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Computer Vision pp 523–531Cite as

Numerical Methods in Curve Evolution Theory

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Synonyms

Active contours; Numerical partial differential equations

Definition

Two numerical approximations of curvature-driven flows are described for use in computer vision and image processing. The level-set methodology of Osher-Sethian that dominates the field is of particular interest, and a more recent, alternative interpretation of curvature flow, based on a stochastic evolution of density functions, is also presented.

Background

Two separate methods for the numerical approximation and computer implementation of curvature-driven flows in the plane are described. The first has become, perhaps, the standard in the field: the level-set methodology of Osher and Sethian [20, 21, 24, 25]. This approach and its variants (fast marching, narrow banding, etc.) dominate the literature and practice in computer vision and image processing.

There are, however, other possibilities that may be useful when estimation is necessary. For example, when tracking in a noisy, uncertain environment, the...

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Author information

Authors and Affiliations

  1. Schools of Electrical and Computer and Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Peter Karasev, Ivan Kolesov & Allen Tannenbaum

Authors
  1. Peter Karasev
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  2. Ivan Kolesov
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  3. Allen Tannenbaum
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Editor information

Editors and Affiliations

  1. Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

    Katsushi Ikeuchi

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Karasev, P., Kolesov, I., Tannenbaum, A. (2014). Numerical Methods in Curve Evolution Theory. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_705

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