Mesh Segmentation And Its Application

Mesh segmentation has become a key ingredient of digital geometry processing. It assists mesh parameterization, mesh simplification, mesh compression, mesh editing and more. Due to the widely usage of mesh segmentation, it has become a very hot research area in digital geometry processing. In this thesis, we made a profoundly research on mesh segmentation and its application in mesh simplification. The main contributions are listed as follows:1. To segment the meshes according to the sharp features on the mesh models, we present a new mesh segmentation algorithm based on the tensor voting theory. All the triangles on the mesh cluster to the user-defined number of regions, such that the sharp features of triangles in the same region are as similar as possible. According to the correspondence between the distribution of eigenvalues from the tensor voting matrices based on normals and the sharp features on the mesh model, we converts the mesh segmentation problem to an energy term minimization problem. We simplified the energy term and solve the minimization problem by clustering. By introducing an heuristic constraint, we successfully prevent the separation of regions. The test results show that our algorithm can obtain much higher performance compared with existing algorithm. At the same time, it can detect the sharp area better.2. We present a novel mesh segmentation algorithm based on the planarity, whose target is to make the result regions as planar as possible. The algorithm maximizes regions' planarity by driving an energy term which reflects the planarity of regions down on the mesh directly. It is easy to implement and extremely efficient. The convergence is guaranteed and the results are better compared with existing method. For models of moderate size, interactive performance is achieved with commodity PCs.3. We present a fast method for segmentation, which is suitable for commonly used CAD models. Given a mesh surface, all faces of it cluster to a user-specified number of patches according to similarity of curvatures. Experimental results show that our algorithm is efficient and robust.4. We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on Centroidal Voronoi Tessellations (CVTs). The accuracy and good quality of the output triangular mesh is achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.The algorithms described above are built upon a unified mesh segmentation framework by adopting different geometrical features. And they can not only obtain good segmentation results, but also achieve high performance. How to combine our algorithm framework and semantic feature on the mesh surface is one of our future work.