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Sobolev Active Contours

  • Ganesh Sundaramoorthi
  • Anthony Yezzi
  • Andrea Mennucci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)

Abstract

All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L 2-type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolev-type inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions. This is particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edge-based and region-based active contour models as Sobolev active contours and show the substantial improvements gained in segmentation and tracking applications.

Keywords

Active Contour Active Contour Model Initial Contour Tracking Application Geodesic Active Contour 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ganesh Sundaramoorthi
    • 1
  • Anthony Yezzi
    • 1
  • Andrea Mennucci
    • 2
  1. 1.School of Electrical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of MathematicsScuola Normale SuperiorePisaItaly

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