Skip to main content
SpringerLink
Log in

Sparsity Driven People Localization with a Heterogeneous Network of Cameras

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

This paper addresses the problem of localizing people in low and high density crowds with a network of heterogeneous cameras. The problem is recast as a linear inverse problem. It relies on deducing the discretized occupancy vector of people on the ground, from the noisy binary silhouettes observed as foreground pixels in each camera. This inverse problem is regularized by imposing a sparse occupancy vector, i.e., made of few non-zero elements, while a particular dictionary of silhouettes linearly maps these non-empty grid locations to the multiple silhouettes viewed by the cameras network. The proposed framework is (i) generic to any scene of people, i.e., people are located in low and high density crowds, (ii) scalable to any number of cameras and already working with a single camera, (iii) unconstrained by the scene surface to be monitored, and (iv) versatile with respect to the camera’s geometry, e.g., planar or omnidirectional.

Qualitative and quantitative results are presented on the APIDIS and the PETS 2009 Benchmark datasets. The proposed algorithm successfully detects people occluding each other given severely degraded extracted features, while outperforming state-of-the-art people localization techniques.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alahi, A., Boursier, Y., Jacques, L., Vandergheynst, P.: A sparsity constrained inverse problem to locate people in a network of cameras. In: 16th International Conference on Digital Signal Processing, Santorini, Greece, pp. 189–195 (2009)

    Google Scholar 

  2. Alahi, A., Boursier, Y., Jacques, L., Vandergheynst, P.: Sport players detection and tracking with a mixed network of planar and omnidirectional cameras. In: Third ACM/IEEE International Conference on Distributed Smart Cameras, Challenge Prize Winner, Como, pp. 1–8 (2009)

    Chapter  Google Scholar 

  3. Alahi, A., Jacques, L., Boursier, Y., Vandergheynst, P.: Sparsity-driven people localization algorithm: evaluation in crowded scenes environments. In: Proc. IEEE Int’l Workshop on Performance Evaluation of Tracking and Surveillance, Snowbird, Utah, pp. 1–8 (2009)

    Chapter  Google Scholar 

  4. Alahi, A., Bierlaire, M., Kunt, M.: Cascade of descriptors to detect and track objects across any network of cameras. Comput. Vis. Image Underst. 114(6), 624–640 (2010)

    Article  Google Scholar 

  5. Baraniuk, R., Cevher, V., Duarte, M., Hegde, C.: Model-based compressive sensing. IEEE Trans. Inf. Theory 56(4), 1982–2001 (2010)

    Article  MathSciNet  Google Scholar 

  6. Berclaz, J., Fleuret, F., Fua, P.: Robust people tracking with global trajectory optimization. In: Conference on Computer Vision and Pattern Recognition, pp. 744–750 (2006)

    Google Scholar 

  7. Black, J., Ellis, T., Rosin, P.: Multi view image surveillance and tracking. In: Proc. IEEE Workshop on Motion and Video Computing, pp. 169–174 (2002)

    Chapter  Google Scholar 

  8. Candès, E.J., Wakin, M., Boyd, S.: Enhancing sparsity by reweighted ℓ 1 minimization. J. Fourier Anal. Appl. 14(5), 877–905 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Caspi, Y., Simakov, D., Irani, M.: Feature-based sequence-to-sequence matching. Int. J. Comput. Vis. 68(1), 53–64 (2006)

    Article  Google Scholar 

  10. Cevher, V., Duarte, M., Baraniuk, R.: Distributed target localization via spatial sparsity. In: Proc. European Signal Processing Conference (2008)

    Google Scholar 

  11. Chartrand, R., Yin, W.: Iteratively reweighted algorithms for compressive sensing. In: Proceedings of Int. Conf. on Acoustics, Speech, Signal Processing (ICASSP), pp. 3869–3872 (2008)

