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Projective Joint Invariants for Matching Curves in Camera Networks

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Book cover Distributed Video Sensor Networks

Abstract

A novel method is presented for distributed matching of curves across widely varying viewpoints. The fundamental projective joint-invariants for curves in the real projective space are the volume cross ratios. A curve in m-dimensional projective space is represented by a signature manifold comprising n-point projective joint invariants, where n is at least m+2. The signature manifold can be used to establish equivalence of two curves in projective space. However, without correspondence information, matching signature manifolds is a computational challenge. Our approach in this chapter is to first establish best possible correspondence between two curves using sections of the invariant signature manifold and then perform a simple test for equivalence. This allows fast computation and matching while keeping the descriptors compact. The correspondence and equivalence of curves is established independently at each camera node. Experimental results with simulated as well as real data are provided.

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References

  1. Arora, R., Hu, Y.H., Dyer, C.R.: Estimating correspondence between multiple cameras using joint invariants. In: Proc. Int. Conf. Acoust., Speech and Signal Process (2009)

    Google Scholar 

  2. Astrom, K., Morin, L.: Random cross ratios. In: Proc. 9th Scand. Conf. Image Anal., pp. 1053–1061 (1995)

    Google Scholar 

  3. Chum, O., Philbin, J., Zisserman, A.: Near duplicate image detection: min-hash and tf-idf weighting. In: Proc. British Mach. Vision Conf. (2008)

    Google Scholar 

  4. Clarot, P., Ermis, E.B., Jodoin, P.M., Saligrama, V.: Unsupervised camera network structure estimation based on activity. In: Proc. 3rd ACM/IEEE Int. Conf. Dist. Smart Cameras (2009)

    Google Scholar 

  5. Collins, R., Lipton, A., Fujiyoshi, H., Kanade, T.: Algorithms for cooperative multisensor surveillance. Proc. IEEE 89(10), 1456–1477 (2001)

    Article  Google Scholar 

  6. Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24, 381–395 (1981)

    Article  MathSciNet  Google Scholar 

  7. Hann, C.E.: Recognizing two planar objects under a projective transformation. PhD dissertation, Univ. of Canterbury (2001)

    Google Scholar 

  8. Hann, C.E., Hickman, M.S.: Recognising Two Planar Objects under a Projective Transformation. Kluwer Academic, Dordrecht (2004)

    Google Scholar 

  9. Hu, W., Tan, T., Wang, L., Maybank, S.: A survey on visual surveillance of object motion and behaviors. IEEE Trans. Syst. Man Cybern. Part C, Appl. Rev. 34(3), 334–352 (2004)

    Article  Google Scholar 

  10. Huynh, D.Q.: The cross ratio: a revisit to its probability density function. In: Proc. 11th British Machine Vision Conf. (2000)

    Google Scholar 

  11. Lee, L., Romano, R., Stein, G.: Monitoring activities from multiple video streams: establishing a common coordinate frame. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 758–767 (2000)

    Article  Google Scholar 

  12. Lowe, D.: Object recognition from local scale-invariant features. In: Proc. 7th Int. Conf. Computer Vision, pp. 1150–1157 (1999)

    Google Scholar 

  13. Marhic, B.M., Mouaddib, E.M., Pegard, C.: A localisation method with an omnidirectional vision sensor using projective invariant. In: Proc. Int. Conf. Intelligent Robots Systems, pp. 1078–1083 (1998)

    Google Scholar 

  14. Mariottini, G., Prattichizzo, D.: EGT for multiple view geometry and visual serving. IEEE Robot. Autom. Mag. 12(4), 26–39 (2005)

    Article  Google Scholar 

  15. Maybank, S.J.: Probabilistic analysis of the application of the cross ratio to model based vision. Int. J. Comput. Vis. 14, 199–210 (1995)

    Article  Google Scholar 

  16. Mundy, J.L., Zisserman, A. (eds.): Geometric Invariance to Computer Vision. MIT Press, Cambridge (1992)

    Google Scholar 

  17. Mundy, J.L., Zisserman, A., Forsyth, D. (eds.): Applications of Invariance in Computer Vision. Springer, Berlin (1993)

