The Solution Of The Level Set Equation And Its Applications

The level set model represents the interface as the 0-level set of the embedded field function and the evolution is driven by the level set equation. This elegant perspective processes the topological change of interface evolution naturally and robustly. It has been widely applied to many fields including computational physics, computer graphics, image processing, computer vision, chemistry, control theory, etc.The thesis addresses the topics about the efficient solution of the level set equation and its applications. The mathematic background and some traditional solution methods are briefly introduced. Then the state of arts on level set methods are summarized and analyzed, meanwhile our technical contributions on level set method are described.Numerically solving level set equation is a time consuming procedure. Uniform and isotropic approach is simple but somewhat inefficient. Many researches are conducted on accelerating the numerical solution. To efficiently trace the 2-D triangular mesh manifold in 3-D space, a novel adaptive level set solution is proposed which is based on narrow band method. It builds coarse resolution grid for global mesh evolution, then high curvature grid points are detected and clustered using fast diffusion method. The corresponding fine resolution grids are built to capture the details on the interface. The adaptive method is applied to the mesh morphing animation. Implementation results and error analysis show that the proposed adaptive method has advantages on computational efficiency and accuracy.A hybrid curve offset method is proposed by combining the grid approach and vector approach. The topological information of the offset curves can be extracted from the solution of the static level set equation. The iso-level set curves are finally represented as a set of the basic graph elements through vertex adjustment, singularity processing and feature detection procedure. By calculating the offset curves and geodesic curves on the mesh, a desirable parameterization of the mesh with boundaryis obtained.