Reconfiguration of face expressions based on the discrete capture data of radial basis function interpolation

Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure,thereby reducing the complexity of the algorithm.Firstly,based on the compactly supported radial basis function,the paper makes the complex quadratic function(Multiquadric,MQ for short) to be transformed and proposes a class of compactly supported MQ function.Secondly,the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction.Finally,according to this characteristic of the uneven distribution of the face markers,the markers are numbered and grouped in accordance with the density level,and then be interpolated in line with each group.The approach not only ensures the accuracy of the deformation of face local area and smoothness,but also reduces the time complexity of computing.     

Image zooming via surface fitting based on edge constraint

In this paper we present a new image zooming algorithm based on surface fitting with edge constraint.In surface fitting,we consider not only the relationship of corresponding pixels between the original image and the enlarged image,but also the neighbor pixels in the enlarged image according to the local structure of original image.Furthermore,during surface fitting,more interpolation constraints are used in the new algorithm for improving the precision of the super sampling pixels.The experimental results show that the new method outperforms the previous methods which based on surface fitting.     

Optimizing widths with PSO for center selection of Gaussian radial basis function networks

The radial basis function （RBF） centers play different roles in determining the classification capa- bility of a Gaussian radial basis function neural network （GRBFNN） and should hold different width values. However, it is very hard and time-consuming to optimize the centers and widths at the same time. In this paper, we introduce a new insight into this problem. We explore the impact of the definition of widths on the selection of the centers, propose an optimization algorithm of the RBF widths in order to select proper centers from the center candidate pool, and improve the classification performance of the GRBFNN. The design of the objective function of the optimization algorithm is based on the local mapping capability of each Gaussian RBF. Further, in the design of the objective function, we also handle the imbalanced problem which may occur even when different local regions have the same number of examples. Finally, the recursive orthogonal least square （ROLS） and genetic algorithm （GA）, which are usually adopted to optimize the RBF centers, are separately used to select the centers from the center candidates with the initialized widths, in order to testify the validity of our proposed width initialization strategy on the selection of centers. Our experimental results show that, compared with the heuristic width setting method, the width optimization strategy makes the selected cen- ters more appropriate, and improves the classification performance of the GRBFNN. Moreover, the GRBFNN constructed by our method can attain better classification performance than the RBF LS-SVM, which is a state-of-the-art classifier.     

Higher-Order Level-Set Method and Its Application in Biomolecular Surfaces Construction

We present a general framework for a higher-order spline level-set(HLS) method and apply this to biomolecule surfaces construction. Starting from a first order energy functional,we obtain a general level set formulation of geometric partial differential equation,and provide an efficient approach to solving this partial differential equation using a C2 spline basis. We also present a fast cubic spline interpolation algorithm based on convolution and the Z-transform,which exploits the local relationship of interpolatory cubic spline coefficients with respect to given function data values. One example of our HLS method is demonstrated,which is the construction of biomolecule surfaces(an implicit solvation interface) with their individual atomic coordinates and solvated radii as prerequisites.     

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.     

Hermite variational implicit surface reconstruction

We propose a new technique for reconstructing surfaces from a large set of unorganized 3D data points and their associated normal vectors. The surface is represented as the zero level set of an implicit vol-ume model which fits the data points and normal constraints. Compared with variational implicit sur-faces,we make use of surface normal vectors at data points directly in the implicit model and avoid of introducing manufactured off-surface points. Given n surface point/normal pairs,the proposed method only needs to solve an n×n positive definite linear system. It allows fitting large datasets effectively and robustly. We demonstrate the performance of the proposed method with both globally supported and compactly supported radial basis functions on several datasets.     

Feature-Preserving Mesh Denoising via Anisotropic Surface Fitting

We propose in this paper a robust surface mesh denoising method that can effectively remove mesh noise while faithfully preserving sharp features. This method utilizes surface fitting and projection techniques. Sharp features are preserved in the surface fitting algorithm by considering an anisotropic neighborhood of each vertex detected by the normal-weighted distance. In addition, to handle the mesh with a high level of noise, we perform a pre-filtering of surface normals prior to the neighborhood searching. A number of experimental results and comparisons demonstrate the excellent performance of our method in preserving important surface geometries while filtering mesh noise.     

