A framework for the construction of level set methods for shape optimization and reconstruction | Zendy

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A framework for the construction of level set methods for shape optimization and reconstruction

Author(s) -

Martin Burger

Publication year - 2003

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/81

Subject(s) - norm (philosophy) , shape optimization , computer science , mathematical optimization , set (abstract data type) , level set method , inverse problem , inverse , scale (ratio) , mathematics , boundary value problem , finite element method , mathematical analysis , geometry , artificial intelligence , image (mathematics) , image segmentation , programming language , physics , quantum mechanics , political science , law , thermodynamics

The aim of this paper is to develop a functional-analytic framework for the constructionof level set methods, when applied to shape optimization and shape reconstructionproblems. As a main tool we use a notion of gradient flows for geometric configurationssuch as used in the modelling of geometric motions in materials science. The analogiesto this field lead to a scale of level set evolutions, characterized by the norm used for thechoice of the velocity. This scale of methods also...

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