Sobolev active contours

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Sobolev active contours (2007)

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by Andrea C. Mennucci , Ganesh Sundaramoorthi , Anthony Yezzi

Venue:	INTERNATIONAL JOURNAL OF COMPUTER VISION
Citations:	66 - 9 self

BibTeX

@ARTICLE{Mennucci07sobolevactive,
    author = {Andrea C. Mennucci and Ganesh Sundaramoorthi and Anthony Yezzi},
    title = {Sobolev active contours},
    journal = {INTERNATIONAL JOURNAL OF COMPUTER VISION},
    year = {2007},
    volume = {73},
    number = {3},
    pages = {109--120}
}

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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 regionbased active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.

Keyphrases

sobolev active contour generic geometric active contour model sobolev-type inner product various energy gradient flow certain type global translation local minimum general methodology sobolev metric active contour model previous geometric active contour model smooth curve undesirable feature inner product induces inner product favorable regularity property substantial improvement traditional active contour 2-type inner product recent work

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