利用Voronoi协方差矩阵重建隐式曲面

目的 针对含少量离群点的噪声点云,提出了一种Voronoi协方差矩阵的曲面重建方法。方法 以隐函数梯度在Voronoi协方差矩阵形成的张量场内的投影最大化为目标,构建隐函数微分方程,采用离散外微分形式求解连续微分方程,从而将曲面重建问题转化为广义特征值求解问题。在点云空间离散化过程中,附加最短边约束条件,避免了局部空间过度剖分。并引入概率测度理论定义曲面窄带,提高了算法抵抗离群点能力,通过精细剖分曲面窄带,提高了曲面重建精度。结果 实验结果表明,该算法可以抵抗噪声点和离群点的影响,可以生成不同分辨率的曲面。通过调整拟合参数,可以区分曲面的不同部分。结论 提出了一种新的隐式曲面重建方法,无需点云法向、稳健性较强,生成的三角面纵横比好。     

基于参数优化的多层次单元划分曲面重建

为了提高现有MPU曲面重建的稳定性,提出了一种基于参数优化的MPU曲面重建算法。通过分析包围球半径的比例系数α和包围球内点云最小数目Nmin对曲面重建的影响,根据局部隐含数逼近的条件,对Nmin进行调整。同时,结合不同形态特征的点云模型对覆盖密度的要求,对α进行调整,使得α和Nmin达到一个最优组合,进而使得曲面重建算法更稳定。实验结果表明,该算法能快速准确的对不同点云模型进行参数选取,从而得到更理想的曲面重建效果。     

Toward a model-based Bayesian theory for estimating and recognizingparameterized 3-D objects using two or more images taken from differentpositions

A parametric modeling and statistical estimation approach is proposed and simulation data are shown for estimating 3-D object surfaces from images taken by calibrated cameras in two positions. The parameter estimation suggested is gradient descent, though other search strategies are also possible. Processing image data in blocks (windows) is central to the approach. After objects are modeled as patches of spheres, cylinders, planes and general quadrics-primitive objects, the estimation proceeds by searching in parameter space to simultaneously determine and use the appropriate pair of image regions, one from each image, and to use these for estimating a 3-D surface patch. The expression for the joint likelihood of the two images is derived and it is shown that the algorithm is a maximum-likelihood parameter estimator. A concept arising in the maximum likelihood estimation of 3-D surfaces is modeled and estimated. Cramer-Rao lower bounds are derived for the covariance matrices for the errors in estimating the a priori unknown object surface shape parameters     

Relational generative topographic mapping

The generative topographic mapping (GTM) has been proposed as a statistical model to represent high-dimensional data by a distribution induced by a sparse lattice of points in a low-dimensional latent space, such that visualization, compression, and data inspection become possible. The formulation in terms of a generative statistical model has the benefit that relevant parameters of the model can be determined automatically based on an expectation maximization scheme. Further, the model offers a large flexibility such as a direct out-of-sample extension and the possibility to obtain different degrees of granularity of the visualization without the need of additional training. Original GTM is restricted to Euclidean data points in a given Euclidean vector space. Often, data are not explicitly embedded in a Euclidean vector space, rather pairwise dissimilarities of data can be computed, i.e. the relations between data points are given rather than the data vectors themselves. We propose a method which extends the GTM to relational data and which allows us to achieve a sparse representation of data characterized by pairwise dissimilarities, in latent space. The method, relational GTM, is demonstrated on several benchmarks.     

Principal surfaces from unsupervised kernel regression

We propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the Nadaraya-Watson kernel regression estimator. As compared with previous approaches to principal curves and surfaces, the new method offers several advantages: First, it provides a practical solution to the model selection problem because all parameters can be estimated by leave-one-out cross-validation without additional computational cost. In addition, our approach allows for a convenient incorporation of nonlinear spectral methods for parameter initialization, beyond classical initializations based on linear PCA. Furthermore, it shows a simple way to fit principal surfaces in general feature spaces, beyond the usual data space setup. The experimental results illustrate these convenient features on simulated and real data.     

