Study On Denoising And 3D Reconstruction For Point-Based Models

With the demands of various application fields such as industrial design, aviation simulation, computer-aided medical diagnosis, 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. In recent years, with rapid development and great improvement in the hardware and software for acquiring 3D data, people may obtain raw data representations of real objects with complex shape via a variety of ways. The 3D data obtained by reverse engineering are mainly classified into CT data, MRI data, and unorganized 3D point-based or mesh-based data. Compared to mesh-based models, point primitives are not only simple and easy to operate, but also not need to store any topological connectivity information between points. Point primitives are also suitable for representing irregular real objects such as statue and hair etc, which may have complex geometry and appearance. However, even with 3D high fidelity scanners, the obtained point cloud data may be polluted by various kinds of noise. Thus, denoising is necessary for point-based models before further processing. Due to the convenience to reconstruct complex geometry and no need to manage the topology information of points, implicit surface reconstruction has become an important technique in reverse engineering and scientific visualization. So, how to compute the implicit function from scattered points efficiently and accurately has also become an important problem. The visualization of implicit surface has been studied widely, but there are no efficient visualization methods by now. Most researchers convert implicit surfaces into polygonal meshes, which inherently reintroduced heavy topological constraints.Focused on point-based models, the denoising for point-based models, implicit surfaces reconstruction from point clouds and visualization of implicit surfaces are studied and a number of novel algorithms are proposed in this dissertation. The main contributions include:1) In order to denoise efficiently and preserve the sharp features of the models, a denoising algorithm of a multilateral filter for point-sampled models is presented. The algorithm takes into account the relationship between noise and underlying geometric information, such as normal and curvature. First, by choosing a control function for a local adaptive optimal neighborhood, the filter window is set in the region with similar normals to avoid the problem of shrinkage and over-smoothing. Second, normals and curvatures of sampling points in the optimal neighborhood are estimated by using covariance matrix analysis. Third, based on the filter reference plane, normals and positions of surface points are smoothed respectively, i.e., the normals of surface points are calculated firstly by using multilateral filter, then, by applying multilateral filter again, the position offsets of sampling points are obtained, finally, each point is moved in the direction of normals being smoothed. Experiments show that the multilateral filter can not only denoise efficiently but also preserve the geometric features of the surface successfully.2) A denoising algorithm for noisy point clouds based on Bayesian statistics is presented. The main idea is to perform a search for a maximum of posterior probability(MAP) in the space of possible positions. First, a mathematical model of noisy measurement process and a prior over surface shapes are computed respectively. Second, an approximate MAP-position for each point is found by using a conjugated gradient optimization method. Finally, the Surface Splatting algorithm is applied to render the denoised point-based models. The proposed prior can smooth away noise of the scanned point clouds while enhancing visible surface features.3) An algorithm for reconstructing implicit surface from point clouds with noise and outliers acquired by 3D scanners is presented in this dissertation. First, a clustering optimization operator based on mean shift scheme is introduced, which shifts each point to local maximum of kernel density function, resulting in suppression of noise with different amplitudes and removal of outliers. Second, the clustered data points are divided into subdomains using an adaptive octree subdivision method. Third, a local radial basis function is constructed at each octree leaf cell, and these local shape functions are blent together with their associated weight functions by using a partition of unity to approximate the entire global function.4) A fast implicit surface reconstruction algorithm from point clouds is presented in this dissertation. A new least square reproducing kernel method is proposed based on reproducing kernel particle approximation and applied to implicit surface reconstruction from point clouds. It can improve the reconstruction efficiency by combining the partition of unity. Moreover, in order to further decrease the computational cost, three methods are used to speed the reconstruction. First, VS tree scheme is used to subdivide the global domain into subdomains. Second, a cost function defined for each point is used to iteratively simplify the input point clouds according to its values. Third, the computation of local shape functions is transplanted on the GPU by a sparse matrix solver.5) A novel visualization algorithm for implicit surfaces based on particle system and Surface Splatting is presented. First, an alternative initial technique based on bundles of parallel lines is used to find initial points that are evenly distributed on the surface. Because of its characteristics, the usual split-and-death criterion of particle system is not needed. Second, each elliptical particle is moved towards a progressively lower energy state using a conjugate gradient method, which replaces the gradient-descent as an optimization method to avoid very long convergence times and irreconcilable oscillation around the minimum. Third, a greedy selection strategy is used to choose a subset of active particles which guarantee a hole-free approximation. Finally, a relaxation process further improves the curvature driven anisotropic particle sampling. The proposed elliptical particles are especially designed for splat-based representation and can be directly converted into elliptical surface splats as rendering primitives without any modification, thus high-performance rendering of complex implicit surfaces can be obtained.