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闭形解
相关语句
  closed form solution
     The algorithms can be classified into two categories: a closed form solution and an iterative least squares fitting.
     目前算法可以分成两类:即闭形解和最小二乘迭代拟合。
     So this paper concentrates on the closed form solution for camera calibration.
     因此,本文研究了相机定标的闭形解
  “闭形解”译为未确定词的双语例句
     In three classical backgrounds, it analyses one of them, OS R CA for two sensor network, and derives the closed form solutions of detection and false alarm performance, and compares its performance with the COS and S+OS distributed CFAR detections.
     在三种典型背景环境中和两个局部处理器的条件下,分析了其中一种方案:OS-R-CA,推导出了它的检测和虚警性能的闭形解,并将其与COS,S+OS等分布式CFAR检测进行了性能比较。
短句来源
     Referring to the closed solution formula used to calculate vertical Velocity gradient β(M) from surface seismic data in J. F. Claerbout equa- tion inversion algorithm,we can directly derive a simple algorithm from β(M) integral equation by means of Fourier transform and interpolation.
     参照克雷尔伯特方程反演算法中由地表观测记录计算地下介质速度关于深度变化率β(M)的闭形解公式,直接由β(M)的积分方程利用傅里叶变换和插值法,导出一种便于应用的算法。
短句来源
  相似匹配句对
     So this paper concentrates on the closed form solution for camera calibration.
     因此,本文研究了相机定标的
     Embedding Method for Studying Mixed Plate
     嵌入法
短句来源
     Solving Complicated Form Plate with EmbeddingMethod
     嵌入法
短句来源
     A Closed Form Solution for Direct Identification Of System Parameter
     直接识别系统参数的
短句来源
     Some Research on the Problem of Closed Solution of Abel Equation
     Abel方程问题的一些研究
短句来源
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  closed form solution
It is well known that this model is a nonlinear problem, and it has no closed form solution.
      
A closed form solution for the backscattered electric field strength in the far zone is derived in the frequency domain for the case of a normally-incident plane wave having the time variation of a generalized Gaussian pulse (GGP).
      
We show that in an appropriate formal system there is a closed form solution to the problem of determining precisely what sentencesP can be used.
      
A closed form solution for the integral formulation of the attractive potential between like-particles is first obtained based on certain assumptions made in this work.
      
A closed form solution to the second order clasticity problem, when an isotropic compressible elastic half-space undergoes a deformation owing to a non-uniformly distributed normal load, is presented.
      
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Referring to the closed solution formula used to calculate vertical Velocity gradient β(M) from surface seismic data in J.F.Claerbout equa- tion inversion algorithm,we can directly derive a simple algorithm from β(M) integral equation by means of Fourier transform and interpolation. Because the β(M)is a δ function on reflectors,the reflector can be po- sitioned from the output of β(M).The velocity inversion of several theo- retical sections synthesized by Kirchhoff integral formulas shows that the velocity inversion...

Referring to the closed solution formula used to calculate vertical Velocity gradient β(M) from surface seismic data in J.F.Claerbout equa- tion inversion algorithm,we can directly derive a simple algorithm from β(M) integral equation by means of Fourier transform and interpolation. Because the β(M)is a δ function on reflectors,the reflector can be po- sitioned from the output of β(M).The velocity inversion of several theo- retical sections synthesized by Kirchhoff integral formulas shows that the velocity inversion method also can make seismic migration both good and fast.

参照克雷尔伯特方程反演算法中由地表观测记录计算地下介质速度关于深度变化率β(M)的闭形解公式,直接由β(M)的积分方程利用傅里叶变换和插值法,导出一种便于应用的算法。由于β(M)在反射界面上呈δ函数形状,从而可以通过β(M)的输出来确定反射面的位置。在二维情况下,通过若干个由克希霍夫积分公式合成的理论剖面进行速度反演的试算,结果表明速度反演法亦能较好地实现反射界面的偏移归位,而且具有计算速度快的优点。

A new type of distributed constant false alarm rate (CFAR) scheme based on the ratio of signal to noise (SNR) of local observations (referred as R type scheme) is presented, to improve the performance of distributed CFAR detection based on binary local decision. Its characteristics are that CFAR algorithms are used in local processor to form the estimation of SNR of local observations, and then the estimation is transmitted to the data fusion center (DFC). Compared with the S+OS, the R type scheme not only...

