Implicit Surface Reconstruction From 3D Scattered Points

Reverse engineering, as an important design and manufacture technique, is significant to shorten the period of product redesign and manufacture in CAD/CAM. It also can be widely applied in automobile, entertainment, medical treatment and other fields. Furthermore, surface reconstruction is the crucial aspect in reverse engineering. With the wide application of 3D scanner, how to reconstruct surface from the dense and non-uniform sampled data without topological connectivity is a hot research topic, which is called surface reconstruction from point cloud. The dissertation focuses on the issues of data preprocessing and implicit surface reconstruction from point cloud, which is sampled from arbitrary complex object, and aims to build a continuous implicit surface model. The creative points of the dissertation are as follows:First, implicit and PDE-based surface reconstruction methods from point cloud are surveyed. The variational level set theory and radial basis functions (RBFs) interpolation are introduced. According to energy functional the geometric flow is deduced for evolving surface.On the principle of simpleness, speediness and effectiveness for data preprocessing, three preprocessing methods are proposed. According to the factors of distance, directions of normal vectors and their interaction, near neighbor probability is utilized to reserve surface features. Then an improved k-MEANS algorithm and a curvature-based rule are put forward for data simplification. Last curvature-based data segmentation method, which uses a given curvature estimate algorithm to compute curvature for scattered point cloud, can divide the closer points with similar features into one domain, in order for feature-based surface reconstruction. Results demonstrate that the proposed methods can keep feature points, reduce the redundant data and storage space with good accuracy and fast speed. The bottleneck of computation in 3D RBFmodelor modeling system has been solved.A fast implicit surface reconstruction method is presented, which is an improvement on RBF surface reconstruction method. Based on the differential geometry theorem, which local ellipse is the best linear approximation for smooth surface, an ellipsoidal basis function surface reconstruction method is given. Since the smoothing property of RBF reconstruction method, the details of edges and corners are difficult to reconstruct. A feature based RBF reconstruction means is introduced to improve the reconstruction precision.Level set method is limited in dealing with detail feature. Thus, a variational level set surface reconstruction method based on normal vector constraint is presented. On condition that normal vector is known or its estimation is useable, energy functional with normal constraint is constructed by a continuous normal vector field. According to the given energy functional, the geometric flow is deduced, which drives the surface to move with erergy functional decreasing. When functional reaches its equilibrium, the zero isosurface of level set function is just the reconstructed surface model.Above data preprocessing methods and the fast implicit surface reconstruction algorithm have been embedded in 3D RBFmodelor modeling system. The variational level set method based on normal vector constraint is added into TexMol sysytm. And experimental results demonstrate good reconstructed surfaces.