主曲线在复杂指纹图像特征提取中的应用

在自动指纹识别系统中,特征抽取是关键步骤之一。主曲线具有自相合特性,对模式特征能够进行很好的描述,并能够有效维持结构信息。因此,选用推广的多边形主曲线算法并加以改进来提取指纹主曲线,并在此基础上进一步实现指纹特征提取和伪特征检测。实验结果表明,该算法能够在短时间内获得更好的指纹骨架,指纹特征提取的准确率也较高。     

基于主曲线的脱机手写英文字母结构特征分析及选取

要提高脱机手写英文字母识别的识别率,关键是特征的提取与有效鉴别特征的抽取。主曲线是主成分分析的非线性推广,它是通过数据分布"中间"并满足"自相合"的光滑曲线。它较好地反映了数据分布的结构特征。首先将主曲线用于训练数据的特征提取;其次在详细分析字母主曲线的结构特点的基础上,选择出用于字母识别的粗分类、细分类特征;最后在对手写字母进行识别时,先用这些特征进行一级分类;对个别不能很好区分的相似字母用模糊数学方法进行二级模糊分类。所提方法在CEDAR手写体小写字母数据库上的实验结果表明:利用这些特征能有效区分相似字母,提高手写小写英文字母的识别率,不但能为脱机手写小写英文字母识别的研究提供一条新途径,而且能为手写单词识别提供有用信息。     

基于主曲线的相似字符模糊分类方法

要提高手写字符的识别率,抽取方法,它是通过数据分布"中间"并满足"自相合"的光滑曲线,较好地反映了数据分布的结构特征.本文尝试用主曲线这种新的方法来提取手写字符的结构特征,并基于这些特征来对相似字符进行模糊分类.所提方法在CE-DAR和OCRD手写体字符数据库上的实验结果表明:该方法不但是可行的,而且能有效提高相似字符的识别率.它为字符识别的研究提供了一条新途径.     

主曲线研究综述

主曲线（principal curves)是第一主成分的非线性推广，第一主成分是对数据集的一维线性最优描述，主轴线强调寻找通过数据分布的“中间（middle)并满足“自耦合”的光滑一维曲线，其理论基础是寻找嵌入高维空间的非欧氏低维流形，该文着重介绍了主曲线发展的动机，理论基础，典型的主曲线方法和算法实现及其不同领域的应用，并对存在的问题进行了分析。     

平面自治系统相位图的MATLAB软件设计

围绕平面自治系统的相位图这个核心概念,利用MATLAB求解微分方程组的优势,得到了求解自治微分方程组相位图曲线、相位图方向场等各种算法的程序实现,实现了MATLAB仿真工具箱设计,利用图形用户界面(GUI)方法,设计了良好的人-机交互系统的主界面,最后给出了实际例子的程序运行结果,对推动微分方程组在具体实践中的应用和普及具有实际意义。     

自组织拓扑映射与主曲线学习

本文利用自组织拓扑映射方法设计了一种简易主曲线学习的算法,该算法继承了 HS 主曲线算法和 K 主曲线算法的主要优点.同时降低了一般主曲线算法的难度,使其变得更简洁明了。     

基于复杂形态数据的主曲线提取算法及其在图像骨架提取中的应用

针对目前存在的主曲线算法对提取分散度大、高度弯曲及自相交等复杂形态数据效果不好的情况,提出从复杂数据集中找到主曲线的新方法.算法首先用细化算法初始化顶点集得到初步骨架图,并合并邻近顶点;然后采用Kégl主曲线算法的拟合光滑步思想并加以改进来平滑顶点位置,通过迭代构建出主图;最后采用Kégl主曲线算法的重构步进一步修正主图.算法在模拟数据集上进行试验而且还被运用于图像骨架提取,实验结果表明它对提取复杂数据的主曲线是非常有效的.     

