lec11 - Generalized Hough Transform + Line Fitting
应用地球化学元素丰度数据手册-原版
应用地球化学元素丰度数据手册迟清华鄢明才编著地质出版社·北京·1内容提要本书汇编了国内外不同研究者提出的火成岩、沉积岩、变质岩、土壤、水系沉积物、泛滥平原沉积物、浅海沉积物和大陆地壳的化学组成与元素丰度，同时列出了勘查地球化学和环境地球化学研究中常用的中国主要地球化学标准物质的标准值，所提供内容均为地球化学工作者所必须了解的各种重要地质介质的地球化学基础数据。
本书供从事地球化学、岩石学、勘查地球化学、生态环境与农业地球化学、地质样品分析测试、矿产勘查、基础地质等领域的研究者阅读，也可供地球科学其它领域的研究者使用。
图书在版编目（CIP）数据应用地球化学元素丰度数据手册/迟清华，鄢明才编著. －北京：地质出版社，2007.12ISBN 978－7－116－05536－0Ⅰ. 应… Ⅱ. ①迟…②鄢…Ⅲ. 地球化学丰度－化学元素－数据－手册Ⅳ. P595－62中国版本图书馆CIP数据核字（2007）第185917号责任编辑：王永奉陈军中责任校对：李玫出版发行：地质出版社社址邮编：北京市海淀区学院路31号，100083电话：（010）82324508（邮购部）网址：电子邮箱：zbs@传真：（010）82310759印刷：北京地大彩印厂开本：889mm×1194mm 1/16印张：10.25字数：260千字印数：1－3000册版次：2007年12月北京第1版•第1次印刷定价：28.00元书号：ISBN 978－7－116－05536－0（如对本书有建议或意见，敬请致电本社；如本社有印装问题，本社负责调换）2关于应用地球化学元素丰度数据手册（代序）地球化学元素丰度数据，即地壳五个圈内多种元素在各种介质、各种尺度内含量的统计数据。
它是应用地球化学研究解决资源与环境问题上重要的资料。
将这些数据资料汇编在一起将使研究人员节省不少查找文献的劳动与时间。
这本小册子就是按照这样的想法编汇的。
参数更新公式
参数更新公式参数更新公式通常用于机器学习和深度学习中，用于根据学习率和当前参数来更新模型参数。
下面是一些常见的参数更新公式：1. 梯度下降（Gradient Descent）：$\theta = \theta - \alpha \nabla J(\theta)$其中，$\theta$ 是模型参数，$\alpha$ 是学习率，$J(\theta)$ 是损失函数。
2. 随机梯度下降（Stochastic Gradient Descent）：$\theta = \theta - \alpha \nabla J(\theta^{(i)})$其中，$\theta^{(i)}$ 是第 $i$ 个样本的梯度。
3. 牛顿法（Newton's Method）：$\theta = \theta - \alpha H(\theta)^{-1} \nabla J(\theta)$其中，$H(\theta)$ 是海森矩阵（Hessian Matrix）。
4. 共轭梯度法（Conjugate Gradient Method）：$\theta = \theta - \alpha p$其中，$p$ 是共轭方向。
5. 拟牛顿法（Quasi-Newton Method）：$\theta = \theta - B(\theta)^{-1} \nabla J(\theta)$其中，$B(\theta)$ 是拟海森矩阵（Approximate Hessian Matrix）。
6. 坐标梯度下降（Coordinate Gradient Descent）：$\theta_j = \theta_j - \alpha \frac{\partial J(\theta)}{\partial \theta_j}$ 其中，$\theta_j$ 是第 $j$ 个参数。
7. 带动量的梯度下降（Momentum Gradient Descent）：$v = \beta v - \alpha \nabla J(\theta)$$\theta = \theta + v$其中，$v$ 是动量，$\beta$ 是动量系数。
语义相似矩阵公式
语义相似矩阵公式是一种用于计算语义相似度的方法，通常用于自然语言处理和信息检索领域。
该公式基于词汇之间的共现关系，通过统计词汇之间同时出现的频率来评估它们的语义相似度。
一种常用的语义相似矩阵公式是余弦相似度，其计算方法如下：
1.首先，将文本中的每个单词表示为一个向量，向量的维度是词汇表的大小，
每个维度的值表示该单词在文本中出现的频率。
2.然后，计算两个单词向量之间的点积，即它们在所有维度上的值的总和。
3.接着，计算两个单词向量的模长，即它们的每个维度的值的平方和的平方
根。
4.最后，将两个单词向量的点积除以它们的模长，得到余弦相似度值。
该值越
接近1，表示两个单词的语义越相似；越接近-1，表示语义越不相似；等于0表示没有相似性。
除了余弦相似度，还有其他一些常用的语义相似矩阵公式，如基于编辑距离、基于同义词集、基于WordNet等。
这些公式各有优缺点，可以根据具体的应用场景选择适合的方法。
常用的相似准则数
常用的相似准则数相似性准则是一种用于测量或衡量两个或多个对象之间的相似性或相关性的方法或模型。
在不同领域和应用中，存在许多常用的相似性准则，以下是其中一些常见的准则。
1. 欧几里德距离（Euclidean Distance）：欧几里德距离是空间中两个点之间的直线距离，根据勾股定理计算。
2. 曼哈顿距离（Manhattan Distance）：曼哈顿距离是两个点在坐标系上的绝对差值之和，通常用于城市街区距离的度量。
3. 余弦相似度（Cosine Similarity）：余弦相似度是向量空间中两个向量的夹角余弦值，可用于衡量文本、图像等数据的相似性。
4. 杰卡德相似系数（Jaccard Similarity Coefficient）：杰卡德相似系数用于衡量两个集合的相似度，计算两个集合交集的大小与并集的大小之比。
5. 皮尔逊相关系数（Pearson Correlation Coefficient）：皮尔逊相关系数是一种用于衡量两个连续变量之间线性相关程度的方法，取值范围为-1到16. 汉明距离（Hamming Distance）：汉明距离是用于衡量两个等长字符串之间的差异度量，计算相同位置不同字符的个数。
7. K-L散度（Kullback-Leibler Divergence）：K-L散度是一种度量两个概率分布之间差异的方法，用于衡量一个概率分布相对于另一个分布的不确定性。
10. 汉明重量（Hamming Weight）：汉明重量是二进制数中非零位的个数，用于衡量两个二进制数的相似性。
11. 简化模式（Simplification Metric）：简化模式是一种度量模型简化程度的方法，通常用于优化问题解的复杂度。
这些相似性准则在数据挖掘、机器学习、自然语言处理、图像处理等领域中得到广泛应用。
它们可以帮助我们理解和比较不同对象之间的相似性、相关性或差异性，从而为我们提供洞察和决策支持。
利用长轴检测椭圆
利用长轴检测椭圆姜春涛【摘要】利用霍夫变换进行椭圆检测,需要寻找椭圆的参数.使用椭圆主半轴的长度,可以快速地寻找椭圆的参数.这种方法需要将椭圆的短半轴长度求解出来,然后仅使用一维的聚集数组收集椭圆短半轴的长度信息.该方法不需要计算椭圆的边的切线或者曲率,因此不易受到噪声的影响.该方法的实现不需要大量的内存.合成的图像和真实的图像测试表明,这种方法是有效的.【期刊名称】《微型机与应用》【年(卷),期】2017(036)004【总页数】4页(P43-46)【关键词】图像处理;霍夫变换;椭圆检测【作者】姜春涛【作者单位】四川大学计算机学院,四川成都610000【正文语种】中文【中图分类】TP751椭圆检测是图像处理中的一个重要的问题，已经有很多种椭圆检测的方法[1-10]。
完全定义一个椭圆需要五个参数，因此变化霍夫变换[11]进行椭圆检测需要五维的参数空间。
这需要很大的内存和时间，所以需要使用几何上的限制以减少参数空间。
为了减少椭圆检测中时间和空间的需求，以前的技术大部分将 5 维的参数空间分为更少维数的子空间。
参考文献[1]介绍了一种基于几何属性的椭圆检测方法。
参考文献[2]通过在相同的水平和垂直位置上的边缘点构造两个中间点矩阵，然后，利用霍夫变换从这两个矩阵中检测出直线[12-13]，这些直线的交提供了可能的椭圆中心。
文献[3]提出了一种包含切线信息的用于椭圆提取的映射方法。
文献[4]提出了一种有效的从图像的边中检测椭圆的方法，其思路是在霍夫变换基础上从边缘中检测对称轴，一个高维的问题转化成两个二维的问题。
先从边缘中找到对称轴，然后从边缘中找到椭圆。
文献[4]介绍了一种利用椭圆长轴进行椭圆检测的方法。
利用短半轴的长度获取在同一椭圆上的点，然后椭圆的参数被计算出来。
本文的椭圆检测方法基于文献[9]介绍的方法。
这种方法使用新的方式计算椭圆的短半轴，需要的运算量稍微少一些。
对于给定的椭圆长轴的两个端点，文中提供了一种用于减少计算短半轴长度的点数的方法。
HT检测技术研究与进展
第27卷第6期增刊 2006年6月仪 器 仪 表 学 报Chinese Journal of Scientific InstrumentVol.27No.6J une.2006 HT检测技术研究与进展陈高华 卓东风 王 云(太原科技大学电子信息工程学院 太原 030024)摘 要 介绍了哈夫变换(Hough Transform,H T)检测技术的检测原理,全面回顾并总结分析了哈夫检测技术研究的历史与现状,指出了目前存在的关键问题,并对今后将要进行的工作进行了展望。
关键词 Hough变换 图像 检测技术HT detection technique research and headw ayChen Gaohua Zhuo Dongfeng Wang Yun (T ai y uan Universit y of Science&Technology,Elect ronic I nf ormation Engineering B ranch,Tai y uan 030024,China)Abstract The recent progress and history in t he research on Hough detection technology are overall reviewed and generalized.Then point out t he existent pivotal problem and prospect the working t hat be going to proceed hencefort h.The t heory of Hough Transform detection technical are also introduced.K ey w ords Hough transform image detection technology1 引 言哈夫变换(H T)是Paul Hough在1962年提出的一种图像边缘检测技术,它可以识别和检测图像空间的任意解析曲线。
汽车转向器毕业设计
汽车转向器毕业设计【篇一：毕业设计汽车转向系统】摘要本设计课题为汽车前轮转向系统的设计，课题以机械式转向系统的齿轮齿条式转向器设计及校核、整体式转向梯形机构的设计及验算为中心。
首先对汽车转向系进行概述，二是作设计前期数据准备，三是转向器形式的选择以及初定各个参数，四是对齿轮齿条式转向器的主要部件进行受力分析与数据校核，五是对整体式转向梯形机构的设计以及验算，并根据梯形数据对转向传动机构作尺寸设计。
在转向梯形机构设计方面。
运用了优化计算工具matlab进行设计及验算。
matlab强大的计算功能以及简单的程序语法，使设计在参数变更时得到快捷而可靠的数据分析和直观的二维曲线图。
最后设计中运用autocad和catia作出齿轮齿条式转向器的零件图以及装配图。
