Using a level set approach for image segmentation under interpolation conditions |
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Authors: | Carole Le Guyader Dominique Apprato Christian Gout |
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Institution: | (1) Laboratoire de Mathématiques de lINSA, INSA de Rouen, Place Emile Blondel, BP 08, 76 131 Mont-Saint-Aignan Cedex, France;(2) UFR Sciences et Techniques de la Côte Basque, Université de Pau, 64 600 Anglet, France |
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Abstract: | In this paper, we propose a new 2D segmentation model including geometric constraints, namely interpolation conditions, to detect objects in a given image. We propose to apply the deformable models to an explicit function using the level set approach (Osher and Sethian 24]); so, we avoid the classical problem of parameterization of both segmentation representation and interpolation conditions. Furthermore, we allow this representation to have topological changes. A problem of energy minimization on a closed subspace of a Hilbert space is defined and introducing Lagrange multipliers enables us to formulate the corresponding variational problem with interpolation conditions. Thus the explicit function evolves, while minimizing the energy and it stops evolving when the desired outlines of the object to detect are reached. The stopping term, as in the classical deformable models, is related to the gradient of the image. Numerical results are given.
AMS subject classification 74G65, 46-xx, 92C55 |
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Keywords: | segmentation deformable models energy minimization level set method variational formulation |
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