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July  2009, 8(4): 1333-1349. doi: 10.3934/cpaa.2009.8.1333

Existence and uniqueness results for the gradient vector flow and geodesic active contours mixed model

Laurence Guillot 1, and  Maïtine Bergounioux 1,

1. 

UMR 6628-MAPMO, Fédération Denis Poisson, Université d'Orléans, BP. 6759, F-45067 Orléans Cedex 2, France, France

Received  June 2008 Revised  October 2008 Published  March 2009

This article deals with the so called GVF (Gradient Vector Flow) introduced by C. Xu, J.L. Prince [26, 27]. We give existence and uniqueness results for the front propagation flow for boundary extraction that was initiated by Paragios, Mellina-Gottardo and Ralmesh [22, 23]. This model combines the geodesic active contour flow and the GVF to determine the geometric flow. The motion equation is considered within a level set formulation to result an Hamilton-Jacobi equation.
Keywords: Image segmentation, geodesic active contour, viscosity solution., gradient vector flow, Hamilton-Jacobi equation.
Mathematics Subject Classification: Primary: 49L25; Secondary: 62H3.
Citation: Laurence Guillot, Maïtine Bergounioux. Existence and uniqueness results for the gradient vector flow and geodesic active contours mixed model. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1333-1349. doi: 10.3934/cpaa.2009.8.1333
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