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International Conference on Scale-Space Theories in Computer Vision

Scale-Space 2003: Scale Space Methods in Computer Vision pp 599–614Cite as

A Multiphase Level Set Framework for Motion Segmentation

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2695))

Abstract

We present a novel variational approach for segmenting the image plane into a set of regions of piecewise constant motion on the basis of only two consecutive frames from an image sequence.

To this end, we formulate the problem of estimating a motion field in the framework of Bayesian inference. Our model is based on a conditional probability for the spatio-temporal image gradient, given a particular velocity vector, and on a prior on the estimated motion field favoring motion boundaries of minimal length. The corresponding negative log likelihood is a functional which depends on motion vectors for a set of regions and on the boundary separating these regions. It can be considered an extension of the Mumford-Shah functional from intensity segmentation to motion segmentation.

We propose an implementation of this functional by a multiphase level set framework. Minimizing the functional with respect to its dynamic variables results in an evolution equation for a vector-valued level set function and in an eigenvalue problem for the motion vectors. Compared to most alternative approaches, we jointly solve the problems of segmentation and motion estimation by minimizing a single functional. Numerical results both for simulated ground truth experiments and for real-world sequences demonstrate the capacity of our approach to segment several — possibly multiply connected — objects based on their relative motion.

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References

  1. S. Ayer and H.S. Sawhney. Layered representation of motion video using robust maximum likelihood estimation of mixture models and MDL encoding. In Proc. of the Int. Conf. on Comp. Vis., pages 777–784, Boston, USA, 1995.

    Google Scholar 

  2. M. J. Black and P. Anandan. The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields. Comp. Vis. Graph. Image Proc.: IU, 63(1):75–104, 1996.

    Google Scholar 

  3. V. Caselles and B. Coll. Snakes in movement. SIAM J. Numer. Anal., 33:2445–2456, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  4. V. Caselles, R. Kimmel, and G. Sapiro. Geodesic active contours. In Proc. IEEE Internat. Conf. on Comp. Vis., pages 694–699, Boston, USA, 1995.

    Google Scholar 

  5. T. Chan and L. Vese. Active contours without edges. IEEE Trans. Image Processing, 10(2):266–277, 2001.

    Article  MATH  Google Scholar 

  6. D. Cremers. A variational framework for image segmentation combining motion estimation and shape regularization. In C. Dyer and P. Perona, editors, IEEE Int. Conf. on Comp. Vis. and Patt. Recog., Madison, Wisconsin, June 2003. To appear.

    Google Scholar 

  7. D. Cremers and C. Schnörr. Motion Competition: Variational integration of motion segmentation and shape regularization. In L. van Gool, editor, Pattern Recognition, volume 2449 of LNCS, pages 472–480, Zürich, Sept. 2002. Springer.

    Chapter  Google Scholar 

  8. D. Cremers and C. Schnörr. Statistical shape knowledge in variational motion segmentation. Image and Vision Computing, 21(1):77–86, 2003.

    Article  Google Scholar 

  9. G. Farnebäck. Very high accuracy velocity estimation using orientation tensors, parametric motion, and segmentation of the motion field. In Proc. 8th ICCV, volume 1, pages 171–177, 2001.

    Google Scholar 

  10. J. Gomes and O. D. Faugeras. Level sets and distance functions. In D. Vernon, editor, Proc. of the Europ. Conf. on Comp. Vis., volume 1842 of LNCS, pages 588–602, Dublin, Ireland, 2000. Springer.

    Google Scholar 

  11. B.K.P. Horn and B.G. Schunck. Determining optical flow. Artif. Intell., 17:185–203, 1981.

    Article  Google Scholar 

  12. A. Jepson and M.J. Black. Mixture models for optic flow computation. In Proc. IEEE Conf. on Comp. Vision Patt. Recog., pages 760–761, New York, 1993.

    Google Scholar 

  13. S. Kichenassamy, A. Kumar, P. J. Olver, A. Tannenbaum, and A. J. Yezzi. Gradient flows and geometric active contour models. In Proc. IEEE Internat. Conf. on. Comp. Vis., pages 810–815, Boston, USA, 1995.

