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.

Sobolev Active Contours

MENNUCCI, Andrea Carlo Giuseppe
2005

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.
2005
VLSM 2005
Beijing, China,
October 16, 2005
VARIATIONAL, GEOMETRIC, AND LEVEL SET METHODS IN COMPUTER VISION
3540293485
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/6571
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