New Possibilities with Sobolev Active Contours

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 c...

• Type: Conference
• Year: 2007
• Where: SCALESPACE
• Authors: Ganesh Sundaramoorthi, Anthony J. Yezzi, Andrea Mennucci, Guillermo Sapiro
• Keywords: Active Contour, Gradient flows, SCALESPACE 2007, Sobolev Gradient