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Joint Applied Math and Probability Seminar
Discretization of the Stefan Problem: Fast Hybrid Levelset/k-Means
Algorithm for Image Segmentation
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In this talk, I will first describe a fourth order accurate finite difference numerical discretization for the Laplace and heat equations with Dirichlet boundary conditions on irregular domains. In the case of the heat equation we consider an implicit time stepping discretization to avoid the stringent time step restrictions due to stability requirements induced by explicit schemes. We then turn our focus to the Stefan problem and construct a third order accurate implicit discretization. Multidimensional computational results are presented to demonstrate the order accuracy of these numerical methods. If time permits I will describe a fast hybrid levelset/k-Means algorithm for image segmentation. In particular, we will apply this algorithm to the segmentation of organs in the context of radiation oncology. |