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

Laurence Guillot (1) , Carole Le Guyader (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Gradient Vector Flow; infinity Laplacian; AMLE; partial differential; equations; viscosity solutions; segmentation; partial-differential equations; total variation minimization; hamilton-jacobi equations; active contours; edge-detection; interpolation; decomposition; uniqueness; approximation

Domaines: Analyse numérique [math.NA]

Laurence Guillot, Carole Le Guyader. Extrapolation of vector fields using the infinity laplacian and with applications to image segmentation. Communications in Mathematical Sciences, 2009, 7 (2), pp.87-99. ⟨hal-00435898⟩