Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate nonlinear second-order differential equations on Euclidean space. One naturally wonders, “What is the regularity of solutions?” A priori solutions are only defin...

A narrow-band-based adaptive level set method is proposed for mesh evolution in this paper. In the preprocessing step, the portions of the mesh with high curvature are detected and clustered as fine geometric details. Then the fine grids with optimal orientations are defined for each detected portions, while the coarse grid is chosen for global evolution. The solutions on different scale grids ...

In this paper, we proposed a mechanism based on level set method to find the bone marrow parts of the knee MR images. The segmentation can be divided into three steps. The first step is to do rough segmentation on the image using level set method. The second step is to do further segmentation on the result of level set method, and then eliminating the fragments caused by level set method. The t...

In this thesis, the level set method and its application in cell segmentation are investigated. The main task is to segment images with clustered cells provided by FLLL-Hagenberg. Starting with the traditional level set method, the formulation of the level set function and its property are introduced in Chapter 1. The traditional method appears suitable for segmenting cells that don’t stick tog...

ii Preface This report is written at the Technological University of Denmark. The Department of Micro and Nanotechnology offers the three week course 33443 Microfluidics Theory and Simulation, which sorts under the Microfluidics Theory and Simulation (MIFTS) group [4], headed by Professor Henrik Bruus. The motivation for the present report is built on a contact from the Swedish company HemoCue ...

A propagating interface can develop corners and discontinuities as it advances. Level set algorithms have been extensively applied for the problems in which the solution has advancing fronts. One of the most popular level set algorithms is the so called fast marching method (FMM), which requires total O(N log2N) operations, where N is the number of grid points. The article is concerned with the...

We study a level-set method for numerical shape optimization of elastic structures. Our approach combines the level-set algorithm of Osher and Sethian with the classical shape gradient. Although this method is not specifically designed for topology optimization, it can easily handle topology changes for a very large class of objective functions. Its cost is moderate since the shape is captured ...

1. Generalities about domain, or surface evolution problems 2 2. The Level Set Method for describing domain or interface evolution 3 2.1. Level Set framework and geometry 3 2.2. Surface evolution in the level set framework 4 2.3. A glimpse at the mathematical framework 5 2.4. Domain evolution as a boundary value problem: Eikonal equations 9 3. A model application of the level set framework 10 4...

A new high-resolution flux-based finite volume method for general advection equations in non-divergent form including a level set equation for moving interfaces is introduced. The method is applicable to the case of non-divergence free velocity and to general unstructured grids in higher dimensions. We show that the method is consistent and that the numerical solution fulfils discrete minimum/m...