An intuitive method for circle fitting is proposed. Assuming an approximate circle(CA,n) for the fitting of some scattered points, it can be imagined that every point would apply a force to CA,n, which all together fo...An intuitive method for circle fitting is proposed. Assuming an approximate circle(CA,n) for the fitting of some scattered points, it can be imagined that every point would apply a force to CA,n, which all together form an overall effect that "draws" CA,n towards best fitting to the group of points. The basic element of the force is called circular attracting factor(CAF) which is defined as a real scalar in a radial direction of CA,n. An iterative algorithm based on this idea is proposed, and the convergence and accuracy are analyzed. The algorithm converges uniformly which is proved by the analysis of Lyapunov function, and the accuracy of the algorithm is in accord with that of geometric least squares of circle fitting. The algorithm is adopted to circle detection in grayscale images, in which the transferring to binary images is not required, and thus the algorithm is less sensitive to lightening and background noise. The main point for the adaption is the calculation of CAF which is extended in radial directions of CA,n for the whole image. All pixels would apply forces to CA,n, and the overall effect of forces would be equivalent to a force from the centroid of pixels to CA,n. The forces from would-be edge pixels would overweigh that from noisy pixels, so the following approximate circle would be of better fitting. To reduce the amount of calculation, pixels are only used in an annular area including the boundary of CA,n just in between for the calculation of CAF. Examples are given, showing the process of circle fitting of scattered points around a circle from an initial assuming circle, comparing the fitting results for scattered points from some related literature, applying the method proposed for circular edge detection in grayscale images with noise, and/or with only partial arc of a circle, and for circle detection in BGA inspection.展开更多
In this paper we give a parallel algorithm for obtaining the eigenvalues and eigenvectors of a matrix.The practical background of this algorithm is the numerical computation in conjunction with the symbolic computation.
Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direc...Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.展开更多
高能动力电池是供配电系统的核心储能模块,针对高能动力电池的应用构建了二阶等效电路模型。在等效电路模型的基础上,提出联合递推最小二乘(Recursive Least Squares,RLS)法和扩展卡尔曼滤波(Extended Kalman Filter,EKF)的荷电状态(Sta...高能动力电池是供配电系统的核心储能模块,针对高能动力电池的应用构建了二阶等效电路模型。在等效电路模型的基础上,提出联合递推最小二乘(Recursive Least Squares,RLS)法和扩展卡尔曼滤波(Extended Kalman Filter,EKF)的荷电状态(Stage of Charge,SOC)算法,并在其基础上改进为基于温度补偿的联合RLS法和EKF融合的SOC算法。基于MATLAB软件,设计改进前和改进后联合算法的仿真验证程序,并对结果进行了比较分析。仿真结果表明,基于温度补偿的联合算法可实现当SOC处于(0.25,1)的区域内,相对误差基本小于5%,验证了所提出的建模方法和求解方法的有效性。展开更多
基金Project(2013CB035504) supported by the National Basic Research Program of ChinaProject(2012zzts078) supported by the Fundamental Research Funds for the Central Universities of Central South University,ChinaProject(2009ZX02038) supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China
文摘An intuitive method for circle fitting is proposed. Assuming an approximate circle(CA,n) for the fitting of some scattered points, it can be imagined that every point would apply a force to CA,n, which all together form an overall effect that "draws" CA,n towards best fitting to the group of points. The basic element of the force is called circular attracting factor(CAF) which is defined as a real scalar in a radial direction of CA,n. An iterative algorithm based on this idea is proposed, and the convergence and accuracy are analyzed. The algorithm converges uniformly which is proved by the analysis of Lyapunov function, and the accuracy of the algorithm is in accord with that of geometric least squares of circle fitting. The algorithm is adopted to circle detection in grayscale images, in which the transferring to binary images is not required, and thus the algorithm is less sensitive to lightening and background noise. The main point for the adaption is the calculation of CAF which is extended in radial directions of CA,n for the whole image. All pixels would apply forces to CA,n, and the overall effect of forces would be equivalent to a force from the centroid of pixels to CA,n. The forces from would-be edge pixels would overweigh that from noisy pixels, so the following approximate circle would be of better fitting. To reduce the amount of calculation, pixels are only used in an annular area including the boundary of CA,n just in between for the calculation of CAF. Examples are given, showing the process of circle fitting of scattered points around a circle from an initial assuming circle, comparing the fitting results for scattered points from some related literature, applying the method proposed for circular edge detection in grayscale images with noise, and/or with only partial arc of a circle, and for circle detection in BGA inspection.
文摘In this paper we give a parallel algorithm for obtaining the eigenvalues and eigenvectors of a matrix.The practical background of this algorithm is the numerical computation in conjunction with the symbolic computation.
基金the National Natural Science Foundation of China(No.11901359)Shandong Provincial Natural Science Foundation(No.ZR2019QA017)。
文摘Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.
文摘高能动力电池是供配电系统的核心储能模块,针对高能动力电池的应用构建了二阶等效电路模型。在等效电路模型的基础上,提出联合递推最小二乘(Recursive Least Squares,RLS)法和扩展卡尔曼滤波(Extended Kalman Filter,EKF)的荷电状态(Stage of Charge,SOC)算法,并在其基础上改进为基于温度补偿的联合RLS法和EKF融合的SOC算法。基于MATLAB软件,设计改进前和改进后联合算法的仿真验证程序,并对结果进行了比较分析。仿真结果表明,基于温度补偿的联合算法可实现当SOC处于(0.25,1)的区域内,相对误差基本小于5%,验证了所提出的建模方法和求解方法的有效性。
