![]() Osher Department of Mathematics, University of California, Los Angeles, CA, USAĮasy to implement, allows us a fast global minimization of the snake energy. Esedo¯glu Department of Mathematics, University of Michigan, Ann Arbor, MI, USA S. Thiran Signal Processing Institute, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland e-mail: S. ![]() From a numerical point of view, we propose a new practical way to solve the active contour propagation problem toward object boundaries through a dual formulation of the minimization problem. We will establish theorems with proofs to determine the existence of a global minimum of the active contour model. More precisely, we propose to unify three well-known image variational models, namely the snake model, the Rudin– Osher–Fatemi denoising model and the Mumford–Shah segmentation model. Our approach is based on the unification of image segmentation and image denoising tasks into a global minimization framework. In this paper, we propose to solve this problem by determining a global minimum of the active contour model. The only drawback of this model is the existence of local minima in the active contour energy, which makes the initial guess critical to get satisfactory results. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. ![]() It consists of evolving a contour in images toward the boundaries of objects. Published online: 14 July 2007 © Springer Science+Business Media, LLC 2007Ībstract The active contour/snake model is one of the most successful variational models in image segmentation. J Math Imaging Vis (2007) 28: 151–167 DOI 10.1007/s1085-0įast Global Minimization of the Active Contour/Snake Model Xavier Bresson
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