Efficient three-dimensional multi-resolution modeling, segmentation, and segmentation-based mesh compression

3D polygonal models are increasingly being deployed in a wide range of Virtual Reality (VR) applications, including scientific visualization, collaborative design, entertainment, e-commerce, and remote education, etc. These models, produced by the 3D laser scanning systems, are often represented as complex polyhedral meshes with hundreds of thousands or millions of vertices and triangles. Although this representation can achieve high level of realism, these models usually demand a huge amount of storage space and/or transmission bandwidth in the raw data format. Also, a polygonal mesh does not capture a high-level structure, which is useful for managing data in applications, such as object registration, object retrieval and indexing, feature modeling, etc. One way to impose such a high-level description is through mesh segmentation. Therefore, mesh simplification, segmentation and compression have recently been the main areas in 3D mesh processing. In this dissertation, we present an efficient 3D mesh multi-resolution modeling algorithm, which can output arbitrary resolutions of an input model. This algorithm considers edge curvature and neighborhood face area change as the error metrics for the edge collapse operation. Compared with most of the existing simplification algorithms, the proposed method is simple and effective. We also present an efficient and robust neighborhood based algorithm for 3D mesh segmentation. This approach uses discrete Gaussian curvature and concaveness estimation to detect the boundary vertices between the distinct regions of a given mesh. To capture more accurate and relevant geometric information of a vertex on the mesh surface, we enlarge the 1-ring neighborhood to an eXtended Multiple-Ring (XMR) neighborhood. After feature detection, a fast marching watershed method is deployed, followed by an efficient region merging scheme. Simulation results show that this algorithm is efficient and robust to high-resolution models. Finally, we propose a segmentation based mesh compression scheme. Most of the existing 3D mesh coding algorithms compress the model as a whole. Our algorithm separately compresses the partitioned regions that are obtained by the segmentation method described above. The compressed data are put into one stream part by part. Each part is independent of the others. The boundary strips between the different regions are also encoded and appended to the end of the stream. In an inactive or selective application, the users can get the interested parts or the whole object after all the parts and the boundary strips that can connect all the parts together have been received