Emmanuel Maitre - Homepage
Emmanuel Maitre - Homepage

Level-set method

With Fadil Santosa (U. Minnesota, Minneapolis) we worked on the determination of potential on the heart surface given measures of electric potential inside the ventricle (with a small passive balloon). As this inverse problem amounts to solve a Cauchy problem for an elliptic operator, it is ill-posed. Rather than regularizing it, which several authors proposed, and which leads to non satisfactory results (in that case), we chose to add information on the object to be identified. We looked for potential taking only two possible values, and thus turn the problem into finding the interface between these two polarization domains. We devised a method to move efficiently curves onto a 3D surface via a Level Set method in the parametric space of the surface. This leads to small computation costs since we solve only 2D problems. As an illustration we tested our method to solve the isoperimetric problem on various surfaces. This amounts to find a curve of minimal length and enclosing a given surface area.

Maitre E. et Santosa F. Level set methods for optimization problems involving geometry and constraints II. Optimization over a fixed surface. J. Comput. Phys., 227 (22), 9596–9611, 2008.


Isoperimetric problem on a paraboloid (last picture is without perspective)
Isoperimetric problem on a cylinder (last picture is without perspective)
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levelset.txt · Last modified: 2010/12/30 14:57 by maitre