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Extrapolation of vector fields using the infinity laplacian and with applications to image segmentation
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | Guillot, Laurence Le Guyader, Carole |
| Copyright Year | 2009 |
| 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. |
| Related Links | https://hal.science/hal-00435898/file/LGCLG.pdf |
| ISSN | 15396746 |
| Issue Number | 2 |
| Volume Number | 7 |
| Journal | Communications in Mathematical Sciences |
| e-ISSN | 19450796 |
| Language | English |
| Publisher | HAL CCSD International Press |
| Publisher Date | 2009-01-01 |
| Access Restriction | Open |
| Subject Keyword | approximation infinity Laplacian edge-detection hamilton-jacobi equations decomposition Gradient Vector Flow equations partial-differential equations interpolation partial differential uniqueness segmentation active contours AMLE viscosity solutions total variation minimization |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics Applied Mathematics |
