Shrink-Wrapped Boundary Face Algorithm for Mesh Reconstruction from Unorganized Points

In this work we consider 3D point sets, which in a typical setting represent unorganized point clouds. Segmentation of these point sets requires first to single out structural components of the unknown surface discretely approximated by the point cloud. Structural components, in turn, are surface patches approximating unknown parts of elementary geometric structures, such as planes, ellipsoids, spheres and so on. The approach used is based on level set methods computing the moving front of the surface and tracing the interfaces between different parts of it. Level set methods are widely recognized to be one of the most efficient methods to segment both 2D images and 3D medical images. Level set methods for 3D segmentation have recently received an increasing interest. We contribute by proposing a novel approach for raw point sets. Based on the motion and distance functions of the level set we introduce four energy minimization models, which are used for segmentation, by considering an equal number of distance functions specified by geometric features. Finally we evaluate the proposed algorithm on point sets simulating unorganized point clouds.

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants which are polygonal approximations of planar curves and surfaces verifying a local sampling criterion. Properties of regular interpolants lead to new polygonal reconstruction methods from sets of organized and unorganized points. These methods do not need any parameter of additional information apart from the original points and allow unorganized sets of points to be easily handled.

Wavelet frame based surface reconstruction from unorganized points

Point cloud data is a popular representation of object shape information. Triangulation of scanned point data is an important means for 3d surface reconstruction. In this paper, a new interpolation method is introduced to reconstruct object surface automatically from unorganized point cloud. Our proposed method generates some accurate interpolation points to make the results more reliable based on 3d Delaunay triangular mesh. Each center of the 3d Delaunay triangles is mapped onto the tangent plane of the three vertexes of the triangle, and further accurate interpolation points (also called growing points) are acquired by simplifying the mapping points. Triangulation by a mixture of the growing points and original point cloud data could make the triangular mesh reconstruction of the object more realistic and retaining more detailed information. Experimental results display that our method is effective and robust.

The paper presents a method for surface reconstruction from large unorganized and noisy point sets without any normal or orientation information. Firstly, the outliers will be selected and deleted, and acquire new point sets being less noisy with improved method of fuzzy c-means clustering. Secondly, we compute the normal of the new point sets through PCA analysis. Then we interpolate single-level and multi-level the new points acquired by clustering method by compactly supported radial basis function (CSRBF). The experiments show that the outliers will be selected well and the noisy point sets will be smoothed. The interpolation points are renewed by clustering method, and implicit reconstruction by CSRBF may provide a solution for surface reconstruction from noisy and incomplete data. In our algorithm, we represent the point sets by an octree-based subdivision of the bounding box to reduce computation complexity

Quantitative positron emission tomography imaging often requires correcting the image data for deformable motion. With cyclic motion, this is traditionally achieved by separating the coincidence data into a relatively small number of gates, and incorporating the inter-gate image transformation matrices into the reconstruction algorithm. In the presence of non-cyclic deformable motion, this approach may be impractical due to a large number of required gates. In this paper, we propose an alternative approach to iterative image reconstruction with correction for deformable motion, wherein unorganized point clouds are used to model the imaged objects in the image space, and motion is corrected for explicitly by introducing a time-dependence into the point coordinates. The image function is represented using constant basis functions with finite support determined by the boundaries of the Voronoi cells in the point cloud. We validate the quantitative accuracy and stability of the proposed approach by reconstructing noise-free and noisy projection data from digital and physical phantoms. The point-cloud-based maximum likelihood expectation maximization (MLEM) and one-pass list-mode ordered-subset expectation maximization (OSEM) algorithms are validated. The results demonstrate that images reconstructed using the proposed method are quantitatively stable, with noise and convergence properties comparable to image reconstruction based on the use of rectangular and radially-symmetric basis functions.

In this paper, we propose a novel edge and corner detection algorithm for an unorganized point cloud. Our edge detection method classifies a query point as an edge point by evaluating the distribution of local neighboring points around the query point. The proposed technique has been tested on generic items such as dragons, bunnies, and coffee cups from the Stanford 3D scanning repository. The proposed technique can be directly applied to real and unprocessed point cloud data of random clutter of objects. To demonstrate the proposed technique's efficacy, we compare it to the other solutions for 3D edge extractions in an unorganized point cloud data. We observed that the proposed method could handle the raw and noisy data with little variations in parameters compared to other methods. We also extend the algorithm to estimate the 6D pose of known objects in the presence of dense clutter while handling multiple instances of the object. The overall approach is tested for a warehouse application, where an actual UR5 robot manipulator is used for robotic pick and place operations in an autonomous mode.

