Studies On Denoising And Smoothing Of 3D Digital Geometry

For the demands from various application fields like Computer-aided medical diagnosis, aviation simulation, industrial design, entertainment and so on, studies on 3D data acquisition, processing and visualization are becoming more and more important and attractive among the computer graphics researchers. Actually, in the recent years, with rapid development and great improvement in the hardware and software for processing 3d data, people may obtain raw data representations of real objects with complex shape via a variety of ways, then analyze and process them. This kind method of acquiring and processing data is called reverse engineering, and the obtained data are mainly classified into CT data, MRI data, and irregular 3D point-based or mesh-based data. The work in this paper will process 3D point-based models and meshes, with operations like scanning, parameterization, denoising, surface reconstruction, etc.Due to a variety of physical factors of the acquisition procedure, the derived raw models always are prone to various kinds of undesirable noise and distortions. The purpose of 3D denoising is to remove the effects caused by isolated noises from the derived surface whilst preserving the appearance of geometrically sharp features and minimizing distortion locally or globally.In this paper, we focus on the research on denoising and smoothing of 3D geometry and propose a number of novel algorithms on smoothing/denoising for point-based models and triangular meshes, and main contributions include: A introduction to classical 3D smoothing algorithms as well as some new smoothing/-denoising methods in the recent years is presented. After analyzing and summarizing the fundamental theories, the disadvantages and advantages of different methods are induced. And brief comparisons between various algorithms on their theoretical basis, time and space complexity, applied environments and numerical implementations are presented. Based on a linear convex combination of spherical vectors, a spherical parameterization method for a genus-zero mesh or a mesh with single boundary are presented. The parameterization allows us to apply spectral analysis and filtering for 3D geometry, especially, the smoothing and enhancing of 3D models. A vertex-estimation-based, feature-preserving smoothing technique for meshes is pro-posed. One contribution is to introduce mean value coordinates, in essence barycentric coordinates on arbitrary irregular polygons, to make mesh smoothing robust. Another key insight is that we combine local predictions from the second order triangles with the mean value coordinates-weighted bilateral filter, in a three-pass way, to smooth meshes. The approach reduces shrinkage and preserves sharp features.? We extend image mean shift filtering to 3D surface smoothing by taking the vertex normal and curvature as range component and the vertex position as the spatial component. First use 3D mean shift procedure to cluster point-based surfaces and adaptively select neighbors of each vertex. Then apply a trilateral point filter which adjusts positions of sample points along their normal directions to reduce noise while preserving geometric features.? Extended functions for the hand-held scanner FastSCAN are presented and implemented. Especially practicable solutions to integration and denoising of multiple scans are discussed, and some other operations include automatic or interactive deletion, B-Spline surface based resampling, and feature restoration of point-based model. The stableness and reliability of FastSCAN system increase with our extended functions.? A digital geometry processing system of point-based models and triangular meshes 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 representation, local geometry estimation, parameterization, smoothing, feature detection, boolean operation, deformation and morphing.