Math @ Duke

Publications [#265009] of Guillermo Sapiro
Papers Published
 Sundaramoorthi, G; Yezzi, A; Mennucci, AC; Sapiro, G, New possibilities with Sobolev active contours,
Lecture notes in computer science, vol. 4485 LNCS
(2007),
pp. 153164, ISSN 03029743
(last updated on 2017/12/11)
Abstract: Recently, the Sobolev metric was introduced to define gradient flows of various geometric active contour energies. It was shown that the Sobolev metric outperforms the traditional metric for the same energy in many cases such as for tracking where the coarse scale changes of the contour are important. Some interesting properties of Sobolev gradient flows are that they stabilize certain unstable traditional flows, and the order of the evolution PDEs are reduced when compared with traditional gradient flows of the same energies. In this paper, we explore new possibilities for active contours made possible by Sobolev active contours. The Sobolev method allows one to implement new energybased active contour models that were not otherwise considered because the traditional minimizing method cannot be used. In particular, we exploit the stabilizing and the order reducing properties of Sobolev gradients to implement the gradient descent of these new energies. We give examples of this class of energies, which include some simple geometric priors and new edgebased energies. We will show that these energies can be quite useful for segmentation and tracking. We will show that the gradient flows using the traditional metric are either illposed or numerically difficult to implement, and then show that the flows can be implemented in a stable and numerically feasible manner using the Sobolev gradient. © SpringerVerlag Berlin Heidelberg 2007.


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