基于软K段主曲线的LPR字符特征的提取方法

车牌识别是智能交通系统的重要组成部分,提高车牌字符识别率的关键在于提取字符的特征。主曲线是主成分分析的非线性推广,它是通过数据分布“中间”并满足“自相合”的光滑曲线。通过对现有主曲线算法的分析可知:软K段主曲线算法对提取分布在弯曲度很大或相交曲线周围的数据的主曲线的效果较好。因此,尝试用该主曲线算法来提取车牌字符的结构特征。实验结果表明,利用该主曲线算法来提取车牌识别的结构特征能够取得较好的实验效果。所提方法为提取 车牌字符特征的研究提供了一条新途径。     

基于软K段主曲线算法的字符特征提取研究及实现

要提高脱机手写字符识别的识别率,关键是特征的提取。主曲线是主成分分析的非线性推广,是通过数据分布“中间”并满足“自相合”的光滑曲线。通过对现有主曲线算法分析可知：软K段主曲线算法对提取出分布在弯曲度很大或相交曲线周围的数据的主曲线效果较好。因此本文尝试用谊主曲线算法来提取脱机手写字符的结构特征。实验结果表明,利用该主曲线算法来提取脱机手写字符的结构特征不但是可行的,而且取得较好的实验效果。它为脱机手写字符特征提取的研究提供了一条新途径。     

基于主曲线的指纹细节特征提取方法

要提高指纹识别的识别率,关键是指纹特征的提取。主曲线是主成份分析的非线性推广,它是通过数据分布“中间’’并满足“自相合”的光滑曲线,较好地反映了数据分布的结构特征。本文尝试使用主曲线这种新的方法来提取指纹的细节特征。实验结果表明利用主曲线来提取指纹的结构特征是可行的,它为指纹特征提取的研究提供了一条新途径。     

Limitations of nonlinear PCA as performed with generic neuralnetworks

Kramer's (1991) nonlinear principal components analysis (NLPCA) neural networks are feedforward autoassociative networks with five layers. The third layer has fewer nodes than the input or output layers. This paper proposes a geometric interpretation for Kramer's method by showing that NLPCA fits a lower-dimensional curve or surface through the training data. The first three layers project observations onto the curve or surface giving scores. The last three layers define the curve or surface. The first three layers are a continuous function, which we show has several implications: NLPCA "projections" are suboptimal producing larger approximation error, NLPCA is unable to model curves and surfaces that intersect themselves, and NLPCA cannot parameterize curves with parameterizations having discontinuous jumps. We establish results on the identification of score values and discuss their implications on interpreting score values. We discuss the relationship between NLPCA and principal curves and surfaces, another nonlinear feature extraction method.     

基于粒计算的复杂数据多粒度主曲线提取算法

传统的主曲线算法已被广泛应用到很多领域,但在复杂数据的主曲线提取上效果不佳,而有效的融合粒计算与主曲线学习算法是解决该类问题最有效的途径之一。为此,本文提出了基于粒计算的复杂数据多粒度主曲线提取算法。首先,利用基于t最近邻（T-nearest-neighbors, TNN）的谱聚类算法对数据进行粒化,提出拐点估计方法来自动确定粒的个数;然后调用软K段主曲线算法对每个粒进行局部主曲线提取,并提出通过消除假边来优化每个粒的主曲线提取过程;最后采用局部到全局的策略进行多粒度主曲线提取,并对过拟合线段进行优化,最终形成一条能较好描述数据原始分布形态的主曲线。实验结果表明该算法是一种行之有效的多粒度主曲线提取算法。     

Stochastic Level Set Dynamics to Track Closed Curves Through Image Data

We introduce a stochastic filtering technique for the tracking of closed curves from image sequence. For that purpose, we design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-set representation and the stochastic dynamics is expressed on the level-set function. It takes the form of a stochastic partial differential equation with a Brownian motion of low dimension. The evolution model we propose combines local photometric information, deformations induced by the curve displacement and an uncertainty modeling of the dynamics. Specific choices of noise models and drift terms lead to an evolution law based on mean curvature as in classic level set methods, while other choices yield new evolution laws. The approach we propose is implemented through a particle filter, which includes color measurements characterizing the target and the background photometric probability densities respectively. The merit of this filter is demonstrated on various satellite image sequences depicting the evolution of complex geophysical flows.     

