVC (London, UK, 2009)

    Google Scholar 

  89. H. Wang, A. Klaser, C. Schmid, C. L. Liu, Action recognition by dense trajectories, in CVPR (Colorado Springs, CO, 2011)

    Google Scholar 

  90. Z. Wen, D. Fraser, A. Lambert, H. Li, Reconstruction of underwater image by bispectrum, in ICIP (San Antonio, Texas, 2007)

    Google Scholar 

  91. S. Wu, Y.F. Li, Flexible signature descriptions for adaptive motion trajectory representation, perception and recognition. Pattern Recognit. 42, 194–214 (2009)

    Article  MATH  Google Scholar 

  92. S. Wu, B. Moore, M. Shah, Chaotic invariants of lagrangian particle trajectories for anomaly detection in crowded scenes, in CVPR (San Fransisco, CA, 2010)

    Google Scholar 

  93. L. Xu, J. Jia, Two-phase Kernel estimation for robust motion deblurring, in ECCV (Crete, Greece, 2010)

    Google Scholar 

  94. Y. Yang, M. Shah, Complex events detection using data-driven concepts, in ECCV (Firenze, Italy, 2012)

    Google Scholar 

  95. G. Ye, D. Liu, I.-H. Jhuo, S.-F. Chang, Robust late fusion with multi-task low rank minimization, in CVPR (Providence, Rhode Island, 2012)

    Google Scholar 

  96. A. Yilmaz, C. Rao, M. Shah, View-invariant representation and recognition of actions, in IJCV, 2002

    Google Scholar 

  97. Y. Yu, D. Schuurmans, Rank/norm regularization with closed-form solutions: application to subspace clustering, in Conference on Uncertainty in Artificial Intelligence (Barcelona, Spain, 2011)

    Google Scholar 

  98. Y. Zhang, An alternating direction algorithm for nonnegative matrix factorization Technical report, Rice University, 2010

    Google Scholar 

  99. X. Zhu, P. Milanfar, Image reconstruction from videos distorted by atmospheric turbulence, in SPIE (San Diego, CA, 2010)

    Google Scholar 

  100. X. Zhu, P. Milanfar, Stabilizing and deblurring atmospheric turbulence, in ICCP (Pittsburgh, PA, 2011)

    Google Scholar 

  101. Z. Zivkovic, Improved adaptive Gausian mixture model for background subtraction, in ICPR (Cambridge, UK, 2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California, Berkeley, Berkeley, CA, USA

    Omar Oreifej

  2. Department of Computer Science, University of Central Florida, Orlando, FL, USA

    Mubarak Shah

Authors
  1. Omar Oreifej
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mubarak Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Oreifej, O., Shah, M. (2014). Background and Literature Review. In: Robust Subspace Estimation Using Low-Rank Optimization. The International Series in Video Computing, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-04184-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-04184-1_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04183-4

  • Online ISBN: 978-3-319-04184-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation