度量的变换

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。

The contourlet transform used in the system was constructed by dual tree complex wavelet transform followed by critically subsampled directional filter banks, sub-bands energy and standard deviations were cascaded to form feature vectors, and the similarity metric was Canberra distance. The performance of retrieval system was compared including original contourlet transform, non-subsampled contourlet transform, semi-subsampled contourlet transform and CCT under the same system structure.

该系统采用的复数轮廓波变换由双树复小波变换级联临界下采样方向滤波器构成，特征向量采用子带系数的能量和标准偏差连接而成，以Canberra距离为相似度度量标准；比较了基于同样架构的基本轮廓波变换、无下采样轮廓波变换、半下采样轮廓波变换和CCT纹理检索系统的性能。

The contourlet transform used in the system was constructed by dual tree complex wavelet transform followed by critically subsampled directional filter banks, sub-bands energy and standard deviations were cascaded to form feature vectors, and the similarity metric was Canberra distance.

该系统采用的复数轮廓波变换由双树复小波变换级联临界下采样方向滤波器构成，特征向量采用子带系数的能量和标准偏差连接而成，以Canberra 距离为相似度度量标准；比较了基于同样架构的基本轮廓波变换、无下采样轮廓波变换、半下采样轮廓波变换和CCT 纹理检索系统的性能。

It solves the problem that the unitary contour presentation can not correctly extract face contour in a face image which suffers from scale, rotation etc. The definition of the internal and external energy function is provided. At the same time, the global matching algorithm and local matching algorithm is given. The experiment shows that this presentation and the accompanying matching algorithm can be used to extract the face contour very well. So the image segmentation can be implemented by using it.②By analyzing the recognition principle of PCA method, we can conclude that the face images coming from different surrounding consist of different face image space. This is the essential reason that makes the generality of PCA method worse. Also, we give a measurement means to measure the distance from different face image space, so we can analyze face image space more conveniently.③We also construct various scale models and rotation pose models to detect the scale and rotating angle of face image to be recognized. The experiment results show that the detecting precision is very high. So it is good for face image feature extraction and face image representation.④Similarly, we construct local feature models of face image and utilize them to detect the local feature of face image. At the same time, we put forward a novel face image local feature detection algorithm, locating step by step. The experiment results show that this method can accurately detect the location of local face feature in a image.⑤A novel face image presentation model, dual attribute graph , is put forward. Firstly, it utilizes attribute graph to present the face image, then exact the local principal component coefficient and Gabor transform coefficient of thc pixels which corresponds to the nodes of the graph as the attribute of the nodes. This representation fully makes use of the statistical characteristic of the local face feature and utilizes Gabor transform to present the topographical structure of face image. So DAG has more general property.⑥Based on the DAG presentation, we give a DAG matching function and matching algorithm. During the design of the function and algorithm, the noise factor, e. g., lighting, scale and rotation pose are considered and tried to be eliminated. So the algorithm can give more general property.⑦A general face image recognition system is implemented. The experiment show the system can get better recognition performance under the noise surrounding of lighting, scale and rotation pose.

本文在上述研究的基础上，取得了如下主要研究成果：①构造了一个通用的人脸轮廓模型表示，解决了由于人脸图象尺度、旋转等因素而使得仅用单一轮廓表示无法正确提取人脸轮廓的问题，并给出了模型内、外能函数的定义，同时给出了模型的全局与局部匹配算法，实验表明，使用这种表示形式以及匹配算法，能够较好地提取人脸图象的轮廓，可实际用于人脸图象的分割；②深入分析了PCA方法的识别机制，得出不同成象条件下的人脸图象构成不同的人脸图象空间的结论，同时指出这也是造成PCA方法通用性较差的本质原因，并给出了不同人脸空间距离的一种度量方法，使用该度量方法能够直观地对人脸图象空间进行分析；③构造了各种尺度模板、旋转姿势模板以用于探测待识人脸图象的尺度、旋转角度，实验结果表明，探测精确度很高，从而有利于人脸图象特征提取，以及图象的有效表示；④构造了人脸图象的各局部特征模板，用于人脸图象局部特征的探测；同时提出了一种新的人脸图象局部特征探测法---逐步求精定位法，实验结果表明，使用这种方法能够精确地得到人脸图象各局部特征的位置；⑤提出了一种新的人脸图象表示法---双属性图表示法；利用属性图来表示人脸图象，并提取图节点对应图象位置的局部主成分特征系数以及Gabor变换系数作为图节点的属性，这种表示方法充分利用了人脸图象的局部特征的统计特性，并且使用Gabor变换来反映人脸图象的拓扑结构，从而使得双属性图表示法具有较强的通用性；⑥在双属性图表示的基础上，给出双属性图匹配函数及匹配算法，在函数及算法设计过程中，考虑并解决了光照、尺度、旋转姿势变化等因素对人脸图象识别的影响，使得匹配算法具有较强的通用性；⑦设计并实现了一个通用的人脸图象识别系统，实验结果表明，该系统在图象光照、尺度、旋转姿势情况下，得到了较好的识别效果。

Finally, based on the Choquet integral of distortion probability, the characterization of dynamic coherent measures is discussed. It provides theoretical evidence for the methods of different transaction dates risk measurement in empirical application. It i...

