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.
@article{1243443988,
author = {Le Guyader, Carole and Guillot, Laurence},
title = {Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation},
journal = {Commun. Math. Sci.},
volume = {7},
number = {1},
year = {2009},
pages = { 423-452},
language = {en},
url = {http://dml.mathdoc.fr/item/1243443988}
}
Le Guyader, Carole; Guillot, Laurence. Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation. Commun. Math. Sci., Tome 7 (2009) no. 1, pp. 423-452. http://gdmltest.u-ga.fr/item/1243443988/