查询词典 affine transformation

In this paper,the area ratio of plane figure affine transformation in space is investigated,and the transformation equation of λ multiple of area is got , the area change of plane figure under affine transformation in space is studied, a important property of three axis ellipsoid is given and proved.

探讨了空间场的仿射变换下平面图形的面积比，推导出λ倍积变换方程式，进而探讨了空间场的仿射变换下平面图形面积的变化规律，给出并证明了三轴椭球体的一个重要性质。

They include:collinearity--an invariance under the projective transformation group;Parallelisminvariance under the affine transformation group;the direction of angles--aninvariance under the rotation transformation group.

这些几何不变性质包括共线性——在射影变换群下的不变性；平行性——在仿射变换群下的不变性；角的方向——在欧氏平移变换群下的不变性。

Thismethod adopted affine transformation model and a Lie derivative-based analytical algorithm.We introduced the process and characters in extracting information of biological visionsystem, studied the feasibility of the generalized Gabor function used as receptive fieldfunction in extracting information and analyzed affine transformation group and Liederivatives. Finally, we deduced the mathematical denotation for Lie derivatives, i.e. theinfinitesimal generator of the geometric distortion in affine transformation.

对生物视觉信息提取的过程及特点进行了介绍，其中主要研究了广义Gabor函数作为感受野函数提取初级视觉信息的可行性；对仿射变换作为外界图像信息在视觉成像系统上的投影模型的原理进行了初步讨论；对Lie变换群微分算子用于提取仿射变换不变量的分析方法作了剖析，并推导了该方法中关键部分——仿射变换Lie微分算子的具体表达式，也就是几何变形无限小微分算子的计算表达式，使下一步编程实现该方法成为可能。

To be specific,its generalized characteristic polynomial has positive double roots,which we proved further has only a double,root by using the affine transformation and inverse affine transformation.

为了更好地进行干涉判断，根据椭圆-椭圆外切的代数条件——广义特征多项式具有正的重根，以及进一步证明出的该正重根的唯一性结论，利用仿射变换和逆变换方法，推导出了椭圆-椭圆的不适合边界解析方程。

To be specific, its generalized characteristic polynomial has positive double roots, which we proved further has only a double, root by using the affine transformation and inverse affine transformation, his easy to detect interference accurately between two ellipses using NFB analytic equation.

根据该解析方程不仅可以直接对任意两个椭圆之间的干涉性做出精确判断，并且可由此绘出NFB的轨迹图，同时使用可视化方法给出了快速粗略的判断。

The inverse polynomial and the invertible affine transformation exist by the finite field, linear algebra and matrix theory. The invertible affine transformation and the inversion in are easily realized by using lookup table. An algorithm can be used to get the inverse element of modulo .

本文运用有限域、线性代数和矩阵理论，论证了逆多项式和逆仿射的存在性，并且应用查表法简捷地实现了中元素的求逆和逆仿射变换；设计了一个易于在在计算机上实现的算法，来求形如的多项式模时的逆元，该多项式的系数在上。

The main contributions of the thesis are as follows: Using invariants and matrix theory, especially the special properties of eigenvalues and eigenvectors of the so called irreducible matrix, we put forward several effective new algorithms for the complete matching problem under Euclidean transformation, similarity transformation and general affine transformation.

论文的主要贡献如下：利用不变量和矩阵理论，特别是巧妙地利用了不可约矩阵的特征值和特征向量的特殊性质，提出了求解欧氏变换、相似变换和一般仿射变换下完全匹配情形的点模式匹配问题的几种非常有效的新算法。

First, the proposed scheme uses contourlet transform to extract multidirectional and multiscale texture information, and then obtains the feature points invariant to the affine transformation from the low and middle directional subbands by Harris-Affine detector. Second, the feature regions are adaptively computed by the feature scale of the local structure and normalized by U transform. The watermarking is embedded adaptively in those characteristic regions which are normalized. Finally, by vector quantization, several copies of the watermark are embedded into the no overlapped local feature regions in different directional subbands.

首先，用Contourlet变换提取出多尺度、多方向的纹理信息；再用Harris-Affine检测算子从变换域的中、低频方向子带中提取出仿射不变特征点，结合自适应局部结构的特征尺度确定特征区域，并用U变换对其归一化处理，水印就自适应地嵌入到归一化后的区域中；水印嵌入采纳矢量量化的策略，将水印信息重复嵌入到不同方向子带、多个不相交的局部仿射不变特征区域。

Firstly, affine covariant neighborhoods of visual words are used to verify the spatial consistency. Secondly, a set of affine transformation matrices between the corresponding covariant regions is calculated, and the matrix with the most inliers is chosen as the best matching affine transformation matrix. In this step, only a single pair of corresponding affine covariant regions is used to calculate the 6 degree of freedom affine transformation for acceleration. In the last step, the spatial consistency is verified by the BMATM.

首先通过视觉关键词仿射协变的空间邻近特征集进行初步空间关系一致性匹配；然后计算对应仿射协变区块的多组可能的仿射变换矩阵，并选择满足区块匹配最多的变换矩阵作为对象与图像之间最终仿射变换矩阵，其中，仅利用一对协变区块来计算自由度为6的仿射变换的算法有效地提高了计算速度和鲁棒性；最后通过计算出的仿射变换矩阵来精确验证对象与图像之间的空间位置关系是否一致。

This paper integrates linear affine transformation and nonlinear affine transforma-tion"s approach ability. Integrated affine transformation not only inherits the linear affine transformation"s low bit rate merit,but also inherits the nonlinear affine transformations approach ability.The method proposed in this paper is a new method, and never be proposed in other papers.

本硕士论文综合了线性仿射变换和非线性仿射变换的逼近能力，采用混合型的仿射变换既能发扬线性仿射变换的低比特率的优点，又能发扬非线性仿射变换的相似逼近能力，提高重建质量，本算法是一种新型的算法，文献中尚未提及。

Methods: Five patients with parkinsonism or dystonia were assigned to general anesthesia using an modified endotracheal tube.

本实验依照人体实验之相关规定进行，五位患有帕金森氏症或肌张力异常的病人接受神经立体定位手术。

If you can benefit from this book, it is our honour.

如果您能从本书获益，这将是我们的荣幸。