Studies On The Digital Geometry Processing Of Point-sampled Models

The traditional geometry representation, such as polygonal meshes, needs to store and maintain the connectivity information between vertices as well as the geometry information. They are both memory consuming and computationally expensive. Due to convenient 3D point data acquirement, simple data structure and no need to maintain the globally consistent topology, however, point-sampled geometry is receiving a growing amount of attention as a new type of medium and surface presentation in Computer Graphics. Accordingly, considerable research has been devoted to the field of digital geometry processing of point-sampled models. Point-sampled geometry has thus been applied to many fields, such as computer-aided medical diagnosis, digital entertainment, industrial design, aviation simulation, protection and restoration of cultural relics, etc.Based on the sound theoretical foundation on computer graphics, computer-aidedgeometric design, discrete differential geometry, digital signal processing, thisdissertation investigates some key research area for the digital geometry processing ofpoint-sampled models, and proposes a number of novel algorithms on them. At thesame time, we have presented a nearly complete geometry processing framework forpoint-sample geometry. Our main contributions focus on the following five aspects:·Based on sampling likelihood, a robust denoising algorithm for point-sampledsurfaces is proposed. In terms of moving least squares surface, the samplinglikelihood for each point on point-sampled surfaces is computed. Based on thenormal tensor voting, the feature intensity of sample point is evaluated. Incombination with sampling likelihood and feature intensity, the point-sampledgeometry can be efficiently smoothed while preserving the surface features. Basedon the similarities including geometry intensity and features of sample points, anon-local denoising algorithm for point-sampled surfaces is presented. By usingthe trilateral filtering operator, the geometry intensity of sample point isdetermined. According to their regular grids of geometry intensity, the similarity of geometry intensity between points is measured. Base on Mean Shift clustering, the point-sampled surfaces are clustered into clusters according to the surface-features similarity. By the similarities, the filtered point-sampled geometry with the fine features is attainted.·A method is presented for patching holes on point-sampled model and synthesizing surface with details. By the surface reconstruction based on radial basis functions, the hole is patched with a smooth surface. Using the trilateral filtering operator, the geometry textures of the existing sample points are produced. As a result, the geometric details on the smooth completed patch are generated by optimizing a constrained global texture energy function on the point-sampled surfaces.·Based on geometry images, an adaptive curvature simplification method for point-sampled model is proposed. By projecting its spherical polar coordinates onto a plane, the point-sampled model is represented as geometry images. The simple density is defined as the maximum search radius on geometry images in order to conveniently control it. In combination with the surface variation and simple density, the point-sampled surfaces are simplified. Another simplification algorithm is based on similarity including strong feature-edge intensity and surface feature anisotropy. Using the normal tensor voting, the point-sampled surfaces are segmented into two parts, one for the strong feature-edge intensity and another for the nonstrong feature-edge intensity. Base on Mean Shift clustering, the second part is then clustered into clusters according to the surface-features similarity. The first part and all the clusters are respectively simplified.·Based on spherical parameterization, a robust morphing algorithm for point-sampled geometry is presented. Source and target models represented by point-sampled geometry are first parameterized onto a sphere, respectively. After aligning the corresponding features of two models on their spheres, two spheres are projected onto a common rectangle-parameter domain and the correspondence between sample points on the two models is built using this rectangle domain. In order to preserve the geometric details of point set surfaces, the absolute geometry of the in-between model is computed by means of Laplacian operator and its surfaces are dynamically up-sampled using a moving least squares method so as to eliminate the cracks.·A prototype system for digital geometry processing of point-sampled models is implemented and introduced. The system actually is a framework of 3D geometry acquisition, representation, processing and rendering. The main components of the system include various novel algorithms on rendering, estimation of local surface differentials, denoising, geometry completion, simplification and up-sampling, parameterization, morphing, texture mapping and synthesis.As a new type of media data, the point-sampled geometry is an extreme promising presentation for 3D surface, and so we discuss some directions for future work in the last chapter.