非线性PCA在表面肌电信号特征提取中的应用

针对表面肌电信号的特点,提出了一种应用非线性主分量分析(PCA)提取表面肌电信号特征的新方法.该方法在表面肌电信号滤波的基础上,采用非线性PCA方法完成数据压缩,将多路表面肌电信号转换为一维的特征数据主元,并以主元曲线的形式输出特征提取结果.本文采用基于自组织神经网络的非线性PCA对手臂尺侧腕伸肌和尺侧腕屈肌的两路表面肌电信号进行主元提取,试验结果表明,四种手部运动模式(握拳、展拳、腕外旋、腕内旋)对应的表面肌电信号利用该方法处理后,得到的主元曲线具有很好的类区分性,依据所得主元曲线的形状特征可以有效地进行手部动作类别的识别.     

Generation of Discrete Bicubic G1 B-Spline Ship Hullform Surfaces from a Given Curve Network Using Virtual Iso-Parametric Curves

We propose a method that automatically generates discrete bicubic G1 continuous B-spline surfaces that interpolate the curve network of a ship hullform. First, the curves in the network are classified into two types: boundary curves and "reference curves". The boundary curves correspond to a set of rectangular (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. Next, in the interior of the patches, surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing "virtual" isoparametric curves. Finally, a discrete G1 continuous B-spline surface is generated by a surface fitting algorithm. Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.     

基于神经网络的非线性PCA方法

由于普通的主元分析（PCA）方法无法提取数据中的非线性相关特性,本文提出了一种基于神经网络的非线性PCA（NIPCA）方法,不仅提取了高维原始数据的线性信息还能提取非线性信息。在此基础上进一步提出了样本中显著误差及劣点的检测方法,从而支持对其进行合理剔除或是修正,仿真试验表明它能有效地减小误差点对网络训练精度的影响,大大增强了算法的鲁棒性。     

Application of nonlinear PCA for fault detection in polymer extrusion processes

This paper describes the application of an improved nonlinear principal component analysis (PCA) to the detection of faults in polymer extrusion processes. Since the processes are complex in nature and nonlinear relationships exist between the recorded variables, an improved nonlinear PCA, which incorporates the radial basis function (RBF) networks and principal curves, is proposed. This algorithm comprises two stages. The first stage involves the use of the serial principal curve to obtain the nonlinear scores and approximated data. The second stage is to construct two RBF networks using a fast recursive algorithm to solve the topology problem in traditional nonlinear PCA. The benefits of this improvement are demonstrated in the practical application to a polymer extrusion process.     

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.     

主曲线成分分析

广泛应用的第一主成分是对数据集的一维线性最优描述，主曲线是第一主成分的非线性推广。线性主成分分析是一种线性分析方法，而数据通常是非线性的。用线性方法分析非线性数据在分析能力上常常是受限的。为此在对线性主成分分析非线性数据研究的基础上，提出了一种新的非线性成分分析方法，即主曲线成分分析。该方法从数据本身出发进行非线性分析，强调非参数特性，能有效地建模非线性数据。实现主曲线成分分析时，采用了改进的神经网络建模方法，该建模方法以其较强的近似性能很好地表达了非线性关系。仿真实验结果表明，主曲线成分分析能很好地解决非线性主成分问题，应用前景广阔。     

基于伸缩因子的代数曲线曲面变形方法

提出了一种基于伸缩因子的代数曲线曲面变形方法。首先构造了一种用于代数曲线曲面变形的伸缩因子,然后将所构造的伸缩因子分别作用于待变形的代数曲线与曲面,通过改变伸缩因子各参数的取值实现对代数曲线曲面的变形。实例表明,该方法操作方便,易于控制,可获得丰富的变形效果,是一种简单有效的代数曲线曲面变形方法。     