Synthesizing style-preserving cartoons via non-negative style factorization

We present a complete framework for synthesizing style-preserving 2D cartoons by learning from traditional Chinese cartoons. In contrast to reusing-based approaches which rely on rearranging or retrieving existing cartoon sequences, we aim to generate stylized cartoons with the idea of style factorization. Specifically, starting with 2D skeleton features of cartoon characters extracted by an improved rotoscoping system, we present a non-negative style factorization (NNSF) algorithm to obtain style basis and weights and simultaneously preserve class separability. Thus, factorized style basis can be combined with heterogeneous weights to re-synthesize style-preserving features, and then these features are used as the driving source in the character reshaping process via our proposed subkey-driving strategy. Extensive experiments and examples demonstrate the effectiveness of the proposed framework.     

Edge detection algorithm based on ICA-domain shrinkage in noisy images

We propose a robust edge detection method based on ICA-domain shrinkage （in- dependent component analysis）. It is known that most basis functions extracted from natural images by ICA are sparse and similar to localized and oriented receptive fields, and in the proposed edge detection method, a target image is first transformed by ICA basis functions and then the edges are detected or recon- structed with sparse components. Furthermore, by applying a shrinkage algorithm to filter out the components of noise in ICA-domain, we can readily obtain the sparse components of the original image, resulting in a kind of robust edge detec- tion even for a noisy image with a very low SN ratio. The efficiency of the proposed method is demonstrated by experiments with some natural images.     

An Evolving Autoregressive Predictor for Time Series Forecasting

AR （Autoregressive） model is a common predictor that has been extensively used for time series forecasting. Many training methods can used to update AR model parameters, for instance, least square estimate and maximum likelihood estimate; however, both techniques are sensitive to noisy samples and outliers. To deal with the problems, an evolving AR predictor---EAR, is developed in this work to enhance prediction accuracy and mitigate the effect of noisy samples and outliers. The model parameters of EAR are trained with an ALSE （adaptive least square estimate） method, which can learn samples characteristics more effectively. In each training epoch, the ALSE weights the samples by their fitting accuracy. The samples with larger fitting errors will be given a larger penalty value in the cost function; however, the penalties of difficult-to-predict samples will be adaptively reduced to enhance the prediction accuracy. The effectiveness of the developed EAR predictor is verified by simulation tests. Test results show that the proposed EAR predictor can capture the dynamics of the time series effectively and predict the future trend accurately.     

Gaussian radial basis function interpolant for the different data sites and basis centers

The present study introduces results about unique solvability of Gaussian RBF interpolation with the different data sites and basis centers. For \( N=2 \), we show that the interpolation matrix is singular only when the vector of difference between basis centers and the vector of difference between data sites are perpendicular to each other. For \(N>2\), we show certain states that the interpolation matrix is singular, then we provide several mild conditions which guarantee the interpolation matrix to be non-singular. We propose an algorithm to describe how to choose the basis centers and data sites. The results show that if the basis centers are chosen different from the data sites, the interpolation is uniquely solvable under mild conditions.     

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.     

Selecting radial basis function network centers with recursiveorthogonal least squares training

Recursive orthogonal least squares (ROLS) is a numerically robust method for solving for the output layer weights of a radial basis function (RBF) network, and requires less computer memory than the batch alternative. In the paper, the use of ROLS is extended to selecting the centers of an RBF network. It is shown that the information available in an ROLS algorithm after network training can be used to sequentially select centers to minimize the network output error. This provides efficient methods for network reduction to achieve smaller architectures with acceptable accuracy and without retraining. Two selection methods are developed, forward and backward. The methods are illustrated in applications of RBF networks to modeling a nonlinear time series and a real multiinput-multioutput chemical process. The final network models obtained achieve acceptable accuracy with significant reductions in the number of required centers.     

RBF neural network center selection based on Fisher ratio class separability measure

For classification applications, the role of hidden layer neurons of a radial basis function (RBF) neural network can be interpreted as a function which maps input patterns from a nonlinear separable space to a linear separable space. In the new space, the responses of the hidden layer neurons form new feature vectors. The discriminative power is then determined by RBF centers. In the present study, we propose to choose RBF centers based on Fisher ratio class separability measure with the objective of achieving maximum discriminative power. We implement this idea using a multistep procedure that combines Fisher ratio, an orthogonal transform, and a forward selection search method. Our motivation of employing the orthogonal transform is to decouple the correlations among the responses of the hidden layer neurons so that the class separability provided by individual RBF neurons can be evaluated independently. The strengths of our method are double fold. First, our method selects a parsimonious network architecture. Second, this method selects centers that provide large class separation.     

