Open Access
June 2009 Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation
Carole Le Guyader, Laurence Guillot
Commun. Math. Sci. 7(2): 423-452 (June 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.


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Carole Le Guyader. Laurence Guillot. "Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation." Commun. Math. Sci. 7 (2) 423 - 452, June 2009.


Published: June 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1188.35192
MathSciNet: MR2536446

Primary: 35D05 , 35D10 , 35G25 , 35Q80 , 49L25 , 68U10 , 74G65

Keywords: AMLE , Gradient Vector Flow , infinity Laplacian , partial differential equations , segmentation , viscosity solutions

Rights: Copyright © 2009 International Press of Boston

Vol.7 • No. 2 • June 2009
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