Sparse Motion Segmentation Using Multiple Six-Point Consistencies

  • Vasileios Zografos
  • Klas Nordberg
  • Liam Ellis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6468)


We present a method for segmenting an arbitrary number of moving objects in image sequences using the geometry of 6 points in 2D to infer motion consistency. The method has been evaluated on the Hopkins 155 database and surpasses current state-of-the-art methods such as SSC, both in terms of overall performance on two and three motions but also in terms of maximum errors. The method works by finding initial clusters in the spatial domain, and then classifying each remaining point as belonging to the cluster that minimizes a motion consistency score. In contrast to most other motion segmentation methods that are based on an affine camera model, the proposed method is fully projective.


Image Point Generalise Extreme Value Spectral Cluster Motion Segmentation Epipolar Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Black, M.J., Jepson, A.D.: Estimating Optical Flow in Segmentated Images Using Variable-Order Parametric Models With Local Deformations. PAMI 18, 972–986 (1996)CrossRefGoogle Scholar
  2. 2.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. PAMI 22, 888–905 (2000)CrossRefGoogle Scholar
  3. 3.
    Tomasi, C., Kanade, T.: Shape from motion from image streams under orthography: A factorization method. IJCV 9, 137–154 (1992)CrossRefGoogle Scholar
  4. 4.
    Tron, P., Vidal, R.: A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms. In: CVPR (2007)Google Scholar
  5. 5.
    Elhamifar, E., Vidal, R.: Sparse Subspace Clustering. In: CVPR (2009)Google Scholar
  6. 6.
    Lauer, F., Schnorr, C.: Spectral clustering of linear subspaces for motion segmentation. In: ICCV (2009)Google Scholar
  7. 7.
    Chen, G., Lerman, G.: Motion Segmentation by SCC on the Hopkins 155 Database. In: ICCV (2009)Google Scholar
  8. 8.
    Hu, H., Gu, Q., Deng, L., Zhou, J.: Multiframe motion segmentation via penalized map estimation and linear programming. In: BMVC (2009)Google Scholar
  9. 9.
    da Silva, N.M.P., Costeira, J.: The normalized subspace inclusion: Robust clustering of motion subspaces. In: ICCV (2009)Google Scholar
  10. 10.
    Cheriyadat, A.M., Radke, R.J.: Non-negative matrix factorization of partial track data for motion segmentation. In: ICCV (2009)Google Scholar
  11. 11.
    Sugaya, Y., Kanatani, K.: Geometric Structure of Degeneracy for Multi-body Motion Segentation. In: SMVC (2004)Google Scholar
  12. 12.
    Roweis, S., Saul, L.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. J. Mach. Learn. Res. 4, 119–155 (2003)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Goh, A., Vidal, R.: Segmenting motions of different types by unsupervised manifold clustering. In: CVPR, pp. 1–6 (2007)Google Scholar
  14. 14.
    Rao, S.R., Tron, R., Vidal, E., Ma, Y.: Motion Segmentation via Robust Subspace Separation in the Presence of Outlying, Incomplete, or Corrupted Trajectories. In: CVPR (2008)Google Scholar
  15. 15.
    Vidal, R., Tron, R., Hartley, R.: Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA. IJCV 79, 85–105 (2008)CrossRefGoogle Scholar
  16. 16.
    Nordberg, K., Zografos, V.: Multibody motion segmentation using the geometry of 6 points in 2d images. In: ICPR (2010)Google Scholar
  17. 17.
    Quan, L.: Invariants of Six Points and Projective Reconstruction From Three Uncalibrated Images. PAMI 17, 34–46 (1996)CrossRefGoogle Scholar
  18. 18.
    Carlsson, S.: Duality of Reconstruction and Positioning from Projective Views. In: Workshop on Representations of Visual Scenes (1995)Google Scholar
  19. 19.
    Weinshall, D., Werman, M., Shashua, A.: Duality of multi-point and multi-frame Geometry: Fundamental Shape Matrices and Tensors. In: ECCV (1996)Google Scholar
  20. 20.
    Torr, P.H.S., Zisserman, A.: Robust parameterization and computation of the trifocal tensor. IVC 15, 591–605 (1997)CrossRefGoogle Scholar
  21. 21.
    Nordberg, K.: Single-view matching constraints. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Paragios, N., Tanveer, S.-M., Ju, T., Liu, Z., Coquillart, S., Cruz-Neira, C., Müller, T., Malzbender, T. (eds.) ISVC 2007, Part II. LNCS, vol. 4842, pp. 397–406. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  22. 22.
    Leadbetter, M.R., Lindgreen, G., Rootzn, H.: Extremes and related properties of random sequences and processes. New York (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Vasileios Zografos
    • 1
  • Klas Nordberg
    • 1
  • Liam Ellis
    • 1
  1. 1.Computer Vision LaboratoryLinköping UniversitySweden

Personalised recommendations