A new type of distributed constant false alarm rate (CFAR) scheme based on the ratio of signal to noise (SNR) of local observations (referred as R type scheme) is presented, to improve the performance of distributed CFAR detection based on binary local decision. Its characteristics are that CFAR algorithms are used in local processor to form the estimation of SNR of local observations, and then the estimation is transmitted to the data fusion center (DFC). Compared with the S+OS, the R type scheme not only saves a half of the amount of data transmitted between local processor (LP) and DFC, but also overcomes the drawback of S+OS, which is not suitable to the practical use. In three classical backgrounds, it analyses one of them, OS R CA for two sensor network, and derives the closed form solutions of detection and false alarm performance, and compares its performance with the COS and S+OS distributed CFAR detections. Result shows that the detection and false alarm performance of OS R CA remains at the level similar to that of S+OS.

为了提高基于二元局部判决的分布式CFAR检测的性能,提出一类新的基于局部观测信噪比的分布式CFAR检测方案(称为R类方案)。其特点是以CFAR算法做局部处理以形成局部观测的信噪比估值,然后将其传送给数据融合中心。相对于S+OS,R类方案不仅使局部处理器和数据融合中心间的通信量减少了一半,而且对局部观测的要求也比S+OS宽松。在三种典型背景环境中和两个局部处理器的条件下,分析了其中一种方案:OS-R-CA,推导出了它的检测和虚警性能的闭形解,并将其与COS,S+OS等分布式CFAR检测进行了性能比较。结果表明,OS-R-CA的检测性能和虚警控制能力保持在了与S+OS接近的水平。

>=Camera extrinsic parameters calibration or camera pose estimation can find a variety of applications such as motion analysis, three-dimensional object reconstruction and texture mapping. It is a hot research topic in computer vision as well as virtual reality in recent decades. The algorithms can be classified into two categories: a closed form solution and an iterative least squares fitting. The former approach is generally faster, simpler and more accurate and requires less point-targets. And for the latter,...

>=Camera extrinsic parameters calibration or camera pose estimation can find a variety of applications such as motion analysis, three-dimensional object reconstruction and texture mapping. It is a hot research topic in computer vision as well as virtual reality in recent decades. The algorithms can be classified into two categories: a closed form solution and an iterative least squares fitting. The former approach is generally faster, simpler and more accurate and requires less point-targets. And for the latter, initial value should be sufficiently close to the result to avoid the nasty local minimum and save the precious computation time. So this paper concentrates on the closed form solution for camera calibration. Camera extrinsic parameters can be expressed in the form of extrinsic parameters (RT) matrix E, which can be decomposed into six independent parameters: three rotation angles and a translation vector of three components. For pinhole model, for each point target, two equations can be found from the relationship between image coordinate system (ICS) and world coordinate system (WCS). Thus it requires a minimum of three point-targets to solve the six independent parameters, from which camera extrinsic parameters matrix can be computed. The solution is not necessarily unique because none of the six equations is linear and the number is two or four (upper bound). Since the six equations are extremely complex, simple elimination will not work. This puzzle, however, can be solved in three steps. First, the counterparts of the points on image in camera coordinate system (CCS) are found by utilizing two properties, namely collinearity and Euclidean distance invariability. Collinearity is ensured by pinhole model and it means that object point, optical center and image point are collinear and confines the counterparts on certain lines. Euclidean distance between any two points will not changed by translation and rotation and the transformation between CCS and WCS is sheer translation and rotation. Owing to this invariability, the distances among the three points in CCS are exactly and hence can be computed by those in WCS. These distances will further restrict the counterparts only on some locations on the lines and by now the counterparts in CCS have been computed. Then, E, equivalent to the transformation matrix from WCS to CCS, is computed by transforming them to a common reference coordinate system (RCS). Suppose the three input points in WCS or CCS are p1, p2 and p3, and the chosen common RCS should satisfy the following three requirements: the transformed p1 is on the origin; the transformed p2 is on the positive x-axis and the transformed p3 lies on the first quadrant of xoy plane. The chosen RCS can be shared by both WCS and CCS because it is unique. The transformation from WCS or CCS to common RCS can be done from the way how the common RCS is chosen. Finally the six extrinsic parameters are solved by decomposing E. This step

