奇异变换

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。

This paper combines with pipeline delivery of our countrys actual conditions and other methods of detection and location. To the leakage characteristic of the fault to the long-distance natural gas pipeline, a method is raised, which is on the basis of wavelet and negative-pressure-wave to detect the leakage and locate. Jobs in this paper are as follows:Multi-resolution decomposition and reconstruction of wavelet transform is utilized to filter the noises, which the leakage brings the noises of negative-pressure-wave. The research is worked in the wavelet and wavelet packet filter. The wavelet transform have a fast and accurate recognition capability to signal singularity. This paper chooses wavelet technology to catch the break point of pressure signal.

本文结合我国管道输送的实际情况和目前现有的各种泄漏检测与定位方法，针对天然气长输管线泄漏故障的特点，提出了基于小波分析和负压波相结合的方法检测泄漏并定位，其中主要进行了以下几个方面的工作：利用小波变换的多分辨率分解和重构技术，对采集到的管道发生泄漏时产生的负压波信号进行降噪处理，并对小波及小波包优化的降噪效果进行对比性研究；利用小波变换技术对信号奇异点的快速、准确的识别能力，捕捉负压波信号的突变点，从而判断是否有泄漏发生。

For the linear discrete stochastic descriptor systems with multisensor, using me smgu, ar value decomposition, it is transformed into two reduced order subsystems, and a new fusion method of constructing the original state fuser based on the transformed state fuser is presented.

对于带多传感器的广义线性离散随机系统，应用奇异值分解，将其变换为等价的两个降阶多传感器子系统，提出了基于变换后的状态融合器构造原始状态融合器的新的融合方法。

Though several leak detecting methods are available, they are not ideal inapplication scope, including responses speed and accuracy of leak localization. In thisdissertation, according to the conditions of pipeline transportation in our country,research is carried out on crude oil transported pipelines leak detection and locationtheory and the study on its supervisory system is given.

本文结合我国管道输送的实际情况，针对原油管道泄漏检测技术及其运行监测系统进行了深入的研究，主要进行了以下几个方面的工作：将小波变换技术引入到负压波特征拐点的捕捉，利用连续小波变换时间-尺度特性检测信号的奇异点，能够有效的检测出强噪声背景下的信号边沿，此外，还提出了负压波法泄漏检测中误报警消除的多种方法。

Based on scale SVD transform, a target feature extracting method is proposed to solve this difficult problem. The experimental result shows that this method has favorable stability to target matrix's SVD feature vectors, and high invariant property to displacement, rotation and scale.

为解决这一技术难题，文中提出了基于尺度奇异值变换的红外图像目标特征提取方法，实验表明该方法提取的目标矩阵的奇异值特征向量具有较好的稳定性，对图像的平移、旋转和比例变化具有良好的不变性，是一种实用的特征提取方法。

By using in a sequence the eigen-decomposition,a permutation,the inverse discrete Fourier transformand a truncation on the matrix,an exact and explicit parametrization formula for Loop subdivision surfaces is proposed.

利用控制网格拓扑结构的对称性，通过将奇异点周围1-环和2-环的控制顶点进行离散Fourier变换得到分块对角阵，将其进行特征分解及排序之后，再通过离散Fourier逆变换和截断等操作得到细分矩阵的高次幂的表达式，从而得到Loop 细分曲面新的精确参数化公式

The mixed boundary problem was reduced to a system of singular integral equations by means of Fourier transform.

利用Fourier积分变换技术将混合边值问题转化为一对奇异积分方程，通过数值求解奇异积分方程获得含裂纹功能梯度板条分别在剪切和法向载荷作用下的I型和Ⅱ型应力强度因子，并讨论了材料的非均匀性和裂纹相对尺寸对裂纹尖端应力强度因子的影响。

Last, this paper introduced some concepts of multiscale geometrical analysis and curvelet transform theory. Because curvelet can showed this feature more 'sparsely' in the function included singular curve or singular side in two dimension space or multi-dimension space. This paper provided a robust digital watermarking technology algorithm based on curvelet transform. watermarking information was embedded into coarse scale coefficients after curvelet transforming, choose right embedding strength. Testing proved it has good invisibility and robustness.

最后，介绍了多尺度几何分析和曲波变换理论的相关概念，鉴于曲波能对二维乃至高维空间中含奇异曲线或者曲面的函数进行更"稀疏"地表示这一特性，本章提出了一种基于Curvelet变换的鲁棒数字图像水印算法，该算法将水印信息嵌入到经曲波变换后的图像的粗尺度系数中，合理选择的嵌入强度，试验表明该算法具有较好的隐蔽性和鲁棒性。

The singular value decomposition of wavelet transformation module maximum value matrix is proposed.

提出了基于小波变换模极大值矩阵奇异值分解的方法，用该方法获得的奇异值特征矢量作为信号的特征可以压缩特征维数，而且更容易进行计算机自动识别，同时还具有时间平移不变性的突出优点。

A method based on linear singularity analysis of image is presented. The improved method, called Directional Beamlet Transform is better than traditional Beamlet transform about directional information of image and has the ability of representing linear-singularity of image. According to the analysis of linear singularity, edge detection is transferred to detecting singularity point in the coefficient matrix of DBT.

针对基于图像像素点分析的边缘提取方法存在无法同时满足高抑噪性、连续性、定位性等问题，本文提出了方向Beamle 变换方法，在定义图像线奇异性的理论基础上，利用DBT 对图像进行线奇异性分析，依据Beamlet 变换具有的线段提取能力，将图像边缘检测问题转化为方向Beamlet 变换系数矩阵中奇异点的检测问题，以降低噪声点对边缘检测结果的影响。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。