Vector field visualization is an important topic in scientific visualization. Its aim is to graphically represent field data in an intuitively understandable and precise way. Here a new approach based on anisotropic nonlinear diffusion is introduced. It enables an easy perception of flow data and serves as an appropriate scale space method for the visualization of complicated flow patterns. The approach is closely related to nonlinear diffusion methods in image analysis where images are smoothed while still retaining and enhancing edges. An initial noisy image is smoothed along streamlines, whereas the image is sharpened in the orthogonal direction. The method is based on a continuous model and requires the solution of a parabolic PDE problem. It is discretized only in the final implementational step. Therefore, many important qualitative aspects can already be discussed on a continuous level. Applications are shown in 2D and 3D and the provisions for flow segmentation are outlined.

Processing of large-scale scattered point clouds has currently become a hot topic in the field of computer graphics research. A supposedly valid tool in producing a set of denoised, outlier-free, and evenly distributed particles over the original point clouds, Weighted Locally Optimal Projection (WLOP) algorithm, has been used in the consolidation of unorganized 3D point clouds by many researchers. However, the algorithm is considered relatively ineffective, due to the large amount of the point clouds data and the iteration calculation. In this paper, a resampling method applied to the point set of 3D model, which significantly improves the computing speed of the WLOP algorithm. In order to measure the impact of error, which will increase with the improvement of calculation efficiency, on the accuracy of the algorithm, we define two quantitative indicators, that is, the projection error and uniformity of distribution. The performance of our method will be evaluated by using both quantitative and qualitative analyses. Our experimental validation demonstrates that this method greatly improves calculating efficiency, notwithstanding the slightly reduced projection accuracy in comparison to WLOP.

We propose a new method for constructing a piecewise smooth mesh from a set of unorganized data points, which may be non-uniformly sampled, noisy, and even containing holes. The method is based on the construction of an implicit representation of the surface, by using smooth (C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in our case) T-spline scalar functions. We first generate the T- spline control grid, and use an evolution process such that the resulting T-spline level sets capture the topology and outline of the object to be reconstructed. The initial mesh with high quality is obtained from the implicit T-spline function through the marching triangulation method. Then we project each data point to the initial mesh, and get a scalar displacement field. Detailed features will be captured by the displaced mesh. We also propose an additional evolution process, which combines data-driven velocities and feature- preserving bilateral filters, in order to reproduce sharp features.

We study the reconstruction of smooth surfaces from point clouds. We use a new squared distance error term in optimization to fit a subdivision surface to a set of unorganized points, which defines a closed target surface of arbitrary topology. The resulting method is based on the framework of squared distance minimization (SDM) proposed by Pottmann et al. Specifically, with an initial subdivision surface having a coarse control mesh as input, we adjust the control points by optimizing an objective function through iterative minimization of a quadratic approximant of the squared distance function of the target shape. Our experiments show that the new method (SDM) converges much faster than the commonly used optimization method using the point distance error function, which is known to have only linear convergence. This observation is further supported by our recent result that SDM can be derived from the Newton method with necessary modifications to make the Hessian positive definite and the fact that the Newton method has quadratic convergence.

ABSTRACTThis paper proposes a novel method for register partially overlapped three-dimensional (3D) point sets when a complete 3D scanned model is constructed from partially scanned 3D point sets. 3D point sets are the most primitive and fundamental surface representations. 3D acquisition devices such as laser scanners and range image finders are popular sources for acquiring point clouds. With the availability of low cost and highly efficient 3D laser scanners, the popularity of such devices is increasing rapidly in various fields. Generally, a standard scanner can obtain only a partial data to build a complete 3D model of the object. These partially scanned 3D patches need to be aligned together in the same coordinate system to construct a complete 3D model, and this process is widely known as registration. A coarse-to-fine alignment technique is proposed to register two partially overlapped point sets. First, the overlapping regions using a novel sampling strategy are identified and the overlapping regions of two point sets are aligned together. Second, fine registration is carried out, in which an auxiliary pair and surface normal constraints are used to find reliable corresponding points in order to achieve higher accuracy.

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

We evaluate our developed conformal method for quantitative shape extraction from unorganized 3D oriented point clouds. The conformal method has been tested previously on real, noisy, 3D data. Here we focus on the empirical evaluation of its performance on synthetic, ground truth data, and comparisons with other methods for quantitative extraction of mean and Gauss curvatures presented in the literature.

This paper presents the methods for data processing technology of 3D points cloud with large unorganized and noisy point sets. Firstly, the noise points will be selected and deleted by the boundary points detection algorithm (BPDA). Secondly, we parameterize the interior points to the sphere model, the octahedron model and the geometry image model. Lastly, we give the error measure of the parameterization. The experiments show that the noisy point sets will be selected well and be deleted. The geometry deformation of our parameterization algorithm is less through the method of the error measure of geometry deformation.