Evolution-based least-squares fitting using Pythagorean hodograph spline curves

The problem of approximating a given set of data points by splines composed of Pythagorean hodograph (PH) curves is addressed. We discuss this problem in a framework that is not only restricted to PH spline curves, but can be applied to more general representations of shapes. In order to solve the highly non-linear curve fitting problem, we formulate an evolution process within the family of PH spline curves. This process generates a family of curves which depends on a time-like variable t. The best approximant is shown to be a stationary point of this evolution process, which is described by a differential equation. Solving it numerically by Euler's method is shown to be related to Gauss–Newton iterations. Different ways of constructing suitable initial positions for the evolution are suggested.     

基于主曲线的微阵列数据分类

提出了一种基于主曲线(principal curves)的微阵列数据分类方法(PC)。主曲线是第一主成分的非线性推广,它是数据集合的“骨架”,数据集合是主曲线的“云”。基于主曲线的微阵列数据分类方法,首先利用专门设计的算法在训练数据集上计算出每类样本的主曲线,然后根据测试样本与各类样本主曲线距离的期望方差来确定测试样本所属的类别。实验结果表明,该分类方法在进行小样本微阵列数据分类时性能优于现有的方法。     

基于MapReduce框架的分布式软K段主曲线算法

传统的主曲线算法在小规模数据集上能获得良好的效果,但单节点的计算和存储能力都不能满足海量数据主曲线的提取要求,而算法分布式并行化是目前解决该类问题最有效的途径之一。本文提出基于MapReduce框架的分布式软K段主曲线算法 (Distributed soft ｋ-segments principal curve,DisSKPC)。首先,基于分布式K-Means算法,采用递归粒化方法对数据集进行粒化,以确定粒的大小并保证粒中数据的关联性。然后调用软K段主曲线算法计算每个粒数据的局部主成分线段,并提出用噪声方差来消除在高密集、高曲率的数据区域可能产生的过拟合线段。最后借助哈密顿路径和贪婪算法连接这些局部主成分线段,形成一条通过数据云中间的最佳曲线。实验结果表明,本文所提出的DisSKPC算法具有良好的可行性和扩展性。     

HS主曲线的数学特性

主曲线被定义作穿过多维数据分布“中间”的满足“自相合”的光滑曲线,它是第一主成分的非线性推广,第一主成分是对数据集的一维线性最优描递。HS主曲线强调非参数模型,对其参数无关性本文给出了具体证明。同时为了全面理解主曲线,本文以空间主曲线为例,分析了它的横截性质。     

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.     

A bottom-up algorithm for finding principal curves with applications to image skeletonization

This paper proposes a new method for finding principal curves from data sets. Motivated by solving the problem of highly curved and self-intersecting curves, we present a bottom-up strategy to construct a graph called a principal graph for representing a principal curve. The method initializes a set of vertices based on principal oriented points introduced by Delicado, and then constructs the principal graph from these vertices through a two-layer iteration process. In inner iteration, the kernel smoother is used to smooth the positions of the vertices. In outer iteration, the principal graph is spanned by minimum spanning tree and is modified by detecting closed regions and intersectional regions, and then, new vertices are inserted into some edges in the principal graph. We tested the algorithm on simulated data sets and applied it to image skeletonization. Experimental results show the effectiveness of the proposed algorithm.     

基于四次方的自由曲线拼接算法

针对AutoCAD、CAXA等软件中的曲线造型问题:当型值点较多时,需绘制的曲线随着鼠标变化时会发生闪烁,有时甚至会出现死机的现象,依据有关"光顺性"的原理,采用了分段拼接曲线的方法,并选取了四次样条曲线方程.经仔细推算和编程实验证明:本算法避免了反求运算,拼接速度快;由于采用的是四次样条曲线,其光顺性的取法更合理,因此,曲线的光顺性比过去的做法更好,同时,在CAD上能直接应用.