    Google Scholar 

  12. Chen, S.S., Donoho, D., Saunders, M.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1998)

    Article  MathSciNet  Google Scholar 

  13. Cheng, H., Zheng, N., Qin, J.: Pedestrian detection using sparse Gabor filter and support vector machine. In: Proc. IEEE Symposium on Intelligent Vehicles, pp. 583–587 (2005)

    Chapter  Google Scholar 

  14. Combettes, P.: Solving monotone inclusions via compositions of nonexpansive averaged operators. Optimization 53(5), 475–504 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Combettes, P., Wajs, V.: Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4(4), 1168–1200 (2006)

    Article  MathSciNet  Google Scholar 

  16. Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: Proc. IEEE Int’l Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 886–893 (2005)

    Google Scholar 

  17. Delannay, D., Danhier, N., De Vleeschouwer, C.: Detection and recognition of sports(wo)man from multiple views. In: Proc. ACM/IEEE Int’l Conference on Distributed Smart Cameras, Como, Italy, pp. 1–7 (2009)

    Chapter  Google Scholar 

  18. Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  19. Elfes, A.: Using occupancy grids for mobile robot perception and navigation. Computer 22(6), 46–57 (1989)

    Article  Google Scholar 

  20. Eshel, R., Moses, Y.: Homography based multiple camera detection and tracking of people in a dense crowd. In: Proc. IEEE Int’l Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2008)

    Google Scholar 

  21. Fadili, M.J., Starck, J.L.: Monotone operator splitting for fast sparse solutions of inverse problems. SIAM J. Imaging Sci., 2005–2006 (2009)

  22. Fleuret, F., Berclaz, J., Lengagne, R., Fua, P.: Multicamera people tracking with a probabilistic occupancy map. IEEE Trans. Pattern Anal. Mach. Intell. 30(2), 267–282 (2008)

    Article  Google Scholar 

  23. Franco, J., Boyer, E.: Fusion of multiview silhouette cues using a space occupancy grid. In: Tenth Proc. IEEE Int’l Conference on Computer Vision, ICCV 2005, vol. 2 (2005)

    Google Scholar 

  24. Gorodnitsky, I., Rao, B.: Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600–616 (1997)

    Article  Google Scholar 

  25. Khan, S., Shah, M.: A multiview approach to tracking people in crowded scenes using a planar homography constraint. In: Proc. European Conference on Computer Vision, vol. 4, pp. 133–146 (2006)

    Google Scholar 

  26. Khan, S.M., Shah, M.: Tracking multiple occluding people by localizing on multiple scene planes. IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 505–519 (2009)

    Article  Google Scholar 

  27. Kim, K., Davis, L.: Multi-camera tracking and segmentation of occluded people on ground plane using search-guided particle filtering. In: Proc. European Conference on Computer Vision, vol. 3, pp. 98–109 (2006)

    Google Scholar 

  28. Kowalski, M., Torresani, B.: Sparsity and persistence: mixed norms provide simple signals models with dependent coefficients. Signal Image Video Process. 3(3), 251–264 (2008)

    Article  Google Scholar 

  29. Malioutov, D., Cetin, M., Willsky, A.: A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal Process. 53(8 Part 2), 3010–3022 (2005)

    Article  MathSciNet  Google Scholar 

  30. Moreau, J.: Fonctions convexes duales et points proximaux dans un espace hilbertien. C. R. Acad. Sci. Paris Ser. A, Math. 255, 2897–2899 (1962)

    MathSciNet  MATH  Google Scholar 

  31. Mueller, K., Smolic, A., Droese, M., Voigt, P., Wienand, T.: Multi-texture modeling of 3d traffic scenes. In: Proc. of the 2003 Int’l Conference on Multimedia, vol. 2, pp. 657–660 (2003)

    Google Scholar 

  32. Natarajan, B.: Sparse approximate solutions to linear systems. SIAM J. Comput. 24, 227–234 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  33. Oren, M., Papageorgiou, C., Sinha, P., Osuna, E., Poggio, T.: Pedestrian detection using wavelet templates. In: Proc. IEEE Int’l Conference on Computer Vision and Pattern Recognition, vol. 97, pp. 193–199 (1997)

