基于RBF神经网络NURBS的散乱数据点自由曲面重建

根据径向基函数(RBF)神经网络可以用任意精度逼近任何非线性函数,以及强大的抗噪、修复能力等优点,该文采用RBF神经网络模型进行自由曲面重构,建立了适合曲面重构的径向基函数网络模型。进行了理论分析,并在非均匀有理B样条(NURBS)曲面上做了仿真试验。结果表明:该模型不仅能够有效地逼近不完善的、带有噪声的曲面,而且学习速度很快,提高了对破损、不完全曲面重建的效率和精度,得到的曲面光顺性好。     

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．     

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．     

地震数据处理中基于RBF网络的函数逼近

该文将径向基函数网络引入地震数据处理中,实现了函数逼近法地震数据的插值处理,在实际地震数据处理中取得了较好的应用效果。主要研究了径向基函数网络的理论、方法、应用及其逼近性能。该网络充分地利用了包含在训练数据中的信息,可自适应地确定网络隐层节点数目、径向基函数中心以及网络的权系数,生成的网络具有规模小、收敛快和数值稳定等优点。对同一函数进行逼近且精度相同时,径向基函数网络所用时间远远小于BP网络,因此是有广阔应用前景的一种新型神经网络。     

基于SOFM与RBF神经网络的自由曲面重建

根据SOFM神经网络重构曲面样本点的内在拓扑关系,实现对散乱数据的工程近似化,利用RBF神经网络具有的强大非线性逼近能力,提出一种基于SOFM网络和RBF网络相结合的自由曲面重建方法.该方法可有效地解决RBF神经网络对大规模密集散乱点的曲面拟合时出现计算量大、数据网格化难、网络收敛速度慢等问题.     

基于径向基函数神经网络的机器人系统辨识

介绍了一种三层径向基函数神经网络,其学习算法采用正交最小二乘算法.首先根据正交最小二乘算法得到径向基函数神经网络的结构;然后对该网络的权值进行训练使它逼近给定的函数.为了验证径向基函数神经网络所具有的对任意非线性映射的任意逼近能力和自学习、自适应能力,以两关节机械手为辨识对象来进行实验研究.实验结果表明,该径向基函数神经网络具有良好的模型学习和逼近能力,并且学习速度快、收敛性好、鲁棒性强,尤其适合于具有连续线性与非线性对象的复杂系统的控制实时性要求.     

一种基于径向基神经网络的车牌字符识别方法

径向基函数神经网络具有局部逼近的能力和局部可调的特性,以车牌字符识别为例,构造了一种实用型的径向基神经网络,并与传统的BP神经网络作了对比.实验结果表明,在车牌字符识别中,径向基网络的识别能力、分类能力及识别速度等均优于BP网络.     

新型广义径向基函数神经网络结构研究

提出了一种新型的广义径向基函数(RBF)神经网络,并研究了该网络的学习方法.不同于传统三层结构的RBF网络,广义RBF网络增加了基函数输出加权层,并在输出层采用超曲面去逼近任意的非线性曲面.实例仿真结果表明,与传统的RBF网络相比,该网络具有良好的逼近性能,收敛速度快,可逼近任意多变量非线性函数.     

一种新型神经网络在自由曲面重构中的应用

以层次划分和模块化为思想基础,提出了一种新型神经网络模型对自由曲面进行重构,即基于径向基函数（RBF）神经网络的混合网络模型。先后运用减聚类方法、正交最小二乘法、最大似然法对网络进行有无监督的混合训练,旨在解决大样本集的简化建模和快速训练问题,提高混合网络输出精度。实验结果表明该网络模型使得曲面的拟合精度有了明显提高。     

点云数据重构三维网格形状的新算法

在分析现有重构方法局限性的基础上,提出了一种基于神经网络的点云数据重构三维网格形状的新算法。首先对点云数据平滑处理;然后进行特征线提取,并以特征线为基础对曲面进行分割。该方法能直接从神经网络的权值矩阵得到曲线的控制顶点/曲面的控制网格,通过神经网络的权值约束实现曲线段/曲面片之间的光滑拼接。能显著提高逼近网格的品质,从而实现了点云数据的精确曲面重构,实际的算例结果表明该方法实用可靠。     

基于表面法向差分近似的表面重建新算法*

提出一种基于表面法向差分的四向加权形状重建算法。该方法利用不同表面法向差分方法的重建核函数所具有的互补特性,通过对不同重建结果的四向线性加权可以克服经典重建矩阵的奇异性,并能增加算法的抗噪能力。     