A unified model for probabilistic principal surfaces

Principal curves and surfaces are nonlinear generalizations of principal components and subspaces, respectively. They can provide insightful summary of high-dimensional data not typically attainable by classical linear methods. Solutions to several problems, such as proof of existence and convergence, faced by the original principal curve formulation have been proposed in the past few years. Nevertheless, these solutions are not generally extensible to principal surfaces, the mere computation of which presents a formidable obstacle. Consequently, relatively few studies of principal surfaces are available. We previously (2000) proposed the probabilistic principal surface (PPS) to address a number of issues associated with current principal surface algorithms. PPS uses a manifold oriented covariance noise model, based on the generative topographical mapping (GTM), which can be viewed as a parametric formulation of Kohonen's self-organizing map. Building on the PPS, we introduce a unified covariance model that implements PPS (0<α<1), GTM (α=1), and the manifold-aligned GTM (α>1) by varying the clamping parameter α. Then, we comprehensively evaluate the empirical performance of PPS, GTM, and the manifold-aligned GTM on three popular benchmark data sets. It is shown in two different comparisons that the PPS outperforms the GTM under identical parameter settings. Convergence of the PPS is found to be identical to that of the GTM and the computational overhead incurred by the PPS decreases to 40 percent or less for more complex manifolds. These results show that the generalized PPS provides a flexible and effective way of obtaining principal surfaces     

Adapting Feature Curve Networks to a Prescribed Scale

Feature curves on surface meshes are usually defined solely based on local shape properties such as dihedral angles and principal curvatures. From the application perspective, however, the meaningfulness of a network of feature curves also depends on a global scale parameter that takes the distance between feature curves into account, i.e., on a coarse scale, nearby feature curves should be merged or suppressed if the surface region between them is not representable at the given scale/resolution. In this paper, we propose a computational approach to the intuitive notion of scale conforming feature curve networks where the density of feature curves on the surface adapts to a global scale parameter. We present a constrained global optimization algorithm that computes scale conforming feature curve networks by eliminating curve segments that represent surface features, which are not compatible to the prescribed scale. To demonstrate the usefulness of our approach we apply isotropic and anisotropic remeshing schemes that take our feature curve networks as input. For a number of example meshes, we thus generate high quality shape approximations at various levels of detail.     

基于神经网络的非线性PCA方法

该文采用基于正交最小二乘方法(OLS)的径向基函数(RBF)神经网络进行非线性主元分析(NLPCA)算法的训练，提高了训练速度，且不存在局部最优问题。将其应用到聚丙烯生产的高维非线性数据相关特性的提取中，仿真试验显示这种NLPCA方法提高了熔融指数(MI)的预报精度，具有实际应用价值。     

带形状参数的四次Bezier曲线曲面

提出一种新的含参数的四次多项式基函数,四次Bemstein基函数是它的特例,给出其与四次Bemstein基的转换矩阵。分析了该组基函数的性质,定义了带有形状参数的四次Bezier曲线曲面,它们具有四次Bezier曲线曲面的特性,且当参数均取1时即为四次Bezier曲线曲面。对于给定的控制顶点,可以通过改变形状参数的值整体或局部调控曲线曲面的形状。实例表明,该方法应用于曲线曲面设计是有效的。     

带形状参数的四次Bézier曲线曲面

提出一种新的含参数的四次多项式基函数,四次Bernstein基函数是它的特例,给出其与四次Bernstein基的转换矩阵。分析了该组基函数的性质,定义了带有形状参数的四次Bézier曲线曲面,它们具有四次Bézier曲线曲面的特性,且当参数均取1时即为四次Bézier曲线曲面。对于给定的控制顶点,可以通过改变形状参数的值整体或局部调控曲线曲面的形状。实例表明,该方法应用于曲线曲面设计是有效的。     

Self-intersections of offsets of quadratic surfaces: Part I, explicit surfaces

Although offset surfaces are widely used in various engineering applications, their degenerating mechanism is not well known in a quantitative manner. Offset surfaces are functionally more complex than their progenitor surfaces and may degenerate even if the progenitor surfaces are regular. Self-intersections of the offsets of regular surfaces may be induced by concave regions of surface where the positive offset distance exceeds the maximum absolute value of the negative minimum principal curvature or the absolute value of the negative offset distance exceeds the maximum value of the positive maximum principal curvature. It is well known that any regular surface can be locally approximated in the neighborhood of a pointp by the explicit quadratic surface of the form r(x,y)=[x,y1/2(x²+y²)]^T to the second order where – and – are the principal curvatures at pointp. Therefore investigations of the selfintersecting mechanisms of the offsets of explicit quadratic surfaces due to differential geometry properties lead to an understanding of the self-intersecting mechanisms of offsets of regular parametric surfaces. In this paper, we develop the equations of the self-intersection curves of an offset of an explicit quadratic surface. We also develop an algorithm to detect and trace a small loop of a self-intersection curve of an offset of a regular parametric surface based on our analysis of offsets of explicit quadratic surfaces. Examples illustrate our method.     

