Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation
Laurence Guillot, Carole Le Guyader · Communications in Mathematical Sciences · 2009
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 regularizer 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.