关键词：转向机构，齿轮齿条，整体式转向梯形，matlab梯形abstractthe title of this topic is the design of steering system. rack and pinion steering of mechanical steering system and integrated steering trapezoid mechanism gear to the design as the center. firstly make an overview of the steering system. secondly take a preparation of the data of the design. thirdly, make a choice of the steering form and determine the primary parameters and design the structure of rack and pinion steering. fourthly, stress analysis and data checking of the rack and pinion steering. fifthly, design of steering trapezoid mechanism, according to the trapezoidal data make an analysis and design of steering linkage.in the design of integrated steering trapezoid mechanism the computational tools matlab had been used to design and checking of the data. the powerful computing and intuitive charts of the matlab can give us accurate and quickly data. in the end autocad and catia were used to make a rack and pinion steering parts diagrams and assembly drawingskeywords: steering system，mechanical type steering gear and gear rack，integrated steering trapezoid，matlab trapezoid目录1 绪论 ....................................................................................................... (1)1.1 汽车转向系统概述 (1)1.2 汽车转向系统的国内外现状及发展趋势 (2)1.3 研究内容及论文构成 (3)2 机械转向系统的性能要求及参数 (5)2.1 机械转向系统的结构组成 (5)2.2 转向系统的性能要求 (6)2.3 转向系的效率 ....................................................................................................... . (7)2.4 传动比特性 ....................................................................................................... .. (9)2.5 转向器传动副的传动间隙 (11)3 机械式转向器总体方案初步设计 (12)3.1 转向器的分类及设计选择 (12)3.2 齿轮齿条式转向器的基本设计 (12)3.2.1 齿轮齿条式转向器的结构选择 (12)3.2.2 齿轮齿条式转向器的布置形式 (14)3.2.3 设计目标参数表以及对应的转向轮偏角计算 (15)3.2.4 转向器参数选取与计算 (16)3.2.5 齿轮轴的结构设计 (19)3.2.6 转向器材料及其他零件选择 (20)4 齿轮齿条转向器校核 ....................................................................................................... (21)4.1 齿条的强度计算 (21)4.1.1 齿条受力分析 (21)4.1.2 齿条齿根弯曲强度的计算 (22)4.2 小齿轮的强度计算 (23)4.2.1 齿面接触疲劳强度计算 (23)4.2.2 齿轮齿根弯曲疲劳强度计算 (26)4. 3 齿轮轴强度校核 (27)5 转向梯形机构的设计 ....................................................................................................... (31)5.1 转向梯形机构概述 (31)5.2 整体式转向梯形机构方案分析 (32)5.3 整体式转向梯形机构数学模型分析 (32)5.4 基于matlab的整体式转向梯形机构优化设计 (35)5.4.1 转向梯形机构的优化概况 (35)5.4.2 转向梯形机构设计思路 (36)5.4.3 基于matlab的转向梯形机构设计 (36)5.5 转向传动机构的设计 (43)5.5.1 转向传送机构的臂、杆与球销 (43)5.5.2 转向横拉杆及其端部 (43)6 基于catia的齿轮齿条式转向系统的三维建模 (45)6.1 catia软件简介 (45)6.2 齿轮齿条式转向系统的主要部件三维建模 (45)结论 ....................................................................................................... .. (49)参考文献 ....................................................................................................... ........................... 50 致谢 ...................................................................................................... 错误！未定义书签。
张量重正化
张量重正化
在机器学习和深度学习领域，"张量重正化"通常指的是对神经网络中的张量进行正则化的过程。
正则化是一种常用的技术，目的是防止模型在训练数据上过拟合，提高其在未见过数据上的泛化能力。
在深度学习中，常见的正则化方法包括L1正则化、L2正则化和批量归一化（Batch Normalization）。
这些方法中的一些可以被认为是对网络中的张量进行正则化的方式。
以下是几种与张量正则化相关的方法：
1.L1正则化：在神经网络的损失函数中加入L1正则化项，强制
使权重矩阵中的一些元素趋向于零。
这可以促使模型学习更加稀疏的表示。
2.L2正则化：类似于L1正则化，L2正则化在损失函数中加入L2
范数的平方项。
这有助于防止权重值过大，促使权重值趋向于分布在较小的范围内。
3.批量归一化（Batch Normalization）：批量归一化是一种通过
规范化输入来加速深度神经网络训练的技术。
它对每一层的输入进行归一化，有助于防止梯度爆炸和消失，并有正则化的效果。
在实际应用中，可以通过在模型的损失函数中引入正则化项，或者在层的定义中添加正则化参数来实现张量的正则化。
这有助于提高模型对未知数据的泛化性能，防止过度拟合。
MinGPU
ORIGINAL RESEARCH PAPERMinGPU:a minimum GPU library for computer visionPavel Babenko ÆMubarak ShahReceived:3September 2007/Accepted:30April 2008ÓSpringer-Verlag 2008Abstract In the field of computer vision,it is becoming increasingly popular to implement algorithms,in sections or in their entirety,on a graphics processing unit (GPU).This is due to the superior speed GPUs offer compared to CPUs.In this paper,we present a GPU library,MinGPU,which contains all of the necessary functions to convert an existing CPU code to GPU.We have created GPU imple-mentations of several well known computer vision algorithms,including the homography transformation between two 3D views.We provide timing charts and show that our MinGPU implementation of homography trans-formations performs approximately 600times faster than its C ++CPU implementation.Keywords GPU ÁGPGPU ÁComputer vision ÁHomography transformation1IntroductionLittle research was conducted on general-purpose compu-tation on GPU before 2000.Since 2002,there has been a great deal of interest in GPU.A comprehensive list of articles is available at [5].In 2001,Rumpf and Strzodka [24]described a method to implement level sets on GPU.In 2002,Yang and Welch [27]studied image segmentation and smoothing on graphics hardware.There were several articles published in 2003–2004,many of which appeared in computer graphics conferences rather than computervision.For example,in 2003Moreland and Angel [18]published an article in SIGGGRAPH conference on how to implement fast Fourier transform on ter that year,Colantoni et al.[4]described color space conversions,PCA and diffusion filtering on GPU.In 2004,‘GPU Gems 2’dedicated a chapter to computer vision on GPU [8].It described correcting radial distortions,Canny edge detec-tor,tracking hands,and image panoramas on GPU.Yang and Pollefeys [26]published a CVPR paper later that year,on implementation of real-time stereo on GPU.Ohmer et al.[22]implemented a face recognition system using Kernel PCA and batut et al.[16]utilized level set-based multi-view stereo.The well-known SIFT algorithm was employed in 2007by Heymann et al.[14].In 2006,another implementation of Fast Fourier transform was done by Govindaraju et al.[11].Other methods that were implemented include [5]:generalized Hough transform,skeletons,depth estimation in stereo,motion estimation,3D convolutions,contour tracking,segmentation and fea-ture tracking,and matching.However,because articles before 2005used previous generations of graphics hard-ware,their contribution is often outdated.MinGPU is a library which hides all graphics-related routines from the end user,which is particularly useful for those who do not have particular skills or desire to delve into low-level details of GPU programming.MinGPU can be used as a basic building block for any GPGPU appli-cation.It can help implement any algorithm on GPU.Besides MinGPU,there exists another library which is dedicated to computer vision on GPU.OpenVIDIA [9,21]is an open source library which contains many useful vision algorithms,like edge and corner detection,feature-based corner,object tracking,and image