Extrapolation of Vector Fields Using the Infinity Laplacian and with Applications to Image Segmentation

Authors:
Laurence Guillot;Carole Guyader
Affiliations:
Laboratoire Jean-Alexandre Dieudonné, UMR 6621, Université de Nice Sophia Antipolis --- CNRS, Faculté des Sciences Parc Valrose, Nice Cedex 02, France 06108;Institut des Sciences Appliquées de Rennes, IRMAR, UMR CNRS 6625, Rennes Cedex, France 35043
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

In this paper, we investigate a new Gradient-Vector-Flow (GVF)([38])-inspired static external force field for active contour models, deriving from the edge map of a given image and allowing to increase the capture range. Contrary to prior related works, we reduce the number of unknowns to a single one v by assuming that the expected vector field is the gradient field of a scalar function. The model is phrased in terms of a functional minimization problem comprising a data fidelity term and a regularizer based on the super norm of Dv . The minimization is achieved by solving a second order singular degenerate parabolic equation. A comparison principle as well as the existence/uniqueness of a viscosity solution together with regularity results are established. Experimental results for image segmentation with details of the algorithm are also presented.