A piecewise constant level set method for elliptic inverse problems

A piecewise constant level set method for elliptic inverse problems

We apply a piecewise constant level set method to elliptic inverse problems. The discontinuity of the coefficients is represented implicitly by a piecewise constant level set function, which allows to use one level set function to represent multiple phases. The inverse problem is solved using a variational penalization method with the total variation regularization of the coefficients. An opera...

Piecewise Constant Level Set Method for In- terface Problems

We apply the Piecewise Constant Level Set Method (PCLSM) to interface problems, especially for elliptic inverse and multiphase motion problems. PCLSM allows using one level set function to represent multiple phases, and the interfaces are represented implicitly by the discontinuity of a piecewise constant level set function. The inverse problem is solved using a variational penalization method ...

A Level Set Method for Inverse Problems

Shape and topology optimization for elliptic bound- ary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization...

Piecewise Constant Level Set Method for 3D Image Segmentation

Level set methods have been proven to be efficient tools for tracing interface problems. Recently, some variants of the OsherSethian level set methods, which are called the Piecewise Constant Level Set Methods (PCLSM), have been proposed for some interface problems. The methods need to minimize a smooth cost functional under some special constraints. In this paper a PCLSM for 3D image segmentat...