    Google Scholar 

  18. Olver, P.J.: Joint invariant signatures. Found. Comput. Math. 1, 3–67 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Orrite, C., Blecua, S., Herrero, J.E.: Shape matching of partially occluded curves invariant under projective transformation. Comput. Vis. Image Underst. 93, 34–64 (2004)

    Article  Google Scholar 

  20. Remagnino, P., Velastin, S., Foresti, G., Trivedi, M.: Novel concepts and challenges for the next generation of video surveillance systems. Mach. Vis. Appl. 18(3), 135–137 (2007)

    Article  Google Scholar 

  21. Roh, K.S., Lee, W.H., Kweon, I.S.: Obstacle detection and self-localization without camera calibration using projective invariants. In: Proc. Int. Conf. Intelligent Robots and Systems, pp. 1030–1035 (1997)

    Google Scholar 

  22. Rothwell, C.A., Zisserman, A., Forsyth, D.A., Mundy, J.L.: Canonical frames for planar object recognition. In: Proc. 2nd European Conf. Computer Vision (1992)

    Google Scholar 

  23. Rothwell, C.A., Zisserman, A., Forsyth, D.A., Mundy, J.L.: Planar object recognition using projective shape representation. Int. J. Comput. Vis. 16, 57–99 (1995)

    Article  Google Scholar 

  24. Shashua, A.: A geometric invariant for visual recognition and 3D reconstruction from two perspective/orthographic views. In: Proc. IEEE Workshop on Qualitative Vision, pp. 107–117 (1993)

    Chapter  Google Scholar 

  25. Snavely, N., Seitz, S., Szeliski, R.: Photo tourism: exploring photo collections in 3D. ACM Trans. Graph. 25(3), 835–846 (2006) (Proc. SIGGRAPH)

    Article  Google Scholar 

  26. Tsonis, V.S., Chandrinos, K.V., Trahanias, P.E.: Landmark-based navigation using projective invariants. In: Proc. Int. Conf. Intell. Robots Systems, pp. 342–347 (1998)

    Google Scholar 

  27. Velipasalar, S., Wolf, W.: Frame-level temporal calibration of video sequences from unsynchronized cameras by using projective invariants. In: Proc. Advanced Video Signal-based Surveillance, pp. 462–467 (2005)

    Google Scholar 

  28. Wisconsin Computer Vision Group: Repository for joint-invariant matching. http://www.cae.wisc.edu/~sethares/links/raman/JICRvid/space.html

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Washington, Seattle, WA, 98105, USA

    Raman Arora

  2. Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Charles R. Dyer

Authors
  1. Raman Arora
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  2. Charles R. Dyer
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Corresponding author

Correspondence to Raman Arora .

Editor information

Editors and Affiliations

  1. Center for Research, Intelligent Systems, University of California, Riverside, Riverside, 92521, California, USA

    Bir Bhanu

  2. Dept. Computer Science & Engineering, University of California, Riverside, Riverside, 92521, California, USA

    Chinya V. Ravishankar

  3. Dept. Electrical Engineering, University of California, Riverside, Riverside, 92521, California, USA

    Amit K. Roy-Chowdhury

  4. Dept. Electrical Engineering, Packard Bldg., Stanford University, Serra Mall 350, Stanford, 94305-9505, California, USA

    Hamid Aghajan

  5. Dept. Computer Science, University of California, Los Angeles, Boelter Hall 4731, Los Angeles, 90095-1596, California, USA

    Demetri Terzopoulos

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© 2011 Springer-Verlag London Limited

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Arora, R., Dyer, C.R. (2011). Projective Joint Invariants for Matching Curves in Camera Networks. In: Bhanu, B., Ravishankar, C., Roy-Chowdhury, A., Aghajan, H., Terzopoulos, D. (eds) Distributed Video Sensor Networks. Springer, London. https://doi.org/10.1007/978-0-85729-127-1_3

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  • DOI: https://doi.org/10.1007/978-0-85729-127-1_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-126-4

  • Online ISBN: 978-0-85729-127-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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