Title:
A Summary of Geometric Level-Set Analogues for a General Class of Parametric Active Contour and Surface Models
A Summary of Geometric Level-Set Analogues for a General Class of Parametric Active Contour and Surface Models
Author(s)
Xu, Chenyang
Yezzi, Anthony
Prince, Jerry L.
Yezzi, Anthony
Prince, Jerry L.
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Abstract
Geometric active contours (GACs) and surfaces (GASs)
implemented via level set techniques enjoy many advantages
over parametric active contours (PACs) and surfaces
(PASs), such as computational stability and the ability to
change topology during deformation. While many capabilities
of earlier PACs and PASs have been reproduced by various
GACs and GASs, and while relationships have been discussed
for a variety of specific cases, a comprehensive accounting
of the connections between these two worlds (particularly
regarding rigid forces) has not been consolidated
thus far. In this paper we present the precise mathematical
relationships between the two for an extensive family of both
active contour and surface models, encompassing spatially-varying
coefficients, both tension and rigidity, and both conservative
and non-conservative external forces. The result
is a very general geometric formulation for which the intuitive
design principles of PACs and PASs can be applied.
We also point out which type of PAC and PAS methodologies
cannot be adapted to the geometric level set framework. We
conclude by demonstrating several geometric adaptations
of specfic PACs and PASs in several simulations.
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Date Issued
2001
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Proceedings