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A Common Viewpoint on Broad Kernel Filtering and Nonlinear Diffusion

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Scale Space Methods in Computer Vision (Scale-Space 2003)

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Abstract

Using a consistent adaptive smoothing formulation we show that both nonlinear diffusion and adaptive smoothing can be extended to an arbitrary window, a process called broad kernel filtering. Based on this idea, this paper presents a unified treatment of a number of well known nonlinear techniques for filtering. We show that bilateral filtering represents a particular choice of weights in the extended diffusion process, that is obtained from geometrical considerations. We then show that kernel density estimation applied in the joint spatial-range domain yields a powerful processing paradigm - the mean shift procedure, related to bilateral filtering but having additional flexibility. This establishes an attractive relationship between the theory of statistics and that of diffusion and energy minimization. We experimentally compare the discussed methods and give insights on their performance.

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Author information

Authors and Affiliations

  1. Department of Chemistry and Courant Institute of Mathematical Sciences, New York University and Howard Hughes Medical Institute, 31 Washington Place, Main 1021, New York, NY, 10003

    Danny Barash

  2. Real-Time Vision and Modeling Department, Siemens Corporate Research, 755 College Road East, Princeton, NJ, 08540

    Dorin Comaniciu

Authors
  1. Danny Barash
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  2. Dorin Comaniciu
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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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Barash, D., Comaniciu, D. (2003). A Common Viewpoint on Broad Kernel Filtering and Nonlinear Diffusion. 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_48

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  • DOI: https://doi.org/10.1007/3-540-44935-3_48

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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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