enhancement/preprocessing routines.The complete algorithm list can be found at [21].OpenVIDIA also maintains a web pageP.Babenko (&)ÁM.Shah Computer Vision Lab,School of Electrical Engineering and Computer Science,University of Central Florida,Orlando,FL,USA e-mail:pavelb@J Real-Time Image ProcDOI 10.1007/s11554-008-0085-xwhich lists many recent computer vision related papers[5]. However,this library is not built upon a reusable core. Another notable effort is the BrookGPU library[2]. BrookGPU was conceived as an extension to the C lan-guage which supports stream programming and data-parallel constructs.It includes a compiler and run-time support libraries.This library has not been updated since 2004.The latest v0.4release of BrookGPU can be down-loaded from[3].Yet another open source GPU library is Sh [25].Sh is a GPU metaprogramming library designed in C++.It defines GPU objects and data types as C++ classes,and also defines operations on these objects in terms of C++.Control structures are defined as C++ macros.Thus,it is possible to write programs for GPU using C++notation.However,the target users for this library are graphics developers;this library serves as a substitute for GPU languages like Cg,GLSL,or HLSL. Both these medium-sized open-source projects feature little documentation and are complex for users,who do not have advanced knowledge of graphics processors and C++ programming.RapidMind[23]is a library similar to Sh in that it wraps GPU constructs into C++classes.In contrast to Sh,the target users of RapidMind are multi-core soft-ware developers.RapidMind is an attempt to provide a unified high-level development platform for parallel com-putations;it works with Cell,multi-core CPUs and GPUs. This commercial library is also somewhat advanced in use and does not give a direct control over GPU processors.Our work makes two contributions to computer vision. First,we have created a C++class library,MinGPU.This library can function as an introduction to GPU world for researchers,who have never used the GPU before.We intentionally designed the library and interfaces to be as straightforward as possible.MinGPU provides simple interfaces,which can be used to load a2D array into the GPU and perform operations.All GPU and OpenGL rela-ted code is encapsulated in the library;therefore users of this library do not need any prior knowledge of GPU.The library is configurable for use in a variety of purposes.It is available online on our web site at[17].Our MinGPU library is designed to work on nVidia7000series cards as well as on ATI Radeon cards series R400(ATI X800)and later versions.We have designed and tested our library on nVidia7300LE card,which is a basic card in7000series and is in widespread use.Some portions may be functional on nVidia6000series cards as well as on former ATI cards.In performance evaluations we used,unless stated otherwise,nVidia GeForce7300LE graphics card(‘GPU’) installed in DELL XPS410desktop,featuring Core2Duo 2.4MHz processor and2Gb of memory(‘CPU’).Second,we have implemented three popular computer vision methods on GPU,as well as the number of simple image operations like taking image derivatives,Gaussian smoothing and image pyramids.In this paper,we have included implementations of pyramids and homography transformations on GPU,while the descriptions and listings of all other methods,including Lukas–Kanade opticalflow and optimized normalized cross-correlation,are included in an extended technical report which can be downloaded from our site[17].For each of these methods,we present timing and provide a detailed timing comparison of GPU homography transformation versus its non-GPU implementations.GPU programming using OpenGL is not a trivial matter even for experienced programmers.In summary,MinGPU is a small,simple library which provides a quick intro-duction to a programming on GPU.It works on most graphics cards currently installed in personal computers, making image processing algorithms portable between different graphics devices from ATI and nVidia.Most PC users probably don’t realize that their PC is equipped with a parallel processor,which they can use with the help of libraries like MinGPU.This paper is organized as follows:in Sect.2,we present general information on the current state of art and the evolution of GPUs,their architecture and design.In Sect.3,we give a brief introduction of our C++class library for the GPU-MinGPU.In Sect.3we also show how to implement few common computer vision algorithms with MinGPU,image derivatives and image pyramids. Sect.4contains the MinGPU implementation of a more complex computer vision method—the homography transformation between two3D views,as well as speed comparisons and discussions.The MinGPU class structure can be found in Appendix1.The Appendix2contains code listings of all programs mentioned in Sects.2,3,4.2Current trends in GPU2.1Graphics processorsMost of today’s graphics cards from the largest GPU makers,nVidia,and ATI,contain two processors,the vertex processor and the fragment processor.2.1.1Vertex processorAll graphics cards operate on3D polygons.Every polygon is defined by(x,y,z)coordinates of its vertices.For example,every triangle is defined by three vertices.The camera vertex is usually set to be at(0,0,0).When the camera moves,the coordinates of all polygon points must be re-computed to reflect a change in the camera position. This operation is performed by the vertex processor.Vertex processors are specially designed to perform this operationJ Real-Time Image Procand therefore,are able to optimize the speed of coordinate transformations.After the coordinates are recomputed,the vertex processor determines which polygons are visible from the current viewpoint.2.1.2Fragment processorAfter the vertex processor re-computes all the