| Nowadays, adaptive meshes, especially the anisotropic meshes are important for improving the accuracy of the numerical simulations as well as better approximating the shapes. It offers a highly flexible way of controlling mesh generation, by letting the user prescribe a direction and density field that steers the shape, size and alignment of mesh elements. In the simulation of fluid dynamics, it is often desirable to have elongated mesh elements with desired orientation and aspect ratio given by a Riemannian metric tensor field.;The motivation of this work is to introduce a novel particle-based approach for anisotropic surface meshing. Given an input surface equipped with an arbitrary Riemannian metric, this method generates a metric-adapted mesh with user-specified number of vertices. The main idea consists of mapping the anisotropic space into a higher dimensional isotropic one, called "embedding space". Through energy optimization, when the particles are distributed uniformly and isotropically in this higher dimensional embedding space, the particle distribution on the original manifold will exhibit the desired anisotropic property. The triangles are then generated by computing the Restricted Anisotropic Voronoi Diagram and its dual Delaunay triangulation. Furthermore, we extend our particle-based framework to 3D volume meshing with some preliminary experiments.;In the medical and biological fields, mesh generation and application are widely used currently. The triangular and tetrahedral meshes can drive the deformation of the 2D and 3D images, which can be employed in the image registration, especially the simulation of the soft deformable human organs and surfaces. However, most current works are using grid meshes or voxel-based method to implement the deformable image registration (DIR), which are not effective and efficient. Undoubtedly, the framework of particle-based mesh generation provides good facilities to 3D-2D DIR for 3D image reconstruction. The particle-based meshing method is applied to automatically generate high quality adaptive tetrahedral meshes for the whole volume or selected region of interest without the need for manual segmentation. Results show that when equal numbers of control points are used, the feature-based meshing method leads to higher image quality compared with that of regular meshes.;In order to further improve the speed and accuracy of volumetric image reconstruction and 3D-2D registration, especially for large deformation on the volume surface, we develop a mesh-based method to realize the 3D-2D boundary-based DIR to obtain the initial deformation, which is helpful for applying in adaptive radiotherapy. |
