Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation

Laurence Guillot, Carole Le Guyader
2009 Communications in Mathematical Sciences  
In this paper, we investigate a new Gradient-Vector-Flow (GVF)-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
more » ... er based on the supremum 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.
doi:10.4310/cms.2009.v7.n2.a8 fatcat:af5zknh2nfff3fs6jig3zni5p4