Communications in Mathematical Sciences
Volume 7 (2009)
Extrapolation of vector fields using the infinity Laplacian and with applications to image segmentation
Pages: 423 – 452
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