The aim of this paper is to construct Levenberg-Marquardt level set methods for inverse obstacle problems, and to discuss their numerical realization. Based on a recently developed framework for the construction of level set methods, we can define LevenbergMarquardt level set methods in a general way by varying the function space used for the normal velocity. In the typical case of a PDE-constr...

We apply the Piecewise Constant Level Set Method (PCLSM) to a multiphase motion problem, especially the pure mean curvature motion. We use one level set function to represent multiple regions, and by associating an energy functional which consists of surface tension (proportional to length), we formulate a variational approach for the mean curvature motion problem. Some operator-splitting schem...

We present an approach for hypothesis-based image segmentation founding on the integration of level set methods and discriminative feature clustering techniques. Building up on previous work, we investigate Localized Generalized Matrix Learning Vector Quantization (LGMLVQ) to train a classifier for foreand background of an image. Here we extend this concept towards level set segmentation algori...

The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a weak material approximation [4], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at ...

Image segmentation is the problem of partitioning an image into meaningful parts, often consisting of an object and background. As an important part of many imaging applications, e.g. face recognition, tracking of moving cars and people etc, it is of general interest to design robust and fast segmentation algorithms. However, it is well accepted that there is no general method for solving all s...

In this paper we investigate the regularization and numerical solution of geometric inverse problems related to linear elasticity with minimal assumptions on the geometry of the solution. In particular we consider the probably severely ill-posed reconstruction problem of a twodimensional inclusion from a single boundary measurement. In order to avoid parameterizations, which would introduce a-p...

Bibliography 83 Preface Since their introduction by Osher and Sethian [14], level set methods have been used to solve a wide range of problems, including, but not limited to • Photolithography Development, Etching and Deposition in Semi-conductor Manufacturing (see [2]), • Robotic Navigation with Constraints (see [9]). More examples of applications, further references, and a survey can be found...

We present a novel approach for the derivation of PDEs modeling curvaturedriven flows for matrix-valued data. This approach is based on the Riemannian geometry of the manifold of Symmetric Positive Definite Matrices P(n). The differential geometric attributes of P(n) −such as the bi-invariant metric, the covariant derivative and the Christoffel symbols− allow us to extend scalar-valued mean cur...

Level set methods are a general and powerful technique to represent an object's boundary by the means of an implicit function that has a specific value on the boundary. This property permits the easy modeling of interfaces between different fluids that interact under prescribed/evolving conditions or that act under specified constraints. The Cactus Code is a general framework for developing com...