Generalized Active Contour Model in an Anisotropic Variable Exponent Sobolev Space

Abstract

Mostly motivated by the practical applications especially in the field of satellite remote sensing of agricultural territories, we develop a novel approach to the domain decomposition basing on the anisotropic version of the Chan-Vese active contour model. With that in mind we propose a new statement of this problem in variable Sobolev spaces, provide a rigorous mathematical analysis of the proposed optimization problem, establish sufficient conditions of its consistency and solvability, show that the objective functional is Gateaux differentiable, and derive the corresponding optimality conditions. To illustrate the validity of the obtained results, we give some examples of numerical simulations with the real satellite images.

Keywords

• active contour model
• existence result
• optimality conditions
• optimal segmentation problem
• anisotropic diffusion tensor
• sobolev spaces with variable exponent