A factorization approach to grouping

  • P. Perona
  • W. Freeman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1406)


The foreground group in a scene may be ‘discovered’ and computed as a factorized approximation to the pairwise affinity of the elements in the scene. A pointwise approximation of the pairwise affinity information may in fact be interpreted as a ‘saliency’ index, and the foreground of the scene may be obtained by thresholding it. An algorithm called ‘affinity factorization’ is thus obtained which may be used for grouping.

The affinity factorization algorithm is demonstrated on displays composed of points, of lines and of brightness values. Its relationship to the Shi-Malik normalized cuts algorithms is explored both analytically and experimentally. The affinity factorization algorithm is shown to be computationally efficient (O(n) floating-point operations for a scene composed of n elements) and to perform well on displays where the background is unstructured. Generalizations to solve more complex problems are also discussed.


Versus Versus Versus Large Eigenvalue Singular Vector Versus Versus Versus Versus Affinity Function 
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.


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  1. 1.
    Y Adini, D Sagi, and M Tsodyks. Excitatory-inhibitory network in the visual cortex: psychophysical evidence. Proc. Natl Academy Sci., 94(19):10426–10431, September 1997.CrossRefGoogle Scholar
  2. 2.
    J.Braun and E. Niebur. Perceptual contour completion: a model based on local anisotropic, fast-adapting interactions between oriented filters. Soc. Neurosci. Abstract, 20 (1665), 1994.Google Scholar
  3. 3.
    M. Hedlund, G. H. Granlund, and H. Knutsson. A consistency operation for line and curve enhancement. In Proc. IEEE Comp. Soc. Conf. on Pattern Recognition and Image Processing, pages 93–96, 1982.Google Scholar
  4. 4.
    I Kovacs. Gestalten of today: early processing of visual contours and surfaces. Behavioural brain research, 82:1–11, 1996.CrossRefGoogle Scholar
  5. 5.
    P. Parent and S. Zucker. Trace inference, curvature consistency, and curve detection. IEEE Trans. Pattern Anal. Mach. Intell., 11(8):823–839, 1989.CrossRefGoogle Scholar
  6. 6.
    A. Pinkus. n-Widths in Approximation Theory. Springer Verlag, 1985.Google Scholar
  7. 7.
    A. Shashua and S. Ullman. Structural saliency: the detection of globally salient structures using a locally connected network. In 2nd International Conference on Computer Vision (ICCV), pages 321–327, December 1988.Google Scholar
  8. 8.
    J. Shi and J. Malik. Normalized cuts and image segmentation. In Proc. IEEE Comput. Soc. Conf. Comput. Vision and Pattern Recogn., Puerto Rico, June 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • P. Perona
    • 1
    • 2
  • W. Freeman
    • 3
  1. 1.California Institute of Technology MS 136-93PasadenaUSA
  2. 2.Università di PadovaItaly
  3. 3.Mitsubishi Electric Research Lab.Cambridge

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