## Communications in Mathematical Sciences

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

#### Abstract

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 information

Source
Commun. Math. Sci., Volume 7, Number 2 (2009), 423-452.

Dates
First available in Project Euclid: 27 May 2009