旋转向量

SIFT（Scale Invariant Feature Transform） local feature is chosen because of its scale invariance and the property of accurate key-point localization.The Euclidean distance between different SIFT feature vectors is defined as the measure of similarity to get the pre-matched key-point pairs.The affine transform model is used to realize the registration.In order to get the accurate affine transform parameter,the principal of affine transform error is used to get rid of mismatched key-point pairs from the pre-matched pairs.

该方法选取具有良好尺度、旋转不变性以及精确特征点定位能力的SIFT局部特征，使用其特征向量间的欧氏距离作为相似性度量进行特征点匹配，并依据仿射变换误差准则去除奇异匹配特征点对，采用仿射变换的几何模型，实现了遥感图像的快速自动配准。

In this dissertation, an investigation on the theoretical basis of support vector machine and its application in the fault diagnosis is carried out.

研究发现，统计学习理论中确认的支持向量机可以自动地确定径向基核函数参数这一规律，在旋转机械故障诊断领域中某些条件下并不适用。

In order to model complex hair styles, such as curly hairs and wavy hairs, we first construct five types of surfaces and three curves: curved cylinder, curved circular frustum, curved prism, curved edged frustum, curved revolving paraboloid, and curved cylinder helix, curved circular frustum helix and curved revolving paraboloid helix. Then we give the expressions for points and normal vectors on these surfaces, suitable to composition.

为了构造复杂发型，例如卷发发型和波浪发型，我们首先构造了五种曲面和三种曲线：弯曲圆柱面、弯曲圆台面、弯曲棱柱面、弯曲棱台面和弯曲旋转抛物面，以及弯曲圆柱螺线、弯曲圆台螺线和弯曲旋转抛物螺线，并且给出了这些曲线曲面上适合于拼接的点和向量的表示方式。

In this paper, we discuss the existence problem of rotation surfaces of given Gauss curvature function in H_1~3(-1) and give the position vector field of the surfaces.

中文摘要：本文讨论了三维反de sitter空间H_1~3(-1)中给定Gauss曲率函数的旋转曲面M的存在性问题并给出了这类旋转曲面的位置向量场。

In section three, we mainly discuss the existence problemof rotation surfaces of given Gauss curvature function in H_1~3(-1) and give theposition vector field of the surfaces and obtain theorem one and theorem two.

第三节主要讨论了H_1~3(-1)中给定Gauss曲率函数的旋转曲面M的存在性问题并给出了这类旋转曲面的位置向量场，得到了定理1和定理2。

Based on the methods of Lie group theory, we redefine the general workspace of the symmetry coordination methods.

特别是定义出能够连续描述刚体在空间旋转的姿态向量，避免了欧拉角描述方法所带来的旋转次序问题。

To solve the problem encountered in finding a proper rotation matrix and translation vector, approximate and precise solutions are provided successively. The approximate one has the advantage of utilizing existing solution, with limited range of weight to choose from. The precise one has no limit to weight, and can also prevent the problem of obtaining a mirror matrix of the correct one. Besides, it permits the'hat'to be amplified to fit the size of'head'.

其中近似解可以直接套用现成的公式计算，但是权重的选择余地不大，而精确解则无此限制，而且从理论上解决了不同权重下求解旋转矩阵和平移向量时，可能出现错误的旋转矩阵的问题，并允许在配准时对"帽"进行缩放以适应"头"和"帽"的大小不匹配的问题。

A concept named"Characteristic rotating vector"of images is brought forward in this dissertation, the rotation of target in the image is only represented by change in sequence of elements in the vector, thus disturbance brought by irregular edge of target and random noise is avoided.

提出了图像的特征旋转矢量的概念，当图像中的目标有旋转时，仅表现为向量元素次序的变化，避免了不规则的目标边缘及随机噪声带来的干扰。

The singular values of the project can be used as the character vector. The singular values of the scaling invariant can be obtained by the statistical characteristics of Radon transform. Since the singular values of the matrix are uncorrelated with the position of the column or the row of the matrix. In this way, the character vector of singular values with shift, scaling and rotational invariant is arrived at by this algorithm.

针对各颜色分量，利用Radon变换的奇异值的统计特性提取了具有尺度不变性的奇异值，由于矩阵的奇异值分解具有旋转不变性，因此该奇异值为平移、尺度和旋转不变的特征向量。

Firstly, kinetic energy and potential energy expressions are obtained by a series of derivation, considering the extrinsic momentum. In the symplectic system, control equations of longitude and transverse coupling vibrations of rotating elastic structures, or Hamilton canonical equations are described. So the solution of the problem is boiled down to the eigenvalues and eigensolutions in the symplectic space.

首先，从能量的观点出发，通过一系列的理论推导，给出旋转结构的动能和势能表达式，并考虑外动量的影响，从而得到在辛体系中描述旋转结构纵向和横向耦合振动的控制方程，即哈密顿正则方程，于是将问题归结为辛几何空间的本征值和本征向量问题。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。