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International Journal of Computer Vision

, Volume 73, Issue 3, pp 345–366 | Cite as

Sobolev Active Contours

  • Ganesh Sundaramoorthi
  • Anthony Yezzi
  • Andrea C. Mennucci
Article

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; they are also less susceptible to certain types of local minima in contrast to traditional active contours. These properties are 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.

Keywords

active contours gradient flows Sobolev norm global flows shape optimization 

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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

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

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