The Nyström Extension

work with Serge Belongie, Fan Chung, and Jitendra Malik


  • Spectral graph theoretic methods have recently shown great promise for the problem of image segmentation. However, due to the computational demands of such methods, applications to large problems such as spatiotemporal data and high resolution imagery have been slow to appear. The contribution of this work is a method that substantially reduces the computational requirements of grouping algorithms based on spectral partitioning, making it feasible to apply them to very large grouping problems. Our approach is based on a technique for the numerical solution of eigenfunction problems known as the Nyström method. This method allows extrapolation of the complete grouping solution using only a small number of ``typical'' samples. In doing so, we successfully exploit the fact that there are far fewer coherent groups in an scene than pixels.

  • C. Fowlkes, S. Belongie, F. Chung, J. Malik. "Spectral Grouping Using the Nyström Method", TPAMI. 26 (2) p.214-225 [pdf]

  • S. Belongie, C. Fowlkes, F. Chung, J. Malik. "Spectral Partitioning with Indefinite Kernels using the Nyström Extension", ECCV, Copenhagen, (May 2002). [pdf]

  • C. Fowlkes, S. Belongie, J. Malik. "Efficient Spatiotemporal Grouping Using the Nyström Method", CVPR, Hawaii, (December 2001). [pdf]