Hermite Radial Basis Functions Implicits

The Hermite radial basis functions (HRBF) implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e. unstructured points and their corresponding normals). Experiments suggest that HRBF implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or non‐uniform samplings, even in the presence of close sheets. HRBF implicits theory unifies a recently introduced class of surface reconstruction methods based on radial basis functions (RBF), which incorporate normals directly in their problem formulation. Such class has the advantage of not depending on manufactured offset‐points to ensure existence of a non‐trivial implicit surface RBF interpolant. In fact, we show that HRBF implicits constitute a particular case of Hermite–Birkhoff interpolation with radial basis functions, whose main results we present here. This framework not only allows us to show connections between the present method and others but also enable us to enhance the flexibility of our method by ensuring well‐posedness of an interesting combined interpolation/regularization approach.     

3D Surface Reconstruction Using a Generalized Distance Function

We define a generalized distance function on an unoriented 3D point set and describe how it may be used to reconstruct a surface approximating these points. This distance function is shown to be a Mahalanobis distance in a higher‐dimensional embedding space of the points, and the resulting reconstruction algorithm a natural extension of the classical Radial Basis Function (RBF) approach. Experimental results show the superiority of our reconstruction algorithm to RBF and other methods in a variety of practical scenarios.     

RBF Volume Ray Casting on Multicore and Manycore CPUs

Modern supercomputers enable increasingly large N‐body simulations using unstructured point data. The structures implied by these points can be reconstructed implicitly. Direct volume rendering of radial basis function (RBF) kernels in domain‐space offers flexible classification and robust feature reconstruction, but achieving performant RBF volume rendering remains a challenge for existing methods on both CPUs and accelerators. In this paper, we present a fast CPU method for direct volume rendering of particle data with RBF kernels. We propose a novel two‐pass algorithm: first sampling the RBF field using coherent bounding hierarchy traversal, then subsequently integrating samples along ray segments. Our approach performs interactively for a range of data sets from molecular dynamics and astrophysics up to 82 million particles. It does not rely on level of detail or subsampling, and offers better reconstruction quality than structured volume rendering of the same data, exhibiting comparable performance and requiring no additional preprocessing or memory footprint other than the BVH. Lastly, our technique enables multi‐field, multi‐material classification of particle data, providing better insight and analysis.     

径向基神经网络重建自由曲面的探讨

提出了采用神经网络重建自由曲面的方法,建立了用于曲面重建的径向基函数神经网络模型,提出并论证了神经网络用于密集散乱点曲面重建的方案,与常规的重构方法对比,分析了其优点和关键技术,着重讨论了径向基函数神经网络模型,仿真实验表明：采用二层的径向基函数网络,对单个曲面片的拟合精度和网络训练速度大大优于ＢＰ网,完全满足实用要求,具有一定的理论与实用意义。     

基于径向基函数网络的隐式曲线

将径向基函数网络与隐式曲线构造原理相结合,提出了构造隐式曲线的新方法,即首先由约束点构造神经网络的输入与输出,把描述物体边界曲线的隐式函数转化为显式函数,然后用径向基函数网络对此显式函数进行逼近,最后由神经网络的仿真曲面得到物体边界的拟合曲线．实验表明,基于径向基函数网络的隐式曲线具有很强的物体边界描述能力和缺损修复能力．     

Robust and Efficient Implicit Surface Reconstruction for Point Clouds Based on Convexified Image Segmentation

We present an implicit surface reconstruction algorithm for point clouds. We view the implicit surface reconstruction as a three dimensional binary image segmentation problem that segments the entire space $\mathbb R ^3$ or the computational domain into an interior region and an exterior region while the boundary between these two regions fits the data points properly. The key points with using an image segmentation formulation are: (1) an edge indicator function that gives a sharp indicator of the surface location, and (2) an initial image function that provides a good initial guess of the interior and exterior regions. In this work we propose novel ways to build both functions directly from the point cloud data. We then adopt recent convexified image segmentation models and fast computational algorithms to achieve efficient and robust implicit surface reconstruction for point clouds. We test our methods on various data sets that are noisy, non-uniform, and with holes or with open boundaries. Moreover, comparisons are also made to current state of the art point cloud surface reconstruction techniques.     

