相似变换

This paper illustrates the process where projective transformation and affine transformation are employed to solve advanced geometrical problems.

引言变换是我们在几何解题中常用的方法之一。初等几何中的变换方法有对称变换、平移变换、旋转变换和相似变换，高等几何中的变换有射影变换、仿射变换等。

For general engineering problems, the analytical transformation rules are sufficiently accurate to design the similar cascade profile, but further improvement of the precision is limited by the one-dimensional assumption of the transformation, therefore an inverse blade design method—influence matrix method, based upon the surface vorticity model, is developed to improve the precision effectively.

进一步讨论了在具有相同表面压力系数分布的情形下，进口马赫数对附面层发展的影响，发现在一定条件下，只要表面压力系数的分布相似，则叶面附面层发展情况及无量纲气动力参数也将存在相同精度的相似，这一结论使我们在进行相似流场模拟的模型设计中，得以只进行无粘流场之间的相似变换，从而大大减少相似模型设计的工作量和复杂性。

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。

According to if there exists a one to one mapping between the two point sets to be matched, PPM can be divided into the case of complete matching and the case of incomplete matching. According to transformation type between the two point sets, PPM can be divided into the affine (including Euclidean and similarity) case and the projective case.

点模式匹配问题，根据待匹配的两个点模式是否存在一一对应的匹配关系，可分为完全匹配情形和不完全匹配情形；根据两个点模式之间满足的几何变换关系，可分为仿射变换（包括相似变换和欧氏变换）情形和射影变换情形。

Then choosing suitable transform matrix, and applying TST to it, the satisfactory approximation order of the multi-scaling vector was achieved.

选择适当的变换矩阵，对尺度向量进行双尺度相似变换，可以使其具有满意的逼近阶。

We proposed a general theory and method for objects recognition based on geometric features and studied its application under orthogonal transformation, similarity transformation and affine transformation.

提出了基于几何特征进行物体识别的一般理论和方法，分别研究了它在正交变换、相似变换和仿射变换下的应用。

This paper analyzed the shortcoming of this strategy and then proposed a new correction algorithm based on the viewpoint of projective geometry.

为此从射影几何的观点提出了新算法：利用车牌固有的先验信息，将车牌与车牌图像之间的透视变换矫正为仿射变换，再将仿射变换矫正为相似变换，将此相似变换看做是对原车牌进行旋转和全局缩放的结果，消除其中的旋转因素，就得到一个与车牌仅差一个缩放因子的标准车牌图像，以便于后续的字符处理。

An approach to image interpolation based on local fractal similarity transformation suitablefor complex images in natural scenes is described. Similarity transformation of rectangular image blocks are added and the extremem method in the function with two variables is used to obtain the optical similarity transformation.

提出了适用于复杂自然景物图像的基于局部分形自相似变换的图像插值方法，在常用的局部分形自相似变换基础上增加了矩形图像块的自相似变换，并采用二元函数的极值方法求最佳相似变换。

Fractal ; fractal similarity transformation ; image interpolationl optimal similarity transformation ; rectangular block transformation

分形；自相似分形变换；图像插值；最佳相似变换；矩形块变换

The TST was applied to multi-scaling vector to increase it's approximation order, and with PR condition, the dual of transformed multi-scaling vector was obtained. Then the special TST was taken for this dual, the dual of original multi-scaling vector with higher approximation order obtained, finally the multi-wavelet function with higher vanishing moment maybe constructed.

我们先对已知的尺度向量进行双尺度相似变换，以提高其逼近阶，再求出变换后的尺度向量的对偶，对这个对偶再进行特定的双尺度相似变换，就可得到原尺度向量的有高逼近阶的对偶，从而可能得到具有高阶消失矩的多小波函数。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失