最后 ，对一般概率通过函数变换，应用 Choquet积分思想，对动态一致性风险度量的特征进行了探讨，指出它在实际应用中为多期风险度量方法提供的理论依据，对长期组合投资具有重要的现实指导意义。

Fuzzy distance of the theory of fuzzy sets an important component of the fuzzy set theory from the early stage of development, Fuzzy Sets distance has been attracting a large number of the concerns that people use real theory of practice with a non-negative real numbers to measure the distance of fuzzy sets, is through the appropriate transform its alluding to the real axis.

模糊距离是模糊集理论的一个重要组成部分，从模糊集理论发展之初，模糊集的距离一直吸引着众多的关注，人们沿用实数理论中的作法，用一个非负实数来度量模糊集的距离，也就是通过适当的变换将其影射到实数轴上。

There are three main methods in face localization: localization according to face outline, localization according to complexion and localization according to templates constructed by some standard sample images. As to feature extraction, it can be divided into two parts because face features can be divided into geometrical features and algebraic features. While extracting geometrical features, the features of eyes, nose, mouth, eyebrows can be gained by some image processes: binary, sharpen, smooth, projection, calculating gradient and so on. In order to extract algebraic features, we can do some mathematical transformation for the digital images such as singular value decomposition, K-L transformation.

在人脸检测部分，目前存在的方法有利用人脸的几何轮廓进行检测、利用人脸的肤色信息进行检测、构造标准人脸模板进行匹配检测等等；在人脸特征提取部分，可以用一些图像处理的方法如投影、二值化、求梯度图像等提取人脸中各特征器官如眼睛、鼻子、嘴巴等的几何特征，另外也可以借助于数学变换，求取人脸图像的一些代数特征，如对图像进行奇异值分解，以奇异值代表图象的特征，或对图像进行K-L变换，以图像在构造的特征空间上的投影系数作为图像的特征等；在识别部分，可以通过距离度量或相似度来判断输入图像与样本图像的匹配程度，还可以通过神经网络方法进行人脸的识别。

The basic theories of mathematical morphology for binary image are stated, and the most simple structure elements of morphologic transformation for binary images are proposed and proved. The geodetic morphologic transformation models are also developed. For the purpose of improving the speed of transformation in computer, the"set symmetric difference"is introduced to adapt each model. Some new morphologic filtering models and quantitative evaluating model of filtering effects in image processing are proposed, under the applied condition. The morphologic thinning methods are studied, and two new morphologic thinning models are developed. On the basis of analyzing the characteristics of mining maps, the image vectorizing tactics and a series of algorithms are proposed, including dynamic adaptive image thresholding using two thresholds, graphic and text separation, noise removal, and multi elements extracting models with mathematical morphology. Accuracy preserving compressed vectorizing model for image vectorization is put forward to generate vector data in multi layer.

论文对二值图象形态学的基础理论进行了较系统的阐述，提出并证明了二值图象处理中形态变换的最简单结构元素，并发展了测地形态变换模型；为了提高形态变换的计算机实现速度，引入了集合论中"对称差"的概念对各形态变换模型进行了改化；针对数学形态学在图象处理中的实际应用，提出了新的形态滤波模型及滤波效果的度量评价模型；研究了形态细化方法，提出了快速形态细化和保形快速形态细化算法；在研究矿图基本特征基础上，提出了人机协同矿图扫描图象矢量化处理策略及一系列扫描图象处理算法模型，包括双阈值动态自适应图象二值化、图文分离、噪声去除、图面多种要素提取形态变换模型等；在图象栅格—矢量转换中，提出了保精度压缩矢量化模型，以生成分层要素矢量数据。

Firstly, the definition of image representation, measure of sparsity, and the basic methods of sparse representation are reviewed. And then, we analyze the performance of nonlinear approximation of Ridgelet, Curvelet, Contourlet and Bandelet transform.

论文阐述了信号表示的定义、稀疏性度量以及图像稀疏表示的基本理论方法，分析与比较了脊波变换、曲线波变换、Contourlet变换、Bandelet变换各自的非线性逼近性能。

Which takes the local block variance as the importance measure of the block, and scalar quantizes the important block while vector quantizes the less important block, implelements the Hi-Fi compression of images.

以小波变换高频子图的局部区域方差作为纹理复杂度和区域重要性度量，对重要区域进行标量量化，对不重要区域进行矢量量化，实现了图象的高保真压缩。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。