vertex coordinates,the fragment processor covers the visible por-tions of the polygons with textures.The fragment processor does this with a help of the‘shader’programs.Originally,in the computer graphics world,the purpose of the‘shader’program was to add graphic effects to textures like shade (hence comes the name),but now this feature is being inherited by general-purpose GPU users.Up until a few years ago,all shader programs were written in the assembly language.However,as graphics hardware evolved and became capable of executing much larger shader programs a need for a specially designed language became evident. Many contemporary shader programs are C-like programs written in Cg,‘C for graphics’language.Cg language was created by nVidia.nVidia supplies manuals and examples on Cg,which can be found in the Cg Toolkit[7].The most important difference between contemporary CPUs and GPUs is that GPUs run programs concurrently and are SIMD-type processors.The programs are executed for every output texture pixel independently.Therefore,if the GPU has8instruction pipelines in the fragment pro-cessor,it is able to execute the same program on up to8 texture pixels simultaneously.Contemporary fragment processors have4–128instruction pipelines.While both the vertex and fragment processors are programmable,we are more interested in the fragment processor because it is specifically designed to work with textures which,in our case,can be viewed as2D data arrays.Therefore,all algorithms in this paper are designed to work on a fragment processor.On the other hand,vertex processor is optimized to work with pixels.At the time of writing,the typical upscale desktop computer is equipped with Intel Core2Duo processor working at2.4GHz.Let’s roughly compare a productivity of this processor to a productivity of nVidia7300LE(light edition)GPU,which is a commonplace graphics card installed in the same desktop.We assume single-core CPUs and no SIMD CPU operations are used.The clock rate of 7000series nVidia GPUs lies in400–700MHz range.The 7300LE runs at450MHz.There are4–24pipelines in fragment processor in the currently popular7000series. The7300LE contains4pipelines.We also take into account that nVidia GPU pipelines can typically process two pixels in one clock cycle and they process each of the pixel’s4color channels simultaneously.Each pixel is represented as a4-float number(RGBA).Therefore,if we set up our array so that each of RGBAfloat assumes a data value(see Sect.2),we gain an additional four times the speed.After we multiply all the increases in speed,nVidia 7300LE works as a processor with a virtual14.4Ghz rate, due to parallelism;this rate is already six times higher than that of latest Intel Core2Duo2.4GHz CPU.The Table1 illustrates trends in GPU developments in recent years.Consequently,wefind that the modest GPU card installed in our computer has a performance about six times higher than the latest CPU.If we install the latest nVidia 8800GPU(1.5GHz,128pipelines)it could yield a theo-retical speedup of106times compared with the state-of-the-art CPU.It is hard to make an exact performance comparison of current CPUs to GPUs for many reasons.Modern processors are also equipped with technology which allows simulta-neous processing of multiple data by the same instruction. Starting with Pentium II,all Intel processors are equipped with the MMX technology which allows sequential pro-cessing of4integers.All Intel and AMD processors newer than Pentium III include SSE—similar technology with processing ability of2to4floating point numbers simulta-neously.We also have to mention a recent trend to include more than one processing core on chip.For example,recent Pentium processors feature2–4cores which share the same on-chip cache.Every core can be viewed as separate pro-cessor.Nevertheless,the productivity of current graphics processors significantly exceeds the productivity of CPUs and this trend will continue.Table1The trends in GPU evolution in recent yearsGraphics card Year Shader unit clockrate(MHz)ShaderunitsTexturefillrate(billion/s)Memory bandwidth(GB/s)Memorymax(MB)GeForce8800Ultra May2007150012839.2103.7768 GeForce8800GTX Nov2006135012833.686.4768 GeForce7900GTX Mar20066502415.651.2512 GeForce7800GT May2005550169.632.0256 GeForce FX6800Jun200440016 6.435.2256 GeForce FX5800Jan20034004 4.012.8256 J Real-Time Image ProcOn the other hand,due to physical constraints it is impossible to run a transistor-based conventional processor at a significantly higher speed than what is already attained by the industry.Theoretically the only way to circumvent this limit lies in the use of different base technologies,like quantum technology.At the time of writing such technol-ogy was many years down the line.Researchers in computer vision are aware that many vision algorithms are not currently able to run in real-time due to their high computational complexity.We feel that the one way to make this possible in observable future is the use of parallel technology,such as those present in graphics processors.2.2GPU limitationsAll GPUs suffer from two drastic design limitations.The first limitation is,ironically,the fact that GPU computations are done in parallel.The algorithm must be ready to work in multi-thread mode in order to operate on the GPU,which is not a feature of many algorithms.In the GPU,every pixel in the2D texture is processed independently.It may not be possible to know the sequence in which pixels are processed; therefore it is not possible to pass any data between pixels while they are being processed.For example,let’s consider a popular connected components algorithm which is used in many vision algorithms today,the Canny edge detector. There exist two versions of a connected components algo-rithm:recursive and non-recursive.A recursive