TY - JOUR
T1 - Convexity analysis of active contour problems
AU - Davatzikos, Christos
AU - Prince, Jerry L.
N1 - Funding Information:
The authors would like thank Nick Bryan for his support to this work. This research was partly supported by the NSF grant MIP-9350336 and the NIH grant NICHD P50HD 25806-03. A condensed version of this paper appeared in the Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, June 1996.
PY - 1999
Y1 - 1999
N2 - A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.
AB - A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.
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U2 - 10.1016/S0262-8856(98)00087-0
DO - 10.1016/S0262-8856(98)00087-0
M3 - Article
AN - SCOPUS:0032742016
SN - 0262-8856
VL - 17
SP - 27
EP - 36
JO - Image and Vision Computing
JF - Image and Vision Computing
IS - 1
ER -