一种基于特征向量的高效虚拟现实辐射度算法

辐射度技术对于具有真实感的图像的合成十分重要。提出了一种基于特征向量的虚拟现实环境中辐射度计算的新方法。该方法采用了并行计算方法计算形状因子矩阵的特征值和特征向量,进而实现对虚拟现实环境中的辐射度进行高效的计算。其性能总体评价结果显示该方法显著降低了复杂环境中集群计算机系统的有效计算时间,提高了计算效率和加速比。其成果可广泛应用在图像处理、人机交互、可视化、虚拟现实等领域。     

Computing electromagnetic eigenmodes with continuous Galerkin approximations

Costabel and Dauge proposed a variational setting to solve numerically the time-harmonic Maxwell equations in 3D polyhedral geometries, with a continuous approximation of the electromagnetic field. In order to remove spurious eigenmodes, three computational strategies are then possible. The original method, which requires a parameterization of the variational formulation. The second method, which is based on an a posteriori filtering of the computed eigenmodes. And the third method, which uses a mixed variational setting so that all spurious modes are removed a priori. In this paper, we discuss the relative merits of the approaches, which are illustrated by a series of 3D numerical examples.     

Bipartite isoperimetric graph partitioning for data co-clustering

Data co-clustering refers to the problem of simultaneous clustering of two data types. Typically, the data is stored in a contingency or co-occurrence matrix C where rows and columns of the matrix represent the data types to be co-clustered. An entry C _ij of the matrix signifies the relation between the data type represented by row i and column j. Co-clustering is the problem of deriving sub-matrices from the larger data matrix by simultaneously clustering rows and columns of the data matrix. In this paper, we present a novel graph theoretic approach to data co-clustering. The two data types are modeled as the two sets of vertices of a weighted bipartite graph. We then propose Isoperimetric Co-clustering Algorithm (ICA)—a new method for partitioning the bipartite graph. ICA requires a simple solution to a sparse system of linear equations instead of the eigenvalue or SVD problem in the popular spectral co-clustering approach. Our theoretical analysis and extensive experiments performed on publicly available datasets demonstrate the advantages of ICA over other approaches in terms of the quality, efficiency and stability in partitioning the bipartite graph.     

Computation of eigenvalues of a real matrix

This paper presents a computational procedure for finding eigenvalues of a real matrix based on Alternate Quadrant Interlocking Factorization, a parallel direct method developed by Rao in 1994 for the solution of the general linear system Ax=b. The computational procedure is similar to LR algorithm as studied by Rutishauser in 1958 for finding eigenvalues of a general matrix. After a series of transformations the eigenvalues are obtained from simple 2×2 matrices derived from the main and cross diagonals of the limit matrix. A sufficient condition for the convergence of the computational procedure is proved. Numerical examples are given to demonstrate the method.     

Higher order eigensensitivity analysis of damped systems with repeated eigenvalues

A simplified method for the computation of first-, second- and higher-order derivatives of eigenvalues and eigenvectors associated with repeated eigenvalues is presented. Adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation. The algebraic equation which is developed can be used to compute derivatives of eigenvalues and eigenvectors simultaneously. Since the coefficient matrix in the proposed algebraic equation is non-singular, symmetric and based on N-space, it is numerically stable and very efficient compared to previous methods. To verify the efficiency of the proposed method, the finite element model of the cantilever beam and a mechanical system in the case of a non-proportionally damped system are considered.     

支持向量机在面部神经麻痹检测中的应用

通过提取标准人脸正面图像的鼻尖、眼角、鼻角、嘴角等特征点,构成11维特征向量,在介绍支持向量机(SVM)基本原理和实现算法的基础上,通过SVM对大样本的11维特征向量进行学习,将面部神经麻痹的图像从正常人脸图像中分离出来,为医生诊断提供依据。试验证明,该方法对检测面部神经麻痹的准确率是令人满意的。     

Explicit form for impedance of cauer networks

In this paper a new procedure is established to obtain in closed form the poles and zeros of the impedance function of a first Cauer Network. The technique involves the continued fraction representation of the corresponding Laplace transform as a rational function whose numerators and denominators can be represented by tridiagonal determinants.     

Majorisations for the eigenvectors of graph-adjacency matrices

We develop majorisation results that characterise changes in eigenvector components of a graph's adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterise changes in dominant eigenvector components for single- and multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of the dominant eigenvector. For more limited graph classes (specifically, undirected, and reversibly-structured ones), majorisations for components of the subdominant and other eigenvectors upon graph modifications are also obtained.     

一种基于特征向量的高效虚拟现实辐射度算法

辐射度技术对于具有真实感的图像的合成十分重要。提出了一种基于特征向量的虚拟现实环境中辐射度计算的新方法。该方法采用了并行计算方法计算形状因子矩阵的特征值和特征向量,进而实现对虚拟现实环境中的辐射度进行高效的计算。其性能总体评价结果显示该方法显著降低了复杂环境中集群计算机系统的有效计算时间,提高了计算效率和加速比。其成果可广泛应用在图像处理、人机交互、可视化、虚拟现实等领域。     

Multispectral image compression using eigenregion-based segmentation

In the study, a novel segmentation technique is proposed for multispectral satellite image compression. A segmentation decision rule composed of the principal eigenvectors of the image correlation matrix is derived to determine the similarity of image characteristics of two image blocks. Based on the decision rule, we develop an eigenregion-based segmentation technique. The proposed segmentation technique can divide the original image into some proper eigenregions according to their local terrain characteristics. To achieve better compression efficiency, each eigenregion image is then compressed by an efficient compression algorithm eigenregion-based eigensubspace transform (ER-EST). The ER-EST contains 1D eigensubspace transform (EST) and 2D-DCT to decorrelate the data in spectral and spatial domains. Before performing EST, the dimension of transformation matrix of EST is estimated by an information criterion. In this way, the eigenregion image may be approximated by a lower-dimensional components in the eigensubspace. Simulation tests performed on SPOT and Landsat TM images have demonstrated that the proposed compression scheme is suitable for multispectral satellite image.