A Probabilistic Dynamic Contour Model for Accurate and Robust Lip Tracking
ICMI '02 Proceedings of the 4th IEEE International Conference on Multimodal Interfaces
Segmentation of tissue boundary evolution from brain MR image sequences using multi-phase level sets
Computer Vision and Image Understanding
Active contours using a constraint-based implicit representation
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Segmentation of tissue boundary evolution from brain MR image sequences using multi-phase level sets
Computer Vision and Image Understanding
Stabilization of parametric active contours using a tangential redistribution term
IEEE Transactions on Image Processing
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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 specific PACs and PASs in several simulations.