Automatic reconstruction of B-spline surfaces with constrained boundaries

The aim of this study is to present an automatic surface reconstruction method that can take practical restrictions on scanned points into consideration and efficiently and reliably output a group of G¹ surfaces. The proposed method is mainly composed of three phases: quadrangle frame generation, point and curve networks planning, and surface patches reconstruction. In the first phase, the original triangle mesh is reduced and converted into a quadrangle mesh, the edges of which serve as the frame of the surfaces. In the second phase, the boundary data of the surfaces are prepared. These include a network of serial points, frame curves and surface normals which are also expressed as curves. In the final phase, surface initialization, harmonization mapping and surface warping are presented to yield the desired surfaces. The main advantage of the proposed method is that it can relax the pre-processing of a scanned triangle mesh, and hence, increase the efficiency and quality of the surface reconstruction. Several examples of various types of air bags are presented to demonstrate the feasibility of the proposed method.     

Continuous global optimization in surface reconstruction from an oriented point cloud

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, and allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.     

截面线数据的曲面蒙皮重构技术研究

为了保持曲面形状的平滑性，在曲面重构过程中经常会出现曲面形状的变异，针对带有精确截面信息的截面线数据的三维曲面重构问题，提出了一种NURBS曲面蒙皮重构方法。该方法产生一个连续的NURBS曲面，改进了传统曲面蒙皮重构方法在处理非均匀截面数据点时出现的一系列问题，通过实际系统验证了该方法的有效性。     

Optimizing radial basis function neural network based on rough sets and affinity propagation clustering algorithm

A novel method based on rough sets (RS) and the affinity propagation (AP) clustering algorithm is developed to optimize a radial basis function neural network (RBFNN). First, attribute reduction (AR) based on RS theory, as a preprocessor of RBFNN, is presented to eliminate noise and redundant attributes of datasets while determining the number of neurons in the input layer of RBFNN. Second, an AP clustering algorithm is proposed to search for the centers and their widths without a priori knowledge about the number of clusters. These parameters are transferred to the RBF units of RBFNN as the centers and widths of the RBF function. Then the weights connecting the hidden layer and output layer are evaluated and adjusted using the least square method (LSM) according to the output of the RBF units and desired output. Experimental results show that the proposed method has a more powerful generalization capability than conventional methods for an RBFNN.     

用单幅图像重建三维凸面和两类鞍面的方法

利用Eikonal方程的粘性解给出了基于单幅图像的凸面三维重建算法；定义了2类鞍面——加性鞍面和乘性鞍面．利用凸面法和凹面法从鞍面单幅图像重建2个抛物柱面，然后根据鞍面的结构特点将2个抛物柱面重新合成鞍面．文中算法从临界点开始计算，不要求边界条件，具有较高的精确度．最后通过实验分析了该算法对噪声的敏感性．     

A shape adaptive motion control system with application to robotic polishing

This paper presents a new shape adaptive motion control system that integrates part measurement with motion control. The proposed system consists of four blocks: surface measurement; surface reconstruction; tool trajectory planning; and axis motion control. The key technology used in surface measurement and surface reconstruction is the spatial spectral analysis. In the surface measurement block, a new spectral spectrum comparison method is proposed to determine an optimal digitizing frequency. In the surface reconstruction block, different interpolation methods are compared in the spatial spectral domain. A spatial spectral B-spline method is presented. In the tool trajectory planning block, a method is developed to select a motion profile first and then determine tool locations according to the reconstructed surface in order to improve the accuracy of the planned toolpath. Based on the proposed methods, a software package is developed and implemented on the polishing robot constructed at Ryerson University. The effectiveness of the proposed system has been demonstrated by the experiment on edge polishing. In this experiment, the shape of the part edges is measured first, and then constructed as a wire-frame CAD model, based on which the tool trajectory is planned to control the tool to polish the edges.     

Efficient surface reconstruction method for distributed CAD

This paper describes a new fast Reverse Engineering (RE) method for creating a 3D computerized model from an unorganized cloud of points. The proposed method is derived directly from the problems and difficulties currently associated with remote design over the Internet, such as accuracy, transmission time and representation at different levels of abstraction. With the proposed method, 3D models suitable for distributed design systems can be reconstructed in real time. The mesh reconstruction approach is based on aggregating very large scale 3D scanned data into a Hierarchical Space Decomposition Model (HSDM), realized by the Octree data structure. Then, a Connectivity Graph (CG) is extracted and filled with facets. The HSDM can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the surface reconstruction process becomes robust and stable with respect to sampling noise. Moreover, the data received from different surface/volume sampling devices can be handled naturally. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving significant geometrical features and object topology. As a result, reconstruction and transmission over the network are efficient. Furthermore, the hierarchical representation provides a capability for extracting models at desired levels of detail, thus enabling designers to collaborate at any product development stage: draft or detailed design.