平行断层轮廓线的RBF隐函数曲面造型

将基于径向基函数（Radial Basis Function,RBF)的隐函数插值技术应用于平行断层轮廓线的曲面造型，由于RBF造型方法以曲面能量最小化为目标，因此能够生成较为光滑的曲面，其缺点是计算量较大，文中提出以分段进行曲面重构的局部RBF技术来降低问题的规模和复杂度，并提出相应的快速隐函数多边形化的算法，实验结果表明，该算法是一个较实用的造型方法。     

利用Voronoi协方差矩阵重建隐式曲面

目的 针对含少量离群点的噪声点云,提出了一种Voronoi协方差矩阵的曲面重建方法。方法 以隐函数梯度在Voronoi协方差矩阵形成的张量场内的投影最大化为目标,构建隐函数微分方程,采用离散外微分形式求解连续微分方程,从而将曲面重建问题转化为广义特征值求解问题。在点云空间离散化过程中,附加最短边约束条件,避免了局部空间过度剖分。并引入概率测度理论定义曲面窄带,提高了算法抵抗离群点能力,通过精细剖分曲面窄带,提高了曲面重建精度。结果 实验结果表明,该算法可以抵抗噪声点和离群点的影响,可以生成不同分辨率的曲面。通过调整拟合参数,可以区分曲面的不同部分。结论 提出了一种新的隐式曲面重建方法,无需点云法向、稳健性较强,生成的三角面纵横比好。     

Multi-Level Partition of Unity Algebraic Point Set Surfaces

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.     

Poisson Surface Reconstruction with Envelope Constraints

Reconstructing surfaces from scanned 3D points has been an important research area for several decades. One common approach that has proven efficient and robust to noise is implicit surface reconstruction, i.e. fitting to the points a 3D scalar function (such as an indicator function or signed-distance field) and then extracting an isosurface. Though many techniques fall within this category, existing methods either impose no boundary constraints or impose Dirichlet/Neumann conditions on the surface of a bounding box containing the scanned data. In this work, we demonstrate the benefit of supporting Dirichlet constraints on a general boundary. To this end, we adapt the Screened Poisson Reconstruction algorithm to input a constraint envelope in addition to the oriented point cloud. We impose Dirichlet boundary conditions, forcing the reconstructed implicit function to be zero outside this constraint surface. Using a visual hull and/or depth hull derived from RGB-D scans to define the constraint envelope, we obtain substantially improved surface reconstructions in regions of missing data.     

径向基函数网络的隐式曲面方法

将径向基函数网络与隐式曲面构造原理相结合,提出一种构造隐式曲面的方法．首先以描述物体曲面的隐式函数为基础构造三元显式函数,然后用径向基函数网络逼近显式函数,最后从神经网络的仿真超曲面得到描述物体的封闭曲面;并证明了在理论上此等值面可以以任意精度逼近物体曲面．该方法具有光滑度高、稳定性好,尤其适用少量采样点情形等特点．实验表明,它具有很强的造型能力．     

Optimized Sub-Sampling of Point Sets for Surface Splatting

Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for high‐performance and high‐quality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of primitives that we use to represent a given object. This is why complexity reduction for point‐sampled geometry is as important as it is, e.g., for triangle meshes. In this paper we present a new sub‐sampling technique for dense point clouds which is specifically adjusted to the particular geometric properties of circular or elliptical surface splats. A global optimization scheme computes an approximately minimal set of splats that covers the entire surface while staying below a globally prescribed maximum error toleranceε. Since our algorithm converts pure point sample data into surface splats with normal vectors and spatial extent, it can also be considered as a surface reconstruction technique which generates a hole‐free piecewise linearC^?1 continuous approximation of the input data. Here we can exploit the higher flexibility of surface splats compared to triangle meshes. Compared to previous work in this area we are able to obtain significantly lower splat numbers for a given error tolerance.     

基于径向基函数神经网络在非地震数据中的应用

针对径向基函数（RBF）神经网络的非线性特点,利用已控点来训练RBF网络,而达到预测未知非地震数据控点的目的。综合已知点和预测控制点,把得到的规则数据体大致对应相应空间进行排布用以全空间成像,最后利用相关软件对处理后的非地震数据进行了三维数据的成像,从而可以显示全息的三维信息,该方法显示出很强的处理问题的能力,同时该仿真结果也表明了该方法的有效性和可行性。     

Feature‐Preserving Surface Reconstruction From Unoriented,Noisy Point Data

We propose a robust method for surface mesh reconstruction from unorganized, unoriented, noisy and outlier‐ridden 3D point data. A kernel‐based scale estimator is introduced to estimate the scale of inliers of the input data. The best tangent planes are computed for all points based on mean shift clustering and adaptive scale sample consensus, followed by detecting and removing outliers. Subsequently, we estimate the normals for the remaining points and smooth the noise using a surface fitting and projection strategy. As a result, the outliers and noise are removed and filtered, while the original sharp features are well preserved. We then adopt an existing method to reconstruct surface meshes from the processed point data. To preserve sharp features of the generated meshes that are often blurred during reconstruction, we describe a two‐step approach to effectively recover original sharp features. A number of examples are presented to demonstrate the effectiveness and robustness of our method.     