Two topographic maps for data visualisation

We review a new form of self-organizing map which is based on a nonlinear projection of latent points into data space, identical to that performed in the Generative Topographic Mapping (GTM) [Bishop et al. (1997) Neurl Comput 10(1): 215–234]. But whereas the GTM is an extension of a mixture of experts, our new model is an extension of a product of experts [Hinton (2000) Technical report GCNU TR 2000-004, Gatsby Computational Neuroscience Unit, University College, London]. We show visualisation results on some real data sets and compare with the GTM. We then introduce a second mapping based on harmonic averages and show that it too creates a topographic mapping of the data. We compare these mappings on real and artificial data sets. Responsible editor: Soumen Chakrabarti.     

基于参数化的三维颅面配准

针对颅面配准问题,提出通过对颅面进行参数化将其转换成二维参数域的对应问题。首先,根据人类的生理特征标定6个特征点,利用这些特征点将颅面转换到一个统一的坐标系以实现姿态和大小的统一;其次,以两个外眼角为约束对参考颅面进行最小二乘保角映射,计算出6个特征点的参数值;然后,以这六个生理特征点的参数值为约束,利用最小二乘保角映射将任一待配准模型映射到二维参数域;最后,根据二维参数域确定三维颅面上的对应点,从而实现三维数据配准。为了验证所提方法,以对应点为控制点,利用薄板样条(TPS)变换把参考颅面变形到目标颅面,以变形后两个模型上对应点之间的几何距离的平均为度量,将所提算法和基于主轴分析的迭代最近点(ICP)配准以及基于随机采样控制点的迭代TPS配准方法进行了比较,实验结果表明,所提算法的配准效果优于其他两种方法。     

Principal manifold learning by sparse grids

In this paper, we deal with the construction of lower-dimensional manifolds from high-dimensional data which is an important task in data mining, machine learning and statistics. Here, we consider principal manifolds as the minimum of a regularized, non-linear empirical quantization error functional. For the discretization we use a sparse grid method in latent parameter space. This approach avoids, to some extent, the curse of dimension of conventional grids like in the GTM approach. The arising non-linear problem is solved by a descent method which resembles the expectation maximization algorithm. We present our sparse grid principal manifold approach, discuss its properties and report on the results of numerical experiments for one-, two- and three-dimensional model problems.      

Remote sensing image fusion based on Bayesian linear estimation

A new remote sensing image fusion method based on statistical parameter estimation is proposed in this paper. More specially, Bayesian linear estimation (BLE) is applied to observation models between remote sensing images with different spa- tial and spectral resolutions. The proposed method only estimates the mean vector and covariance matrix of the high-resolution multispectral (MS) images, instead of assuming the joint distribution between the panchromatic (PAN) image and low-resolution multispectral image. Furthermore, the proposed method can enhance the spatial resolution of several principal components of MS images, while the traditional Principal Component Analysis (PCA) method is limited to enhance only the first principal component. Experimental results with real MS images and PAN image of Landsat ETM demonstrate that the proposed method performs better than traditional methods based on statistical parameter estimation, PCA-based method and wavelet-based method.     

基于网格的远程考试系统模型的设计与研究

分析了目前考试系统面临的主要问题,介绍了网格的概念及其特性,提出了基于网格的远程考试系统模型(GTM),讨论了GTM的设计思想、结构、功能及实现方法,阐述了GTM存在的问题及发展趋势。     

Generation of bi-monotone patches from quadrilateral mesh for reverse engineering

Thanks to recent improvements, computational methods can now be used to convert triangular meshes into quadrilateral meshes so that the quadrilateral elements capture well the principal curvature directional fields of surfaces and intrinsically have surface parametric values. In this study, a quadrilateral mesh generated using the mixed integer quadrangulation technique of Bommes et al. is used for input. We first segment a quadrilateral mesh into four-sided patches. The feature curves inside these patches are then detected and are constrained to act as the patch boundaries. Finally, the patch configuration is improved to generate large patches. The proposed method produces bi-monotone patches, which are appropriate for use in reverse engineering to capture the surface details of an object. A shape control parameter that can be adjusted by the user during the patch generation process is also provided to support the creation of patches with good bi-monotone shapes. This study mainly targets shape models of mechanical parts consisting of major smooth surfaces with feature curves between them.     

