Research On Mesh Reconstruction And Repair From Scattered Point Cloud

3D surface reconstruction from point cloud is an attractive subject in computer graphics community, which plays an important role in many application fields, such as scientific computing visualization, CAD/CAM, movie and game. This dissertation comprehensively analyzes and summaries the related methods and techniques of mesh completion and surface mesh reconstruction from scattered point cloud. Based on two main approach integrating quadratic implicit surfaces fitting with triangle meshing from point cloud, the research on denoising, adaptive mesh and mesh completion preserving sharp features is emphasized. The main content reads as follows:In the first chapter, the meaning of meshing point cloud is presented. Then we summarize its techniques, methods and current advances. Finally, the main achievements and plan of contents in this dissertation are presented.In the second chapter, the moving least squares projection procedure is dicussed. It needs to find a reference plane and compute a local bivariate polynomial approximation to the surface, which is a non-linear optimization problem. A simple projection approach is proposed and used to mesh point cloud. By weighted covariance matrix estimating local surface variation, an octree-based subdivision of the box bounding the point cloud is created. Local coordinates are introduced with the origin of coordinates located at the weighted average of local points. Project points are created by projecting the origin to MLS surface. They are connected according to the analysis of the intersections among the spheres bounding the octree cell with mesh vertices. Finally, the mesh generated is cleaned out from non-manifold parts and small hole are filled. The method can generate adaptive high quality triangle mesh within limited time and low memory usage.In the third chapter, a new efficient robust mesh reconstruction, which improves the limited denoising of Ohtake's quadric-error function iterations and low efficiency in region growing mesh reconstruction, is proposed based on Bayesian model. The model estimates the intrinsic property of point cloud. Prior probability part is piecewise quadratic implicit function and the average of local point cloud follow a Gaussian distribution. The maximum of posterior probability smoothes away noise while preserving surface detail and sharp features. After denoising, smaller numbers of points are generated by using surface splatting which decimates adaptively the point cloud. The reconstruction mesh from the new point set uses improved region growing mesh approach which searches neighboring points by a spatial sphere progressively growing along the surface of object. New triangles are generated according to integrating new mesh metric distortion principle with dihedral measurement to preserve sharp features. The resulting model has the reconstruction mesh as close as possible to the surface of the sampled point cloud.In the fourth chapter, surface reconstruction approach based on Fast Fourier Transform (FFT) is discussed. It limits the maximal reconstruction resolution to a level where the reconstruction of fine details of the input data is difficult. A feature-preserving mesh reconstruction algorithm from point cloud is proposed on the basis of the research about the application of the Fast Fourier Transform to surface reconstruction. This algorithm begins on a simple feature-enhancing diffusion applied to the normals estimated roughly by covariance matrix. Gaussian filter is applied to low resolution 3D FFT from point cloud. In time domain outliers are removed and points are moved onto the iso-surface by an iterative clustering along gradient field. Sample data are added to repaired defective surface, and then a new triangle mesh is generated by sphere-intersected method. The experimental results have shown that the algorithm is fast, robust and exhausts low memory.In the fifth chapter, based on the piecewise quadratic polynomial implicit surfaces fitting technology, this dissertation proposes a feature-preserving mesh completion algorithm. To create implicit representation, the algorithm starts with a box that bounds the mesh vertices and creates an octree-based subdivision of this box. Piecewise quadratic polynomial functions which are local smooth differentiable are used to fit the mesh vertices near the hole. Around the sharp features, two or more quadratic functions with different coefficients are used so as to capture sharp features such as edges or corners. The extended Marching Cube algorithm extracts the triangle mesh patch which is stitched with the hole boundary of the original model to complete the polygon mesh. Finally a feature enhancement process is applied to get rid of aliasing artifacts to obtain fine sharp features. The results of experimental tests show that excellent hole repairing mesh can be achieved.In the sixth chapter, the main results are proposed and the main points in future studies are briefly introduced.