version cannot be implemented on the parallel processor,because being‘‘recursive’’implies the knowledge of the order in which pixels are being processed which is not present in a parallel processor.A non-recursive version of the connected components algorithm uses a running variable,which con-tains the largest region label currently assigned.It is not possible,as it was stated above,to maintain this counter on the parallel processor.There exist some parallel versions of connected components[13];however,those versions use binary structures like graphs and trees,which are hard to implement on the GPU.Currently,we do not know of any successful implementation.In the GPU,when one processes a pixel at(x,y)location one can only write the result into(x, y)location of the output texture.There may be more than one output texture(as many as4–24for7000series and up to48 in8000series).We must also consider that every pixel is comprised of4floats(RGBA value).For the7300LE card, one can write16values for every pixel processed,but they cannot be written into any other than(x,y)location in the output textures.This is the second limitation of graphics hardware.Only the latest CUDA-technology based graphics cards from nVidia allow scatter operations in addition to gather operations.For example,let’s consider building a color histogram of a grayscale image.Every pixel in the input image may take values in the range of0–255,which means there are 256bins in the color histogram.For every pixel pro-cessed,we must increment one of256bins,which due to the above limitation is not possible on the GPU.This is a very simple algorithm,yet it is not possible to implement it on the GPU.One source[21]devised an approach which computes approximate color histogram on small set of input values.Many other researchers agree that the most promising algorithms to implement on the GPU arefilter-like algo-rithms,which process every pixel independently of the others.Examples of this include Gaussian smoothing, convolutions,image pyramids,geometric transformations, image de-noising,cross-correlation as well as many other algorithms.Contemporary computer architecture features one impasse with respect to the GPU which we cannot avoid mentioning,which is the transfer rate between main(CPU) memory and GPU memory.The latest computers are equipped with PCI Express memory bus,which is the fastest expansion bus to date in desktop computers.This memory bus has a full duplex transfer rate of250MB/s for every lane(500MB/s for PCI Express 2.0released in January2007).There may be up to32serial lines,however many commodity computers are equipped with less than that.We measured main memory to GPU memory bus transfer rate on our new DELL XPS410desktop to be approximately860MB/s.At this speed it would take approximately4–5ms to transfer an array of1million32-bitfloating point numbers(1k91k image)from the CPU to GPU.Simple operations(addition,for example)over the same array in the CPU(Core2Duo2.4MHz)would take about4ms.Therefore,the time required to complete simple array operations time such as transfering an array from CPU to GPU is comparable to the time required for applying an operation in the CPU.An example of this backlog is given in the beginning of Sect.3;we would like to point out that some older GPU cards feature slower GPU to CPU transfer rate than CPU to GPU.An interesting recent trend in computer design is the appearance of expansion connectors for HyperTransport buses,the front-side buses used in many today’s computers as a fast link between processor and a main memory.The HyperTrans-port protocol supports41.6GB/s bandwidth in two directions making it much faster than PCI Express. Recently,plug-in cards,such as fast speed coprocessors, have appeared and can access the HyperTransport bus.3MinGPU libraryIn the area of computer vision,we often encounter situ-ations in which we need to process every point of a2DJ Real-Time Image Procarray(for example,in an image).It is done in a double for loop as shown in the‘Hello,World!’example in Sect.3.1.Any2D array can be represented as a GPU texture.If we do not need to carry over any information between the points of this array,we can implement the inner part of this double loop as a shader(Cg)program. The array is uploaded into the GPU as texture.Then,the shader program is run and the output texture downloaded back into main memory.In this section we introduce the smallest possible library, MinGPU,which can implement the above mentioned code on a GPU.We attempted to convert the CPU code into GPU in a straightforward manner.In Sect.3.1,we present an implementation of this double loop in MinGPU.The rest of the section is dedicated to few more MinGPU examples based on simple vision algorithms.This section uses a learn-by-example technique.We progress from simple,for instance taking image derivatives and computing image pyramids to more elaborate exam-ples,such as an implementation of a homography transformation on GPU.In the following section we pres-ent an elaborate GPU example,an implementation of a homography transformation on GPU.MinGPU is a C++class library.Due to the incapsula-tion paradigm,users do not need any knowledge of its inner structure;therefore they do not need any knowledge of the details of how the fragment processor or OpenGL drivers operate.MinGPU contains only two classes:Array and Program.The Array Class defines a2D array in the GPU memory,while the Program class defines a Cg program in the GPU memory.All class methods are listed in Appendix A.In a straightforward scenario,the user prepares the data array and uploads it to the GPU using the methods from the Array class.The Cg program is then loaded and compiled. Program parameters can be set using the method from Program class.The Cg program is then run and the