Determination of sunglint location and its characteristics on observation from a METEOSAT 9 satellite

On the basis of observations from a geostationary satellite, a method for the determination of sunlight location on the ocean surface, based on two parameters – (1) the Greenwich time and (2) the longitude of the satellite – was developed. The problem is solved in three stages: first, the position of the Earth in its orbit for any given point of time is determined; second, for this point of time, the relative position of Sun–Earth–satellite is defined; and, third, the latitude and longitude of the principal point of sunglint (PPS) was found. The outputs of the program based on this method are: (1) the geographical coordinates of PPS; (2) the boundary of a simultaneously illuminated and observed region of the Earth; (3) the contour of the sunglint (disk) on the smooth ocean surface; and (4) the distribution of the sunglint brightness on the rough (waved) ocean surface. This method is applied to detect sunglint characteristics in the images gathered from the METEOSAT 9 satellite.     

基于凹凸区域的断裂面匹配算法

针对破碎刚体复原给出一种断裂面匹配算法。根据平均曲率判断顶点的凹凸性,对凹凸顶点进行聚类将断裂面划分为多个凹凸特征区域;定义特征区域的协方差矩阵,根据其主成分和主方向定义特征区域的尺寸特征和各向异性特征,面积相近、类型相同和特征相近的区域为相似区域对,之后再根据距离主方向约束排除伪区域对;采用穷举法对每3对质心不共线的相似区域对,计算三维变换,将断裂面粗略对齐,再根据最近点迭代算法的收敛程度得到最优匹配,同时将两断裂面精细校准。实验结果表明,该算法能够实现较复杂断裂面的部分和完全匹配。     

Dimensionality reduction and topographic mapping of binary tensors

In this paper, a decomposition method for binary tensors, generalized multi-linear model for principal component analysis (GMLPCA) is proposed. To the best of our knowledge at present there is no other principled systematic framework for decomposition or topographic mapping of binary tensors. In the model formulation, we constrain the natural parameters of the Bernoulli distributions for each tensor element to lie in a sub-space spanned by a reduced set of basis (principal) tensors. We evaluate and compare the proposed GMLPCA technique with existing real-valued tensor decomposition methods in two scenarios: (1) in a series of controlled experiments involving synthetic data; (2) on a real-world biological dataset of DNA sub-sequences from different functional regions, with sequences represented by binary tensors. The experiments suggest that the GMLPCA model is better suited for modelling binary tensors than its real-valued counterparts. Furthermore, we extended our GMLPCA model to the semi-supervised setting by forcing the model to search for a natural parameter subspace that represents a user-specified compromise between the modelling quality and the degree of class separation.     

A fast regularity measure for surface defect detection

In this paper, we propose a fast regularity measure for defect detection in non-textured and homogeneously textured surfaces, with specific emphasis on ill-defined subtle defects. A small neighborhood window of proper size is first chosen and they slide over the entire inspection image in a pixel-by-pixel basis. The regularity measure for each image patch enclosed in the window is then derived from the eigenvalues of the covariance matrix formed by the variance–covariance of the x- and y-coordinates with the pixel gray levels as the weights for all pixel points in the window. The two eigenvalues of the weighted covariance matrix will be approximately the same when the image patch contains only a homogeneous region, whereas the two eigenvalues will be relatively different if the image patch in the window contains a defect. The smaller eigenvalue of the covariance matrix is then used as the regularity measure. The integral image technique is introduced to the computation of the regularity measure so that it is invariant to the neighborhood window size. The proposed method uses only one single discrimination feature for defect detection. It avoids the use of complicated classifiers in a high-dimensional feature space, and requires no learning process from a set of defective and defect-free training samples. Experimental results on a variety of material surfaces found in industry, including textured images of plastic surfaces and leather and non-textured images of backside solar wafers and LCD backlight panels, have shown the effectiveness of the proposed regularity measure for surface defect detection. It is computationally very fast, and takes only 0.032 s for a 400 × 400 image on a Pentium 3.00?GHz personal computer. In a test set of 73 backside solar wafer images involving 53 defect-free and 20 defective samples, the proposed regularity measure can correctly identify all the test images.     

