Sobolev active contours

Authors:
Ganesh Sundaramoorthi;Anthony Yezzi;Andrea Mennucci
Affiliations:
School of Electrical Engineering, Georgia Institute of Technology, Atlanta;School of Electrical Engineering, Georgia Institute of Technology, Atlanta;Department of Mathematics, Scuola Normale Superiore, Pisa, Italy
Venue:
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Year:
2005

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Abstract

All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L2-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.