This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is...This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.展开更多
针对机载全景视频流影响,提出了一种基于嵌入式的全景实时拼接方法。提取图像中的SURF(speeded up robust features)特征点,生成特征描述子。通过计算2个特征点之间的欧式距离来确定匹配度,经过仿射变换后,利用泊松变换实现图像间的融...针对机载全景视频流影响,提出了一种基于嵌入式的全景实时拼接方法。提取图像中的SURF(speeded up robust features)特征点,生成特征描述子。通过计算2个特征点之间的欧式距离来确定匹配度,经过仿射变换后,利用泊松变换实现图像间的融合平滑处理。将上述流程在目标设备上进行并发执行,根据每个流程自身的特点进行定制化优化,实现全景实时拼接。试验测试表明,本方法实现了拼接接缝处基本无缝的效果,拼接速度达到30 Hz,能够满足实时显示的要求。展开更多
The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However,even nowadays it is still a challenging task to devise a method that ...The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However,even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness,and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose.To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.展开更多
This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether me...This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether method and the Poisson method. Then the solution of the higher-order equation can be obtained by integrating the solution of the second-order equation.展开更多
In this paper, the integrals appeared in BEM model for Poisson equation are all implemented analytically. Wherein, the boundary and the domain are discretized by linear boundary elements and linear internal triangle c...In this paper, the integrals appeared in BEM model for Poisson equation are all implemented analytically. Wherein, the boundary and the domain are discretized by linear boundary elements and linear internal triangle cells respectively. The closed formulations for all integrals are presented so that the computer effort for numerical solution is reduced considerably with higher accuray. The numerical example shows that the results are more accurate in comparision with Gaussian integration in the same discrezition. The basic idea of this paper could be extended to BEM model for Helmholtz equation and/or the time-dependent second other differential equations.展开更多
We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which ext...We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which extends this classical result from Hilbert space setting to Banach space setting.展开更多
In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth funct...In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.
文摘针对机载全景视频流影响,提出了一种基于嵌入式的全景实时拼接方法。提取图像中的SURF(speeded up robust features)特征点,生成特征描述子。通过计算2个特征点之间的欧式距离来确定匹配度,经过仿射变换后,利用泊松变换实现图像间的融合平滑处理。将上述流程在目标设备上进行并发执行,根据每个流程自身的特点进行定制化优化,实现全景实时拼接。试验测试表明,本方法实现了拼接接缝处基本无缝的效果,拼接速度达到30 Hz,能够满足实时显示的要求。
文摘The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However,even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness,and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose.To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.
基金Project supported by the National Natural Science Foundation of China(Grant No10572021)Doctoral Programme Foundation of Institution of Higher Education of China(Grant No20040007022)
文摘This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether method and the Poisson method. Then the solution of the higher-order equation can be obtained by integrating the solution of the second-order equation.
文摘In this paper, the integrals appeared in BEM model for Poisson equation are all implemented analytically. Wherein, the boundary and the domain are discretized by linear boundary elements and linear internal triangle cells respectively. The closed formulations for all integrals are presented so that the computer effort for numerical solution is reduced considerably with higher accuray. The numerical example shows that the results are more accurate in comparision with Gaussian integration in the same discrezition. The basic idea of this paper could be extended to BEM model for Helmholtz equation and/or the time-dependent second other differential equations.
基金Supported by NNSFC(Grant Nos.11571147,11822106 and 11831014)NSF of Jiangsu Province(Grant No.BK20160004)the PAPD of Jiangsu Higher Education Institutions。
文摘We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which extends this classical result from Hilbert space setting to Banach space setting.
文摘In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.