Neural network methods for one-to-many multi-valued mapping problems

An investigation of the applicability of neural network-based methods in predicting the values of multiple parameters, given the value of a single parameter within a particular problem domain is presented. In this context, the input parameter may be an important source of variation that is related with a complex mapping function to the remaining sources of variation within a multivariate distribution. The definition of the relationship between the variables of a multivariate distribution and a single source of variation allows the estimation of the values of multiple variables given the value of the single variable, addressing in that way an ill-conditioned one-to-many mapping problem. As part of our investigation, two problem domains are considered: predicting the values of individual stock shares, given the value of the general index, and predicting the grades received by high school pupils, given the grade for a single course or the average grade. With our work, the performance of standard neural network-based methods and in particular multilayer perceptrons (MLPs), radial basis functions (RBFs), mixture density networks (MDNs) and a latent variable method, the general topographic mapping (GTM), is compared. According to the results, MLPs and RBFs outperform MDNs and the GTM for these one-to-many mapping problems.     

Theory of fractional covariance matrix and its applications in PCA and 2D-PCA

In this paper, according to the definition and applications of fractional moments, we give new definitions of the fractional variance and fractional covariance. Furthermore, we give the definition of fractional covariance matrix. Based on fractional covariance matrix, principal component analysis (PCA) and two-dimensional principal component analysis (2D-PCA), we propose two new techniques, called fractional principal component analysis (FPCA) and two-dimensional fractional principal component analysis (2D-FPCA), which extends PCA and 2D-PCA to fractional order form, and extends the transition recognition ranges of PCA and 2D-PCA. To evaluate the performances of FPCA and 2D-FPCA, a series of experiments are performed on two face image databases: ORL and Yale. Experiments show that two new techniques are superior to the standard PCA and 2D-PCA if choosing different order between 0 and 1.     

Estimation of evaporative fraction and evapotranspiration from MODIS products using a complementary based model

We present a new formulation to derive evaporative fraction (EF) and evapotranspiration (ET) maps from remotely sensed data without auxiliary relationships or site-specific relationships. This formulation is based on Granger's complementary relationship and Priestley-Taylor's equation. The proposed model eliminates the wind function and resistance parameters commonly applied to ET calculation by including a relative evaporation parameter (ET/Epot). By combining this relative evaporation parameter, Granger's complementary relationship and Priestley-Taylor equation, we obtain a simple equation to estimate ET. We tested and validated the proposed formulation over the Southern Great Plains (SGP) region of the United States for seven clear sky days during March-October 2003. MODIS Atmospheric and Land products were the only source of data used in this study. Estimates of ET show an overall root mean square error and bias of 33.89 and − 10.96 Wm^− 2, respectively. Our results suggest that the proposed approach is robust and valid for a wide range of atmospheric and surface conditions.     

插值细分曲面三角剖分研究

把三维参数化曲面的离散化算法应用到三角网格表示的离散曲面上。用一种可生成C1阶连续曲面的插值分割技术——改进蝶形算法,重新构造极限面。用推进波前法在物理空间直接离散化,所以不需要进行参数化。     

Development of moving window state and parameter estimators under maximum likelihood and Bayesian frameworks

Estimation of slowly varying model parameters/unmeasured disturbances is of paramount importance in process monitoring, fault diagnosis, model based advanced control and online optimization. The conventional approach to estimate drifting parameters is to artificially model them as a random walk process and estimate them simultaneously with the states. However, this may lead to a poorly conditioned problem, where the tuning of the random walk model becomes a non-trivial exercise. In this work, the moving window parameter estimator of Huang et al. [1] is recast as a moving window maximum likelihood (ML) estimator. The state can be estimated within the window using any recursive Bayesian estimator. It is assumed that, when the model parameters are perfectly known, the innovation sequence generated by the chosen Bayesian estimator is a Gaussian white noise process and is further used to construct a likelihood function that treats the model parameters as unknowns. This leads to a well conditioned problem where the only tuning parameter is the length of the moving window, which is much easier to select than selecting the covariance of the random walk model. The ML formulation is further modified to develop a maximum a posteriori (MAP) cost function by including arrival cost for the parameter. Efficacy of the proposed ML and MAP formulations has been demonstrated by conducting simulation studies and experimental evaluation. Analysis of the simulation and experimental results reveals that the proposed moving window ML and MAP estimators are capable of tracking the drifting parameters/unmeasured disturbances fairly accurately even when the measurements are available at multiple rates and with variable time delays.