results are generated in the GPU memory,which are then down-loaded to CPU memory by another call to a method from the Array class.The‘Hello,World’example illustrates this.3.1‘Hello,World!’exampleWe are going to convert this simple CPU code into GPU:All code listings are given in the Appendix2.The code which implements‘Hello,World’on MinGPU is given in Listing1.This,as well as the most other listings,contains two pieces:a C++program and a Cg program.Let’sfirst look at C++program.It matches the idea we discussed above in a straightforward way:we create both array and Cg programs,copy the array to a GPU,set program parameters and run it.As for Cg program,we won’t be able to cover the entire Cg language here(which you canfind in a Cg user manual [6]),but we can highlight some key points.First,our ori-ginal program contains just one function,main,which is its entry point.There are two input parameters to this function, a parameter coords of typefloat2and a parameter texture of type samplerRECT.The parameter coords is bound to pre-defined name TEXCOORD0,which contains(x,y) coordinates of the currently processed pixel.Pre-defined names are set automatically by the hardware,so we do not need to provide values for these.Subsequently,the parameter texture is a regular parameter which we must initialize with a call to the SetParameter function.It is our input array,which we want to increment by1.The standard Cg function texRECT fetches a value of texture array at coords coordinates.In this simplified example,we used the same Cg texture as both an input and an output array. We store the intermediate value in the result variable,a standard4-float RGBA type.The assignment string result=y+1increments each of fourfloat values in result by1.In this way,everyfloat in result will contain the same value.Cg functions return one4-float RGBA value which is the generated value for the current(x,y)texture pixel. When we download this value to the CPU in luminance mode(which is discussed in the following subsection), OpenGL drivers take a mean of the4RGBAfloats to produce a single luminance value for each texture pixel.In color mode,all4RGBA channels are returned.All Cg programs run on every point in an output,not an input, array.These two arrays can have different sizes.3.2MinGPU operating modesThe‘Hello,World’code has some implicit features which we need to clarify.First,we always assume that MinGPU input arrays contain grayscale values in the0–255integer range.This array format is common in computer vision. Second,all numbers a GPU operates on arefloats of8–32 bit length.Therefore,MinGPU converts inputted integer arrays intofloats.MinGPU uses32-bit(4-byte)longfloats. This is the largestfloating point format supported in graphics cards today.J Real-Time Image ProcA fragment processor encodes every texture pixel as a fourfloat RGBA value,a quad.There is onefloat value for the red,green,and blue colors and one for the alpha channel.All operations on a quad are always performed on all fourfloats in parallel by hardware.The Cg language conveniently includes a special vector type definitionfloat4 to define a quad.While all MinGPU input arrays are invariably greyscale MinGPU supports two color modes for arrays—a lumi-nance and a color mode.The reason for this is that GPU color modes are manufacturer-dependent.Since a lumi-nance mode is expected for the nVidia family of processors, it is guaranteed to work in all nVidia cards.However,for all current ATI cards a color mode is required.nVidia also fully supports a color mode.For list of color modes sup-ported by different cards,see tables in[10].In a luminance mode,everyfloat in the quad holds the same value of one input array cell.In a color mode, MinGPU replicates every input value four times,so that eachfloat in a quad contains the same value.Luminance and color modes are compatible on the level of a C++code and on the level of a Cg program.In MinGPU,a color mode is specified on per-texture basis.The luminance mode is the default.Textures can be created in a color mode by setting bMode to enRGBA in a call to Array::Create.3.3MinGPU basic examplesIn the following listings,we used a reduced notation.For brevity,we implied that all required initialization has already been done and omit array and program initializa-tion code from C++program.The example of a simplified ‘Hello,World!’is given in Listing2.3.3.1Taking image derivativesTaking image derivatives is arguably the most straight-forward computer vision algorithm.Image derivatives can be taken in three different directions–d x,d y,and d t.As a derivative kernel,we use Prewitt,Sobel or Laplacian3by3 gradient operators.The C++code and Cg program for taking image derivative in the d x direction are given in Listing3.Texture contains an input array and Kernel contains a smoothing kernel.This code contains one more array,Output,than the ‘Hello World’example.This array accumulates the deriv-ative results.Initially,the Output array does not contain any values,so we do not copy this array from a CPU to the GPU; we create it right in the GPU instead.The array we use in call to Output.Create receives the results when we down-load them from the GPU with the CopyFromGPU method.The programs for completing d y derivations are the same,except for the kernel.The Cg program for d t derivations must take two arrays,image1and image2,as input so it must be different.The chosen kernels K for this derivative are a393matrixfilled with a value of one and the number one.We included Cg programs for d t deriva-tions in Listing4.Array T1is an image at time t and array T2is the same image at time t+1.It must be noted that we cannot use the same texture for both the input and output arrays.This is not possible because the values of the points in the input array are used in