应用NURBS曲面磨光多面体

本文应用ＮＵＲＢＳ曲面磨光多面体,产生了处处Ｃ′连续的过渡曲面．多面体的磨光分为边的磨光和顶点的磨光两种情形,边的磨光相对较容易,而顶点的磨光则很困难．本文所采用的应用ＮＵＲＢＳ曲面磨光多面体的顶点和边的方法,不仅可以统一实现二者的磨光操作,而且方法简单且统一,产生了Ｃ′连续的过渡面．较之以前的方法,首先,利用ＮＵＲＢＳ曲面可以精确地描述对边磨光所用的柱面（等半径或非等半径）,其次,在对顶点的磨光中,同以往的方法不同,将与该顶点相邻的边的过渡曲面相互分离,并首次引入了“补面”的概念,使得对该点所产生的过渡曲面处处Ｃ′连续．本算法首先构造用以磨光多面体顶点和边的ＮＵＲＢＳ曲面的边界曲线网络图产生边界曲线的控制点及其权值（ＮＵＲＢＳ表示）,然后依据连续性准则,产生ＮＵＲＢＳ曲面的控制信息．     

Surface Fairing towards Regular Principal Curvature Line Networks

Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high‐frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high‐quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.     

B Spline Interpolation Based on Optimization

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Geometric Properties of Bisector Surfaces

This paper studies algebraic and geometric properties of curve–curve, curve–surface, and surface–surface bisectors. The computation is in general difficult since the bisector is determined by solving a system of nonlinear equations. Geometric considerations will help us to determine several distinguished curve and surface pairs which possess elementary computable bisectors. Emphasis is on low-degree rational curves and surfaces, since they are of particular interest in surface modeling.     

可调表面上的曲线插值

提出一个带有多特征的曲线插值可调表面算法。引入形状相似形参数,拓扑地修改初始控制网格。这样使得满足曲线插值的同时,结果表面与初始控制网格有不同的相似性;引入双边控制调节参数,更新插值曲线两边位置,调节插值曲线的弯曲程度;形成求解满足控制曲率的公式。实验结果表明此算法使得曲线插值在可调表面上可行,能够表现出多样性。     

Trimming local and global self-intersections in offset curves/surfaces using distance maps

A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented. Our scheme is based on the derivation of a rational distance map between the original curve or surface and its offset. By solving a bivariate polynomial equation for an offset curve or a system of three polynomial equations for an offset surface, all local and global self-intersection regions in offset curves or surfaces can be detected. The zero-set of polynomial equation(s) corresponds to the self-intersection regions. These regions are trimmed by projecting the zero-set into an appropriate parameter space. The projection operation simplifies the analysis of the zero-set, which makes the proposed algorithm numerically stable and efficient. Furthermore, in a post-processing step, a numerical marching method is employed, which provides a highly precise scheme for self-intersection elimination in both offset curves and surfaces. The effectiveness of our approach is demonstrated using several experimental results.     

Computational methods for blending surface approximation

Blending surfaces form a smooth transition between two distinct, intersecting surfaces or smoothly join two or more disconnected surfaces and are normally procedural surfaces which are difficult to exchange and to interrogate in a reliable and efficient manner. In this paper, an approximation method for blending surfaces which are curvature continuous to the underlying surfaces with a non-uniform rational B-spline (NURBS) surface is presented. The use of NURBS is important since it facilitates the exchange of geometric information between various computer aided design and manufacturing systems. In the method, linkage curves on the underlying surfaces are approximated to within a specified tolerance and cross-link curves are created using the linkage curves, a directional curve and the parametric partial derivatives of the underlying surfaces. Cross-link curves are lofted to form the blending surface and an adaptive sampling procedure is used to test the blending surface against specified tolerances. Cross-link curves are added, where necessary, and the surface relofted until the continuity conditions are satisfied to within specified tolerances. Examples illustrate the applicability of the method.