Many inverse problems arising in image processing or material
science consist in finding free boundaries (such as edges in images,
cracks in solid materials, or optimized shapes of objects under physical
constraints). The mathematical models for solving such inverse problems are often geometric motions, arising from a variational formulation with
regularization. Examples of unknowns are: the reconstructed image
or a shape from given data, a curve or surface). In this talk, I will describe various geometric models, and show links between image processing and material science. More precisely, examples of variational models leading to geometric nonlinear partial differential equations, often in a level set formulation, will be presented, together with numerical results.
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