A Numerically Efficient Dissipation-Preserving Implicit Method for a Nonlinear Multidimensional Fractional Wave Equation

The partition of unity (PU) method, performed with local radial basis function (RBF) approximants, has been proved to be an effective tool for solving large scattered data interpolation problems. However, in order to achieve a good accuracy, the question about how many points we have to consider on each local subdomain, i.e. how large can be the local data sets, needs to be answered. Moreover, it is well-known that also the shape parameter affects the accuracy of the local RBF approximants and, as a consequence, of the PU interpolant. Thus here, both the shape parameter used to fit the local problems and the size of the associated linear systems are supposed to vary among the subdomains. They are selected by minimizing an a priori error estimate. As evident from extensive numerical experiments and applications provided in the paper, the proposed method turns out to be extremely accurate also when data with non-homogeneous density are considered.     

改进递归最小二乘RBF神经网络溶解氧预测

为提高溶解氧预测的准确性,将基于改进型递归最小二乘算法优化的径向基函数（ RBF）神经网络方法应用于溶解氧预测。利用K均值聚类算法进行隐层单元中心选择;利用改进型递归最小二乘算法优化RBF神经网络隐含层到输出层的权值。仿真结果表明：该方法对溶解氧的预测具有较好的非线性拟合能力,预测精度优于RBF神经网络和递归最小二乘算法优化的RBF神经网络。     

基于改进RBF网络的多变量序列建模和预测

针对复杂系统多变量序列预测研究中数据样本过多、信息冗余等问题,从学习样本选择和聚类中心优化两方面对径向基函数(RBF)网络进行改进.基于复杂系统多变量时间序列,首先采用一个线性相关函数和一个非线性相关函数分别计算多变量状态间的线性相关性和非线性相关性,确定一个包含系统有效信息的小数据集;然后基于小数据集,采用K均值聚类方法确定RBF网络的隐层聚类中心,并引入局部搜索过程,优化聚类中心结果;输入其它训练样本,确定网络权值.仿真结果表明,与常规RBF网络学习方法比较,在隐层节点数目相同情况下,改进的方法有效地确定了网络的聚类中心,达到更好的预测精度.     

A complex valued radial basis function network for equalization offast time varying channels

This paper presents a complex valued radial basis function (RBF) network for equalization of fast time varying channels. A new method for calculating the centers of the RBF network is given. The method allows fixing the number of RBF centers even as the equalizer order is increased so that a good performance is obtained by a high-order RBF equalizer with small number of centers. Simulations are performed on time varying channels using a Rayleigh fading channel model to compare the performance of our RBF with an adaptive maximum-likelihood sequence estimator (MLSE) consisting of a channel estimator and a MLSE implemented by the Viterbi algorithm. The results show that the RBF equalizer produces superior performance with less computational complexity.     

Curvilinear Mesh Adaptation Using Radial Basis Function Interpolation and Smoothing

We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the coordinate deformation maps in both the interior and boundary of the curvilinear output mesh by using only scattered nodes on the boundary of the input mesh as data sites in an interpolation problem. Our technique produces high-quality meshes in the deformed domain even when the deformation maps are singular due to a new iterative algorithm based on modification of the RBF shape parameter. Due to the use of RBF interpolation, our technique is applicable to both 2D and 3D curvilinear mesh generation without significant modification.     

基于改进遗传算法的RBF神经网络结构优化研究

针对RBF神经网络隐含层节点数过多导致网络结构复杂的问题,提出了一种基于改进遗传算法(IGA)的RBF神经网络优化算法。利用IGA优化基于正交最小二乘法的RBF神经网络结构,通过对隐含层输出矩阵的列向量进行全局寻优,从而设计出结构更优的基于IGA的RBF神经网络(IGA-RBF)。将IGA-RBF神经网络的学习算法应用于电子元器件贮存环境温湿度预测模型,与基于正交最小二乘法的RBF神经网络进行比较的结果表明:IGA-RBF神经网络设计出来的网络训练步数减少了44步,隐含层节点数减少了34个,且预测模型得到的温湿度误差较小,拟合精度大于0.95,具有更高的预测精度。