Feature‐Preserving Reconstruction of Singular Surfaces

Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of ‘singularities’ such as boundaries, sharp features, and non‐manifolds. A few of the current research in reconstruction have addressed handling some of these singularities, but a unified approach to handle them all is missing. In this paper we allow the presence of various singularities by requiring that the sampled object is a collection of smooth surface patches with boundaries that can meet or intersect. Our algorithm first identifies and reconstructs the features where singularities occur. Next, it reconstructs the surface patches containing these feature curves. The identification and reconstruction of feature curves are achieved by a novel combination of the Gaussian weighted graph Laplacian and the Reeb graphs. The global reconstruction is achieved by a method akin to the well known Cocone reconstruction, but with weighted Delaunay triangulation that allows protecting the feature samples with balls. We provide various experimental results to demonstrate the effectiveness of our feature‐preserving singular surface reconstruction algorithm.     

A quasi-Monte Carlo method for computing areas of point-sampled surfaces

A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy-Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.     

基于遗传算法的B样条曲线拟合改进算法

B样条曲线拟合应用于绘制离散数据点的变化趋势,一般采用数据逼近或者迭代的方法得到,是图像处理和逆向工程中的重要内容。针对待拟合曲线存在多峰值、尖点、间断等问题,提出一种基于遗传算法的B样条曲线拟合算法。首先利用惩罚函数将带约束的曲线优化问题转换为无约束问题,然后利用改进的遗传算法来选择合适的适应度函数,再结合模拟退火算法自适应调整节点的数量和位置,在寻优的过程中找到最优的节点向量,持续迭代直到产生最终的优良重建曲线为止。实验结果表明,该算法有效地提高了精度并加快了收敛速度。     

GPU‐Based Spherical Light Field Rendering with Per‐Fragment Depth Correction

Image‐based rendering techniques are a powerful alternative to traditional polygon‐based computer graphics. This paper presents a novel light field rendering technique which performs per‐pixel depth correction of rays for high‐quality reconstruction. Our technique stores combined RGB and depth values in a parabolic 2D texture for every light field sample acquired at discrete positions on a uniform spherical setup. Image synthesis is implemented on the GPU as a fragment program which extracts the correct image information from adjacent cameras for each fragment by applying per‐pixel depth correction of rays. We show that the presented image‐based rendering technique provides a significant improvement compared to previous approaches. We explain two different rendering implementations which make use of a uniform parametrisation to minimise disparity problems and ensure full six degrees of freedom for virtual view synthesis. While one rendering algorithm implements an iterative refinement approach for rendering light fields with per pixel depth correction, the other approach employs a raycaster, which provides superior rendering quality at moderate frame rates. GPU based per‐fragment depth correction of rays, used in both implementations, helps reducing ghosting artifacts to a non‐noticeable amount and provides a rendering technique that performs without exhaustive pre‐processing for 3D object reconstruction and without real‐time ray‐object intersection calculations at rendering time.     

基于RBF神经网络曲线重构的算法研究

提出一种基于径向基(RBF)函数神经网络的曲线重构学习方法,即由描述物体轮廓特征的样本点作为RBF神经网络的学习样本,利用RBF神经网络强大的函教逼近能力对样本点进行学习和训练,从而仿真出包含这些样本点的原始曲线,同时对于曲线一些样本点缺少的情况下,仍然能构通过调整参数训练得到这些样本点的原始拟和曲线.实验表明,基于径向基(RBF)函数的神经网络具有很强的物体边界描述能力和缺损修复能力.     

Compression of Dense and Regular Point Clouds

We present a simple technique for single‐rate compression of point clouds sampled from a surface, based on a spanning tree of the points. Unlike previous methods, we predict future vertices using both a linear predictor, which uses the previous edge as a predictor for the current edge, and lateral predictors that rotate the previous edge 90°left or right about an estimated normal. By careful construction of the spanning tree and choice of prediction rules, our method improves upon existing compression rates when applied to regularly sampled point sets, such as those produced by laser range scanning or uniform tesselation of higher‐order surfaces. For less regular sets of points, the compression rate is still generally within 1.5 bits per point of other compression algorithms.