Geometry Processing And Shape Modeling Of Point-Sampled Models

Recently, as more and more highly detailed geometric models are required in 3D geometric modeling and many graphics applications, the scale and complexity of the model data have dramatically increased. The traditional geometry representation, such as polygonal meshes, need store and maintain the connectivity information between vertices besides the geometry information. They are both memory consuming and computationally expensive. However, owing to convenient 3D point data acquirement and simple data structure, no need to maintain the globally consistent topology, representing and processing 3D models via discrete point samples are particularly flexible and easy. Researches on acquisition, processing and visualization on point-sampled models are becoming more and more attractive in the computer graphics literature, and applied in many applications, such as computer-aided medical diagnosis, digital entertainment, industrial design, aviation simulation, cultural relics protection and so on.Based on the sound theoretical foundation on computer graphics, computer-aided geometric design, discrete differential geometry, digital signal processing, this dissertation investigates some kernel research area for point-based digital geometry processing, such as geometry processing for point set surfaces, shape editing and modeling of point-sampled geometry. Some new key algorithms are proposed. Our main contributions focus on five aspects as following:·1. Estimation of local surface differentials for point set surface. Owing to the principle of energy minimization, an osculating sphere with proper size is to fit neighbor points of each sample point, and the quality of fitting is measured by energy functions, finally the local differentials can be calculated from the extremal points of the energy functions. Another approach to estimate differentials is projection approach, which is inspired by surface differentials analysis in the literature of differential geometry. Based on curvature information of the normal curve at sample point, local surface differentials, such as principal curvatures and principal curvature directions at each sample point are calculated.·2. Parameterization approach for point-based geometry. Based on the spherical mean value properties of harmonic mapping, a new approach for computing the weight in parameterizing point-based geometry is proposed. On the other hand, based upon the IsoMap dimensionality reduction technique, a statistically-based parameterization scheme is proposed, which is termed multidimensional scaling (MDS) in the context of statistics, such that for each pair of sample points, the error between corresponding squared Euclidean distance in the parameter plane and squared geodesic distance in the underlying surface chart is as small as possible.·3. Segmentation approach for point-sampled surface. For segmenting point-sampled surface by clustering scheme, our approach partitions the sample points with two criteria: variation of Euclidean distance between sample points, and angular difference between surface differential directions. Based on these criteria, a k-means clustering algorithm can be used for partitioning the model into subparts. Another approach for segmentation is based on level set scheme. The driven speed function for level set evolution inside narrow band is defined by the curvature field, which approaches zero speed as the propagating front approaches high curvature zone. Our approach can decompose a point-sampled surface into some meaningful components.·4. Denoising and up-sampling for point-based models. Based on the non-local algorithm for image denoising, a novel smoothing technique is proposed, which is based on a global averaging of geometry gray level of all sampled points on the point-based model The final geometry information of sample points can be reconstructed from the geometry gray level information. For up-sampling a given poor point-based model, our novel algorithm aims at holes-covering of point sets, which is based on covariance, analysis for up-sampling model. Our method can be applied for hole-free in many cases as edited model, the model scanned from 3D scanning device and so on.·5. Detail editing and shape modeling of point-sampled geometry. For local editing pointsample geometry, a new definition for normal geo- metric details based on an implicit surface fitting is proposed. Combining the normal geometric details and the position geometric details, a useful interactive local geometry editing method is developed. The method deforms the sample points in a region of interest by manipulating handle points. Based on the transfer functions defined on the frequency domain, a new definition of high frequency geometric details for point-sampled geometry is proposed. Owing to the above definition for geometric details, two means of shape modeling for point models, such as geometric detail scaling and enhancement, are developed. Furthermore, also using the above definition for geometric details, a large range editing framework for point-sampled geometry is presented. The input geometry is first clustered according to its intrinsic geometric features and each cluster is abstracted as a simplification point, then the simplification points are edited while the underlying high frequency geometric details are exactly preserved. Our editing operations intrinsically define deformation fields around the simplification points, which are diffused to other sample points on the original geometry.Geometry processing and shape modeling for point-sampled models are two important research topics in point-based graphics, combining with point-based rendering forms the main framework for point-based digital geometry processing. At the last chapter, we conclude the thesis and discuss some directions for future work.