calculations of more than one output point.Also,the order of calculations is unknown because all the calcula-tions are done in parallel.Listing3contains thefirst Cg program with loops.Of all video cards which exist today,only the latest cards from nVidia support loops in hardware;older graphic hardware does not support hardware loops.This is the reason why the Cg compiler unfolds some loops during the compilation.A Cg compiler can only execute trivial loops.Loops with number of iterations dependent on the input parameters cannot be executed.This leads to using afixed number of iterations in Cg program loops,and consequently multi-plies the number of Cg functions.For example,we have to keep a separate derivative393Cg function for393 derivative kernel,derivative595Cg function for595 derivative kernel and so on.3.3.2Computing image pyramidsThe pyramid computation is another simple vision algo-rithm[1].Pyramids are useful data structures for representing image regions.The lowest level of the pyra-mid is the original image.Each subsequent level in the pyramid is one-fourth of the area of the previous level.The process of going from higher to lower resolution is called reduction,while the opposite operation is called expansion. We have shown only the REDUCE operation,which is computed according to the following formula:g lði;jÞ¼X2m¼À2X2n¼À2wðm;nÞg lÀ1ð2iþm;2jþnÞ:In the above equation,g l is an image at pyramid level l, matrix w contains the weight mask,and i,and j are the indices for the image’s columns and rows,respectively.A C++code and a Cg program for REDUCE operation are listed in Listing5.In this example,the input and output array sizes do not match.Because each pyramid reduction effectively reduces the image size by half in both dimensions,the output array side is half as long as the input array side.The important question is how do we determine the values of array ele-ments outside of the array boundaries?In two previous examples,we were able to access such elements.In all of the aforementioned examples,elements located outside ofJ Real-Time Image Proc。
DB33∕T 1136-2017 建筑地基基础设计规范
5
地基计算 ....................................................................................................................... 14 5.1 承载力计算......................................................................................................... 14 5.2 变形计算 ............................................................................................................ 17 5.3 稳定性计算......................................................................................................... 21
主要起草人： 施祖元 刘兴旺 潘秋元 陈云敏 王立忠 李冰河 （以下按姓氏拼音排列） 蔡袁强 陈青佳 陈仁朋 陈威文 陈 舟 樊良本 胡凌华 胡敏云 蒋建良 李建宏 王华俊 刘世明 楼元仓 陆伟国 倪士坎 单玉川 申屠团兵 陶 琨 叶 军 徐和财 许国平 杨 桦 杨学林 袁 静 主要审查人： 益德清 龚晓南 顾国荣 钱力航 黄茂松 朱炳寅 朱兆晴 赵竹占 姜天鹤 赵宇宏 童建国浙江大学 参编单位： （排名不分先后） 浙江工业大学 温州大学 华东勘测设计研究院有限公司 浙江大学建筑设计研究院有限公司 杭州市建筑设计研究院有限公司 浙江省建筑科学设计研究院 汉嘉设计集团股份有限公司 杭州市勘测设计研究院 宁波市建筑设计研究院有限公司 温州市建筑设计研究院 温州市勘察测绘院 中国联合工程公司 浙江省电力设计院 浙江省省直建筑设计院 浙江省水利水电勘测设计院 浙江省工程勘察院 大象建筑设计有限公司 浙江东南建筑设计有限公司 湖州市城市规划设计研究院 浙江省工业设计研究院 浙江工业大学工程设计集团有限公司 中国美术学院风景建筑设计研究院 华汇工程设计集团股份有限公司
简述离散余弦变换(dct)和行程编码(rle)的原理。
简述离散余弦变换（dct）和行程编码（rle）的原理。
离散余弦变换（DCT）和行程编码（RLE）是常用的信号处理和数据压缩技术。
它们在图像、音频和视频压缩等领域中得到广泛应用。
离散余弦变换（DCT）是一种将时间或空间域的连续信号转换为频率域的离散信号的技术。
其原理是将输入信号分解成一系列频率分量，其中每个分量的幅度和相位信息可以用来表示原始信号的特征。
DCT 主要用于图像和音频压缩中，它能够将信号的能量有效地集中在较少的系数上，从而实现数据的稀疏表示。
常见的DCT变换包括一维DCT 和二维DCT，其中二维DCT常用于图像压缩。
行程编码（RLE）是一种基于重复数据的压缩技术。
其原理是将连续重复的数据序列替换为一个计数值和一个对应的数据值。
这样可以大大减少重复数据的存储空间，提高数据传输的效率。
RLE适用于包含大量相同或相似数据的场景，例如在图像和视频中，通常某些连续的像素值或颜色值会有较高的重复率。
RLE可以分为行程编码和列程编码两种形式，分别针对图像和音频/视频数据的不同特点进行优化。
在实际应用中，DCT和RLE常常结合使用，以实现更高效的信号压缩。
首先，通过DCT将信号转换为频域表示，然后利用RLE对频域系数进行编码。
这样可以利用DCT的能量集中特性减少RLE编码的数据量，进一步提高压缩比。
这种组合方法在JPEG图像压缩和MPEG视频压缩等标准中得到了广泛应用。
总之，离散余弦变换（DCT）和行程编码（RLE）是两种重要的信号处理和数据压缩技术。
通过DCT可以将信号转换为频域表示，而RLE则通过编码重复数据提高数据压缩率。
它们的组合应用可以在图像、音频和视频等领域中实现高效的数据压缩。
《小型微型计算机系统》期刊简介
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《小型微型计算机系统》期刊简介
《小型微型计算机系统》创刊于1980年，由中国科学院主管、中国科学院沈阳计算技术研究所主办,为中国计算机 学会会刊.
创刊40年来，该刊主要面向国内从事计算机研究和教学的科研人员与大专院校的教师，始终致力于传播我国计算 机研究领域最新科研和应用成果，发表高水平的学术文章和高质量的应用文章,坚持严谨的办刊风格，因而受到计算机 业界的普遍欢迎.
IBM Cognos Transformer V11.0 用户指南说明书
generalized hypergeometric functions
generalized hypergeometric functions什么是广义超几何函数（Generalized Hypergeometric Functions）？广义超几何函数是数学中的一类特殊函数，由高阶级数表示，经常用来解决复杂的微分方程、积分以及其他数学问题。
它是实分析、复分析、非线性分析以及应用数学中一个非常重要的工具。
广义超几何函数最早由奥伊勒-柯赫斯的数学家们引入，他们通过对一个收敛的超几何级数进行推广和推导，从而提出了这一概念。
超几何级数是指形如下述形式的级数：\[ \sum_{n=0}^{\infty} \frac{(a_1)_n (a_2)_n \cdots (a_p)_n}{(b_1)_n (b_2)_n \cdots (b_q)_n} \frac{z^n}{n!} \]其中，(a)_n表示升序Pochhammer符号，定义为：\[ (a)_n = a(a+1)(a+2)\cdots(a+n-1), \ (a)_0 = 1 \](a_j)_n和(b_j)_n分别表示a_j和b_j的升序Pochhammer符号的乘积。
这些参数a_j和b_j可以是任意实数或者复数。
超几何级数的收敛性取决于参数a_j、b_j和变量z之间的关系。
当超几何级数收敛时，可以将其理解为一个函数，称为超几何函数。
然而，由于限制收敛性，超几何函数的应用受到一定的限制。
广义超几何函数是超几何函数的推广形式，它通过引入更多的参数来克服超几何函数的收敛性限制。
广义超几何函数的定义如下：\[ F(a_1, a_2, \cdots, a_p; b_1, b_2, \cdots, b_q; z) =\sum_{n=0}^{\infty} \frac{(a_1)_n (a_2)_n \cdots (a_p)_n}{(b_1)_n (b_2)_n \cdots (b_q)_n} \frac{z^n}{n!} \]广义超几何函数的参数a_j、b_j和变量z可以是任意实数或者复数，并且广义超几何函数有更强的收敛性。
LEC11-Ordinary-Kriging