相机外参定标在运动分析、三维物体重建、纹理映射等领域有着广泛的应用,这是最近几十年来计算机视觉和虚拟现实的一个研究热点。目前算法可以分成两类:即闭形解和最小二乘迭代拟合。前者通常快而简单,精度更高,所需的对应点也更少。后者需要初值足够接近结果,以避免陷入讨厌的局部极小点并节约宝贵的计算时间。因此,本文研究了相机定标的闭形解。相机外参可以用外参矩阵(或者RT矩阵)E表示,它又可以分解成6个独立的参数,3个旋转角和包含3个分量的平移向量。如果相机遵守针孔模型,那么每个对应点可以利用图像坐标系(ICS)和世界坐标系(WCS)之间的变换关系列出2个方程。因此,为了解出这6个独立参数(外参矩阵可以由这些参数求得),至少需要3组对应点。因为这6个方程都不是线性方程,所以解是不唯一的,通常是2组或4(上界)组。由于这些方程非常复杂,简单的消元无法奏效。但这一难题还是可以通过以下三步来求解。首先,利用共线性和欧氏距离不变性这两个特性可以求得图像中的点在相机坐标系(CCS)中的坐标。共线性是指物点、光心和像点三点共线。只要遵守针孔模型,就可以保证这点。它将CCS中的对应点限制在某些直线上。欧氏距离不变性...

相机外参定标在运动分析、三维物体重建、纹理映射等领域有着广泛的应用,这是最近几十年来计算机视觉和虚拟现实的一个研究热点。目前算法可以分成两类:即闭形解和最小二乘迭代拟合。前者通常快而简单,精度更高,所需的对应点也更少。后者需要初值足够接近结果,以避免陷入讨厌的局部极小点并节约宝贵的计算时间。因此,本文研究了相机定标的闭形解。相机外参可以用外参矩阵(或者RT矩阵)E表示,它又可以分解成6个独立的参数,3个旋转角和包含3个分量的平移向量。如果相机遵守针孔模型,那么每个对应点可以利用图像坐标系(ICS)和世界坐标系(WCS)之间的变换关系列出2个方程。因此,为了解出这6个独立参数(外参矩阵可以由这些参数求得),至少需要3组对应点。因为这6个方程都不是线性方程,所以解是不唯一的,通常是2组或4(上界)组。由于这些方程非常复杂,简单的消元无法奏效。但这一难题还是可以通过以下三步来求解。首先,利用共线性和欧氏距离不变性这两个特性可以求得图像中的点在相机坐标系(CCS)中的坐标。共线性是指物点、光心和像点三点共线。只要遵守针孔模型,就可以保证这点。它将CCS中的对应点限制在某些直线上。欧氏距离不变性指的是平移和旋转不会改变两点间的欧氏距离,而CCS和WCS之间的变换只是平移和旋转,根据这种不变性,三点之间在CCS中的距离就是在WCS中的距离,而WCS中的距离可以直接计算。三个点之间的距离能够进一步限制CCS中的对应点出现的位置,只能在某些直线上的某些位置上。这样实际上就已经解出了点在CCS中的坐标。然后,求解E。E就是从WCS到CCS的变换矩阵,求解该矩阵可以通过把它们变换到一个公共的参考坐标系(RCS)求解。假设3个输入点在WCS或者CCS中为p1、p2和p3,那么选择的公共的RCS必须满足三个条件:变换后的p1在原点;变换后的p2在x正半轴上;变换后的p3在xoy平面的第一象限。可以证明,该公共的RCS是唯一的,因此可以由WCS和CCS共享,作为连接两者的桥梁。从WCS或者CCS到公共的RCS的变换方法可以从RCS必须满足的三个条件得到,即每次子变换都再满足一个条件,直到最后所有条件都满足。最后,通过分解E求解出6个外参。这步是必须的,因为在第一步中方程两边平方,可能会引入增根。如果分解失败,则E就是增根,必须舍去。平移向量T可以直接从E的第四列读出,从第一行到第三行依次是tx、ty和tz。三个旋转角也可以通过一系列的运算求出。文中提出的算法已经用VC++程序实现,因为算法不需要迭代,理论上,程序应该快而准确,这已被实验所证明。用PIV2.8GHz的CPU,发行版的运算时间不超过20微秒,重投影绝对误差小于百万分之一。该算法至少可以有两种用途,可以用于只能给出三组对应点的场合,如果给出的对应点更多,也可以用于最小二乘迭代拟合时的初值估算。特别地,应用于纹理映射中,对于三角形的物体,通过指定三组顶点在三维模型和照片中的对应关系,能够进行高精度的映射。

 
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