TY - GEN

T1 - New possibilities with Sobolev active contours

AU - Sundaramoorthi, Ganesh

AU - Yezzi, Anthony

AU - Mennucci, Andrea C.

AU - Sapiro, Guillermo

PY - 2007/12/24

Y1 - 2007/12/24

N2 - Recently, the Sobolev metric was introduced to define gradient flows of various geometric active contour energies. It was shown that the Sobolev metric out-performs 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 energy-based 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 edge-based 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 ill-posed 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.

AB - Recently, the Sobolev metric was introduced to define gradient flows of various geometric active contour energies. It was shown that the Sobolev metric out-performs 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 energy-based 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 edge-based 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 ill-posed 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.

UR - http://www.scopus.com/inward/record.url?scp=37249079341&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:37249079341

SN - 9783540728221

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 153

EP - 164

BT - Scale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings

T2 - 1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007

Y2 - 30 May 2007 through 2 June 2007

ER -