    Google Scholar 

  34. Orwell, J., Massey, S., Remagnino, P., Greenhill, D., Jones, G.A.: A multi-agent framework for visual surveillance. In: Proc. IEEE Int’l Conference on Image Analysis and Processing, pp. 1104–1107. IEEE Computer Society, Washington (1999)

    Google Scholar 

  35. Papageorgiou, C., Poggio, T.: Trainable pedestrian detection. In: Proc. IEEE Int’l Conference on Image Processing, vol. 4, pp. 35–39 (1999)

    Google Scholar 

  36. Porikli, F.: Achieving real-time object detection and tracking under extreme conditions. J. Real-Time Image Process. 1(1), 33–40 (2006)

    Article  Google Scholar 

  37. Reddy, D., Sankaranarayanan, A., Cevher, V., Chellappa, R.: Compressed sensing for multi-view tracking and 3-D voxel reconstruction. In: Proc. IEEE Int’l Conference on Image Processing, pp. 221–224 (2008)

    Google Scholar 

  38. Stauffer, C., Grimson, W.: Adaptive background mixture models for real-time tracking. In: Proc. IEEE Int’l Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 246–252 (1999)

    Google Scholar 

  39. Stauffer, C., Tieu, K.: Automated multi-camera planar tracking correspondence modeling. In: Proc. IEEE Int’l Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 259–266 (2003)

    Google Scholar 

  40. Suard, F., Rakotomamonjy, A., Bensrhair, A., Broggi, A.: Pedestrian detection using infrared images and histograms of oriented gradients. In: Proc. IEEE Symposium on Intelligent Vehicles, Tokyo, Japan, pp. 206–212 (2006)

    Chapter  Google Scholar 

  41. Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B, Methodol., 267–288 (1996)

  42. Tuzel, O., Porikli, F., Meer, P.: Pedestrian detection via classification on Riemannian manifolds. IEEE Trans. Pattern Anal. Mach. Intell. 20, 1713–1727 (2008)

    Article  Google Scholar 

  43. Viola, P., Jones, M., Snow, D.: Detecting pedestrians using patterns of motion and appearance. Int. J. Comput. Vis. 63(2), 153–161 (2005)

    Article  Google Scholar 

  44. Yang, D., Gonzalez-Banos, H., Guibas, L.: Counting people in crowds with a real-time network of simple image sensors. In: Proc. IEEE Int’l Conference on Computer Vision, vol. 1, pp. 122–129 (2003)

    Chapter  Google Scholar 

  45. Yilmaz, A., Javed, O., Shah, M.: Object tracking: A survey. ACM Comput. Surv. 38(4), 13 (2006)

    Article  Google Scholar 

  46. Zhao, T., Nevatia, R.: Bayesian human segmentation in crowded situations. In: 2003 Proc. IEEE Int’l Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 459–466 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Signal Processing Lab, EPFL, Lausanne, Switzerland

    Alexandre Alahi & Pierre Vandergheynst

  2. Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), University of Louvain, Louvain-la-Neuve, Belgium

    Laurent Jacques

  3. Centre de Physiques des Particules de Marseille, Aix-Marseille Université, CNRS/IN2P3, Marseilles, France

    Yannick Boursier

Authors
  1. Alexandre Alahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laurent Jacques
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yannick Boursier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pierre Vandergheynst
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexandre Alahi.

Additional information

This work was supported in part by the EU Framework 7 FET-Open project FP7-ICT-225913-SMALL: Sparse Models, Algorithms and Learning for Large-Scale data.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alahi, A., Jacques, L., Boursier, Y. et al. Sparsity Driven People Localization with a Heterogeneous Network of Cameras. J Math Imaging Vis 41, 39–58 (2011). https://doi.org/10.1007/s10851-010-0258-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-010-0258-7

Keywords

Search

Navigation