Communications in Mathematical Sciences

Volume 7 (2009)

Number 2

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

Pages: 423 – 452



Laurence Guillot

Carole Le Guyader


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.


Gradient Vector Flow; infinity Laplacian; AMLE; partial differential equations; viscosity solutions; segmentation

2010 Mathematics Subject Classification

35G25, 49L25, 68U10, 74G65

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