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Imposing Hard Constraints on Soft Snakes
, 1996
"... An approach is presented for imposing generic hard constraints on deformable models at a low computational cost, while preserving the good convergence properties of snakelike models. We believe this capability to be essential not only for the accurate modeling of individual objects that obey kno ..."
Abstract

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An approach is presented for imposing generic hard constraints on deformable models at a low computational cost, while preserving the good convergence properties of snakelike models. We believe this capability to be essential not only for the accurate modeling of individual objects that obey known geometric and semantic constraints but also for the consistent modeling of sets of objects. Many of the approaches to this problem that have appeared in the vision literature rely on adding penalty terms to the objective functions. They rapidly become untractable when the number of constraints increases. Applied mathematicians have developed powerful constrained optimization algorithms that, in theory, can address this problem. However, these algorithms typically do not take advantage of the specific properties of snakes. We have therefore designed a new algorithm that is closely related to Lagrangian methods but is tailored to accommodate the particular brand of deformable models...
Regularization properties for Minimal Geodesics of a Potential Energy
"... . Some new results on our approach [2] of edge integration for shape modeling are presented. It enables to find the global minimum of active contour models' energy between two points. Initialization is made easier and the curve cannot be trapped at a local minimum by spurious edges. We modified ..."
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. Some new results on our approach [2] of edge integration for shape modeling are presented. It enables to find the global minimum of active contour models' energy between two points. Initialization is made easier and the curve cannot be trapped at a local minimum by spurious edges. We modified the "snake" energy by including the internal regularization term in the external potential term. Our method is based on the interpretation of the snake as a path of minimal length on a surface or minimal cost. We then make use of level sets propagation to find the shortest path which is the global minimum of the energy among all paths joining two endpoints. We show that our energy, though only based on a potential integration along the curve, has a regularization effect like snakes. We show a relation between the maximum curvature along the resulting contour and the potential generated from the image. Keywords: Shape modeling, Deformable Models, Weighted distance transform, Shape Segmentation, ...