Reconstruction And Structural Optimization Of3D Geometric Models

With the development of3D scanning technology, digital geometry is becomming a new type of multi-media, and is also widely used in areas including commercial man-ufacture and biological information industry. As a key task in digital geometry pro-cessing, the reconstruction of3D models is the research focus of many applications. Recently, the structural optimization of3D models is getting more and more attension because of the emerge of3D printing technology and its combination with reverse engi-neering and computer aided design. In this thesis we study the problems of point cloud registration, surface reconstruction and structural optimization.On the registration of3D point cloud, we discuss the loop closure problem in mul-tiple view registration. Due to the accumulation of local errors in the pairwise registra-tion process, the point clouds at the ends of a closed scanning path usually don’t match. Many of the previous methods deal with this problem by distributing the accumulated errors to the scanning data near the ends of the path, or by deforming the data non-rigidly. Such operations may enlarge the errors in the regions where scans are already well registered, or damage the rigidity of the data. We observe that a consistent problem exists in the registration of scans in a loop, and propose a globally consistent registraton framework to deal with it. In the pairwise registration of neighbouring scans, we apply parameter-based bi-directional correspondence to enhance the accuracy of the results, and to alleviate the influence of sample rate.In the study of model reconstruction, we focus on the implicit surface reconstruc-tion based on signed distance fields. The shape and topology structure of real world objects are usually quite complicate, which brings big challenge for the task of surface reconstruction. The reconstruction process is difficult to complete at once for large scale input, thus slicing the data into small blocks is necessary. We present a spline-based sequential reconstruction method. The scanning data is fused into the distance filed piecewisely and the complete surface representation is obtained in the end. The implicit surface representation by signed distance funcion can easily handle data with complicated topology structure. The locality of spline basis functions allows us to fit the input scans separately, and the sequential strategy unifies the local updates of the distance function together. In the registration of point cloud and implicit surface, pre-vious methods need to extract point cloud first and then carry out the registration. Such manipulation is time-consuming and will introduce extra approximation error. To deal with this problem, we propose a new registration method which estimate the correspon-dences of the input data by linearizing the distance function. This approach helps to improve the efficiency and accuracy of the registration and fusion process.About the optimal design of3D models, we address the global structural opti-mization problem. Traditional structural optimization methods require predefined load conditions. The resulting structure is optimal under the given conditions, but can be weak under different loads. Objects can suffer from various forces in practical appli-cations. The overall performance of objects cannot be guaranteed through traditional approaches and more material than actually needed is used, which is usually a waste. Different from the traditional methods, we propose a novel approach to enhance the global strength of3D objects under all possible load distribution. By optimizing the distribution of material in the structure, we make the strength of the object isotropic to resist different forces, and reduce the material needed for specified global strength demand. The method is based on modal analysis. We first detect the weak region of the object and then reinforce it by optimizing the eigenvalue of the stiffness matrix. Based on the concept of Rayleigh Quotient, an efficient algorithm is also presented. Experiments show that our method can effectively improve the global strength of3D objects.