尺度系数

Wavelet modulus maxima with high frequency and low frequency coefficients were obtained firstly through multiscale decomposition of well logging data;then important wavelet coefficients were chosen according to the fusion principle where high frequency coefficients were taken as maximal absolute values and low frequency coefficients were selected by edge detection principle;finally alternating projection algorithm was applied to reconstruct the fusion curve.

首先对原始测井曲线进行多尺度分解，得到不同尺度下的小波低频系数和高频模极大值；然后选用高频系数取绝对值极大、低频系数采用边缘法的融合规则，选取重要的小波系数；最后利用交替投影算法重构融合曲线。

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。

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 results of quantitative coding to wavelet transform coefficient show that low-scale extreme wavelet coefficients can accurately localize the subaerial position of fractures.The shifting of extreme wavelet coefficients can be used to judge relative magnitude of dip angle and dip direction of fracture with scale increasing.The value of extreme wavelet coefficients can reflect density difference of formations on both sides of fracture and provide information of physical properties for fracture analysis.

小波变换系数量化编码结果表明，低尺度小波系数极值可以准确定位断裂在地表的位置；随着尺度的增加，小波系数极值会发生偏移，可以判断断裂的倾向和倾角的相对大小；小波系数极值可以反映断裂两侧地层的密度差异，为断裂分析提供物性信息。

A new approach for pattern recognition of ultra-high frequency signals of transformer partial discharge based on multi-scale analysis of wavelet packet and grid dimensionality is proposed, in which the multi-scale transform of wavelet packet is used to extract wavelet coefficients of UHF PD signals and by means of improving difference box-counting method the grid dimensionality of multi-scale wavelet coefficients is calculated and the multi-scale grid dimensionality is taken as the characteristic quantity that is used in the recognition of UHF PD signals.

提出了一种基于小波包多尺度分析和网格维数的变压器局部放电超高频信号模式识别的新方法，采用小波包多尺度变换提取局部放电超高频信号在多尺度上的小波系数，通过改进差盒计数法计算多尺度小波系数的网格维数，并将多尺度网格维数作为特征量用于局部放电超高频信号的识别。

Research makes clear as a result: TC measure has apparent seasonal change feature, average scale is in the biggest April, achieve 230.4km, the smallest Feburary, for 69.5km;TC measure apparent area distributings inhomogenous sex, the area of TC measure occurrence maximum is located in 28.6 ～ 29.5 ° N, 133 ° of 131.1 ～ on the offing of E, and it is to the south of 123 ° E with 12 ° N with south area, TC measure often is under 200km; the TC to different intensity, its measure and intensity luffing have apparent difference, tropical storm (the 24h measure luffing of TS) is the biggest, and typhoon (the dependency of measure of the biggest;TC and intensity is in the 24h intensity luffing of TY) is discrepant below different method, on northwest travel, westing, north model TC measure and intensity show remarkable positive to close, both correlation coefficient achieved 0.93 above, northeast travel and whirly model the correlation coefficient of TC measure and intensity is adjacent 0.6, change direction model the correlation coefficient of TC is in 0.85 or so; in addition, the dependency of TC measure and intensity in its the different level of life history also is put in notable difference, sending exhibition period, the dependency of measure and intensity is best, its correlation coefficient...

探究结果表明：TC尺度有明显的季节变化特征，平均尺度在4月份最大，达到230.4km，2月份最小，为69.5km；TC尺度有明显的区域分布不均匀性，TC尺度出现最大值的区域位于28.6～29.5°N，131.1～133.0°E的海面上，而在123°E以东和12°N以南地区，TC尺度往往都在200km以下；对于不同强度的TC，其尺度和强度变幅有明显差异，热带风暴的24h尺度变幅最大，而台风的24h强度变幅最大；TC尺度和强度的相关性在不同路径下是有差异的，西北行、西行、北上型的TC尺度和强度呈显著的正相关，两者的相关系数达到了0.93以上，东北行和回旋型的TC尺度和强度的相关系数接近0.6，转向型TC的相关系数在0.85左右；此外，TC尺度和强度的相关性在其生命史的不同阶段也存在显著差异，在发展期，尺度和强度的相关性最好，其相关系数。。。

Wavelet multi-resolution analysis is applied to decompose the signal into multiple-level and the wavelet coefficient modules of its high-frequency components are obtained. The wavelet coefficient modules of a broken signal can be extracted by software demising. The threshold of demising is decided by the difference between the wavelet coefficient modules of a broken signal and those of a noise. The wavelet coefficient modules of the broken signal were shown in different levels, then the faults can be detected and distinguished by the integrated features of the variant levels' wavelet coefficient modules.

利用小波多尺度分解技术，将信号进行多尺度的小波分解，得到不同尺度下的信号高频分量的小波系数模值，并根据奇变信号和噪声信号小波系数模值的差异，采用软阈值去噪法，对其高频分量小波系数进行去噪处理，获取不同尺度上突变信号的小波系数模值，实现对故障的检测，并可根据不同尺度上小波系数模值的对应关系，实现对多重并发故障的区分。

On each scale, the signal was rebuilt, so 5 groups of multiscale gyros drift data were got.

根据分解后的各尺度系数进行信号重建，得到5组多尺度陀螺仪漂移数据。

As for jump heighs there are some differences be-tween the continuous and discrete cases.In discrete case we introduce the empiricalscale codfficients to estimate jump heighs base on location estimators given by theabove method.

关于断点的跃度，在离散模型场合，通过引进样本的尺度系数并利用位置的小波估计可得到跃度的相合估计。

On the approximate uncorrelation property of DWT coefficients of LMSV process in the same scale and different scales, first the quasi maximum likelihood estimation method of parameters and the estimation method of volatility process of LMSV model are presented.

根据小波变换可将过程分解到不同的尺度上以及LMSV过程同一尺度下和不同尺度下DWT系数的近似不相关性，提出了建立局部似然函数的方法，又根据DWT系数和MODWT系数之间的关系，将局部似然函数表示为模型参数和局部小波方差估计的形式，并用该方法对中国股市收益进行了时变LMSV模型参数的估计。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。