TY - GEN
T1 - A summary of geometric level-set analogues for a general class of parametric active contour and surface models
AU - Xu, Chenyang
AU - Yezzi, A.
AU - Prince, J. L.
N1 - Funding Information:
The authors thank Xiao Han for his assistance in implementing the narrow-band method for level set evolution and Dzung Pham for providing the fuzzy c-means algorithm. The work was supported in part by an NSF/ERC grant CISST-9731748 and NIH/NINDS grant R01NS37747.
Publisher Copyright:
© 2001 IEEE.
PY - 2001
Y1 - 2001
N2 - Geometric active contours (GAC) and surfaces (GAS) implemented via level set techniques enjoy many advantages over parametric active contours (PAC) and surfaces (PAS), such as computational stability and the ability to change topology during deformation. While many capabilities of earlier PAC and PAS have been reproduced by various GAC and GAS, 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. 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 PAC and PAS 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 specific PAC and PAS in several simulations.
AB - Geometric active contours (GAC) and surfaces (GAS) implemented via level set techniques enjoy many advantages over parametric active contours (PAC) and surfaces (PAS), such as computational stability and the ability to change topology during deformation. While many capabilities of earlier PAC and PAS have been reproduced by various GAC and GAS, 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. 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 PAC and PAS 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 specific PAC and PAS in several simulations.
UR - http://www.scopus.com/inward/record.url?scp=84967278724&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84967278724&partnerID=8YFLogxK
U2 - 10.1109/VLSM.2001.938888
DO - 10.1109/VLSM.2001.938888
M3 - Conference contribution
AN - SCOPUS:84967278724
T3 - Proceedings - IEEE Workshop on Variational and Level Set Methods in Computer Vision, VLSM 2001
SP - 104
EP - 111
BT - Proceedings - IEEE Workshop on Variational and Level Set Methods in Computer Vision, VLSM 2001
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - IEEE Workshop on Variational and Level Set Methods in Computer Vision, VLSM 2001
Y2 - 13 July 2001
ER -