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 - 1996
Y1 - 1996
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 of their convexity, and suggesting that external potentials involving center of mass computations may be better behaved than the unusual potentials based on image gradients. Most importantly, our analysis 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 of their convexity, and suggesting that external potentials involving center of mass computations may be better behaved than the unusual potentials based on image gradients. Most importantly, our analysis 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 - 10.1109/cvpr.1996.517145
DO - 10.1109/cvpr.1996.517145
M3 - Conference article
AN - SCOPUS:0029723587
SN - 1063-6919
SP - 674
EP - 679
JO - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
JF - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
T2 - Proceedings of the 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Y2 - 18 June 1996 through 20 June 1996
ER -