    Google Scholar 

  14. P. Kornprobst, R. Deriche, and G. Aubert. Image sequence analysis via partial differential equations. J. Math. Im. Vis., 11(1):5–26, 1999.

    Article  MathSciNet  Google Scholar 

  15. B. D. Lucas and T. Kanade. An iterative image registration technique with an application to stereo vision. In Proc.7th International Joint Conference on Artificial Intelligence, pages 674–679, Vancouver, 1981.

    Google Scholar 

  16. A. Mansouri, B. Sirivong, and J. Konrad. Multiple motion segmentation with level set. In Proc. SPIE Conf. on Image and Video Communications and Processing, pages 584–595, Santa Fe, 2000.

    Google Scholar 

  17. E. Memin and P. Perez. Dense estimation and object-based segmentation of the optical flow with robust techniques. IEEE Trans. on Im. Proc., 7(5):703–719, 1998.

    Article  Google Scholar 

  18. J.-M. Morel and S. Solimini. Variational Methods in Image Segmentation. Birkhäuser, Boston, 1995.

    Google Scholar 

  19. D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., 42:577–685, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  20. J.-M. Odobez and P. Bouthemy. Robust multiresolution estimation of parametric motion models. J. of Visual Commun. and Image Repr., 6(4):348–365, 1995.

    Article  Google Scholar 

  21. J.-M. Odobez and P. Bouthemy. Direct incremental model-based image motion segmentation for video analysis. Signal Proc., 66:143–155, 1998.

    Article  MATH  Google Scholar 

  22. S. J. Osher and J. A. Sethian. Fronts propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. of Comp. Phys., 79:12–49, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  23. N. Paragios and R. Deriche. Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Trans. on Patt. Anal. and Mach. Intell., 22(3):266–280, 2000.

    Article  Google Scholar 

  24. C. Samson, L. Blanc-Féraud, G. Aubert, and J. Zerubia. A level set model for image classification. Int. J. of Comp. Vis., 40(3):187–197, 2000.

    Article  MATH  Google Scholar 

  25. C. Schnörr. Computation of discontinuous optical flow by domain decomposition and shape optimization. Int. J. of Comp. Vis., 8(2):153–165, 1992.

    Article  Google Scholar 

  26. M. Sussman and E. Fatemi. An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput., 20(4):1165–1191, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  27. M. Sussman, Smereka P., and S. J. Osher. A level set approach for computing solutions to incompressible twophase flow. J. of Comp. Phys., 94:146–159, 1994.

    Article  Google Scholar 

  28. J. Weickert and C. Schnörr. A theoretical framework for convex regularizers in PDE-based computation of image motion. Int. J. of Comp. Vis., 45(3):245–264, 2001.

    Article  MATH  Google Scholar 

  29. Y. Weiss. Smoothness in layers: Motion segmentation using nonparametric mixture estimation. In Proc. IEEE Conf. on Comp. Vision Patt. Recog., pages 520–527, Puerto Rico, 1997.

    Google Scholar 

  30. H.-K. Zhao, T. Chan, B. Merriman, and S. Osher. A variational level set approach to multiphase motion. J. of Comp. Phys., 127:179–195, 1996.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California at Los Angeles, Los Angeles

    Daniel Cremers

Authors
  1. Daniel Cremers
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Editor information

Editors and Affiliations

  1. Imaging Sciences, 5th Floor Thomas Guy House, Guy’s Campus, London, SE1 9RT, UK

    Lewis D. Griffin

  2. IT University of Copenhagen, Glentevej 67-69, Copenhagen NV, Denmark

    Martin Lillholm

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© 2003 Springer-Verlag Berlin Heidelberg

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Cremers, D. (2003). A Multiphase Level Set Framework for Motion Segmentation. In: Griffin, L.D., Lillholm, M. (eds) Scale Space Methods in Computer Vision. Scale-Space 2003. Lecture Notes in Computer Science, vol 2695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44935-3_42

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  • DOI: https://doi.org/10.1007/3-540-44935-3_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40368-5

  • Online ISBN: 978-3-540-44935-5

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