Multiresolution Surface Reconstruction from Scattered Data Based on Hybrid Meshes

We present a novel technique to extract a multiresolution surface representation from a dense set of unorganized points within three dimensional space. Without utilization of additional connectivity or topological information our procedure is able to efficiently produce a precise and topologicaly correct reconstruction of the underlying model. Based on a hierarchical spatial partitioning scheme and regular and irregular mesh refinement techniques we obtain a hierarchical quadrilateral mesh datastructure which is known as Hybrid Mesh (HM). We start by constructing a simple quad-mesh whose faces aggregate the surface of the initial bounding voxel encapsulating the entire point cloud. Through the process of voxel refinement we simultaneously perform a combined regular-irregular mesh refinement whereas the considered quad-mesh is adapted to wrap the remaining non-empty subvoxels. We project the mesh vertices on planes obtained by principal component analysis (PCA) for each voxel. We provide numerical examples for reconstructions obtained by our method.