LEC11: Ordinary Kriging1. Ordinary Kriging with C ij2. Ordinary Kriging with γij3. ExampleREADING ASSIGNMENT •This note and•Chpt. 12 of the textLast time we introduced the idea of kriging and discussed in detail the simple kriging (SK). Today, we will continue our discussion on ordinary kriging (OK). First, we will derive the ordinary kriging equations using covariance, then the OK with variogram, and finally give an example.1.Ordinary Kriging Using CovarianceRemember: Simple Kriging(SK) is the kriging with the second – order stationary hypothesis (i.e., mean is constant and known). Ordinary Kriging(OK) is the kriging also with the second – order stationary hypothesis (i.e., mean is constant but unknown).•Second-order stationary hypothesisE[Z(x)] = m (constant and unknown)andC(h) = E[(Z(x) – m)(Z(x+h) – m)] (depends on h) •Orinary Kriging EstimatorConsider, for example, the following problem: we want to estimate the concentration Z0 = Z(x0) based on five measurements at Z1, (5)Z5Z1 **Z0Z4**Z3Z2 **Note: we can estimate Z i at any location or the field of Z(x) by changing the location of Z 0 ,Also note : When we derive SK, we made the following transformation since m is known . For OK, we can’t do this because m is unknown and we will work with the original variable Z .• We will use the same idea for SK, i.e., finding the estimator Z 0* such that:1)i ni i Z Z ∑==10*0λ (linear )2) )()(0*0Z E Z E = (unbiasedness )3) The variance of the estimation error is minimized. (best )•The Condition for Unbiasedness For Z 0* to be unbiased, we have to havem m orm Z E ormZ E orZ E Z E ni i i ni ii ni i ====∑∑∑===1010100*0)()()()(λλλOr 110=∑=ni i λAbove is the condition for unbiasedness , i.e., the summation of allweights has to be one .Question: Is SK estimator unbiased? Is the sum of SK weights equal to one?•Variance of the Estimation ErrorThe estimation error is given by Z 0* - Z 0 . However, we can’tcalculate the error because the true value, Z 0, is unknown. Instead, we will minimize the variance of the error.The variance of the estimation error is given by20*020*00*0)]([])[()][Z Z E Z Z E Z Z Var −−−=−(because 22)]([][][X E X E X Var −=Since the last term 0)(0*0=−Z Z E (although m is unknown but it is constant), wehave])[()][20*00*0Z Z E Z Z Var −=−Replacing Z 0* with the weighted linear average i ni i Z ∑=10λ in above equation, we have][][2][][2][2])[(200101120010110020100210201020*0Z E Z Z E Z Z E Z E Z Z E Z Z E Z E Z Z E Z E Z Z E Z Z E i ni i n i j i nj j ii n i i n i j i n j j i i n i ii n i i i n i i +−==+⎥⎦⎤⎢⎣⎡−⎥⎦⎤⎢⎣⎡==+⎥⎦⎤⎢⎣⎡−⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛==⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛−=−∑∑∑∑∑∑∑∑∑=========λλλλλλλλλWe need to specify the covariance function, which depends only on the separation distance, h ij , under the 2nd – order stationary assumption:2][),()()(mZ Z E Z Z C h C x x C C j i j i ij j i ij −====−=Note: here m is non-zero.Therefore,)0(2])[(010110020*0C C C Z Z E i ni i ni ij nj j i +−=−∑∑∑===λλλ•Method of Lagrange MultiplierHow do we minimize above error variance under the unbiasedcondition of 110=∑=ni iλ ?Answer:We’ll use the Method of Lagrange Multiplier.The method of Lagrange multiplier is a procedure for converting a constrained minimization problem into an unconstrained one. If we try to tackle the minimization of the error variance, as an unconstrained problem, we run into difficulties. Setting the n partial derivatives to 0 will produce n equations and n unknowns. The unbiasedness condition will add another equation without adding any more unknowns. This leaves us with a system of n +1 equations and only n unknowns, the solution of which is not straightforward. To avoid this awkward problem, we introduce another unknown (μ), into our equation. This new variable (μ) is called Lagrange multiplier or parameter.Let⎟⎠⎞⎜⎝⎛−++−==⎟⎠⎞⎜⎝⎛−+−=−∑∑∑∑∑=====ni ii n i i ij n j j i n i n i i C C C Z Z E Z Z E 1001010011020*020*012)0(212])[(])[(λμλλλλμWarning: we add the last term into the error variance.Adding terms to an equation is a tricky business; we have to be sure we do not upset the equality. The way we have chosen to do it above is safe because the term we are adding at the end is 0 due to the unbiasedness condition:012;01;11011=⎟⎠⎞⎜⎝⎛−=−=∑∑∑===n i ini i ni i λμλλNow, we ready to minimize this new error variance.• Minimizing the Error VarianceTo minimize the Error Variance, we need to take the partial derivatives of thevariance w.r.t. i 0λ(i = 1,…, n) as well as μ, i.e.,{}{}0])[(),...,1(0])[(20*020*00=−∂∂==−∂∂Z Z E n k Z Z E KμλThe derivatives w.r.t. i 0λare rewritten as{}⎭⎬⎫⎩⎨⎧⎟⎠⎞⎜⎝⎛−++−∂∂==−∂∂∑∑∑∑====n i i i n i i n i ij n j j i K KC C C Z Z E 100101100020*0012)0(2])[(λμλλλλλ where the first term on RHS can be derived askj n j j n i ij n j j i K C C ∑∑∑====⎭⎬⎫⎩⎨⎧∂∂10110002λλλλSimilarly, the second term isko i n i i K C C 220100=⎭⎬⎫⎩⎨⎧∂∂∑=λλthe third term is zero, and the fourth term is .μλμλ212100=⎭⎬⎫⎩⎨⎧⎟⎠⎞⎜⎝⎛−∂∂∑=n i i KPutting them together and setting it to zero, we have{}0222])[(1020*00=+−=−∂∂∑=μλλko kj n j j K C C Y Y Eorko kj nj j C C =+∑=μλ10 Also, we need to take care of the derivative w.r.t. μ{}0])[(20*0=−∂∂Z Z E μor{}⎭⎬⎫⎩⎨⎧⎟⎠⎞⎜⎝⎛−++−∂∂==−∂∂∑∑∑∑====n i i i n i i ij n j j i n i C C C Z Z E 10010100120*012)0(2])[(λμλλλμμ Notice only the last term is a function of μ. So,{}012])[(1020*0=⎟⎠⎞⎜⎝⎛−=−∂∂∑=n i i Z Z E λμor∑==ni i 101λFinally, putting them together, the system of linear equation we need to solve is1),...,1(101===+∑∑==ni i ko kj n j jn k C C λμλAbove is the Oridinary Kriging equations which is a system of linear equation about i0λ, i.e.,1......... (020100)0120110202022202110101012201110=+++=++++=++++=++++n n nn n n n n n n n C C C C C C C C C C C C λλλμλλλμλλλμλλλWe can write above system in matrix notationC λ0 = C 0where⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=01...11.............1...1111nn n n C C C C C ⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=μλλλn 0100... ⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=1...0100n C C C• The Estimation ErrorRecall),...,1(10n i C C io ij n j j==+∑=μλMultiplying each of the n equations by λi produces the following:),...,1(10n i C C io i ij n j j i ==⎟⎟⎠⎞⎜⎜⎝⎛+∑=λμλλSumming these n equations leads to an expression for the double summation:io n i i ij n j j n i i C C ∑∑∑====⎟⎟⎠⎞⎜⎜⎝⎛+1101λμλλ orio ni i n i i n i ij n j j i C C ∑∑∑∑=====+1101100λμλλλio ni i n i ij n j j i C C ∑∑∑====+11100λμλλμλλλ−=∑∑∑===io ni i n i ij n j j i C C 11100 We know from previous derivation,=+−==−=−∑∑∑===)0(2])[()][010110020*00*0C C C Z Z E Z Z Var i ni in i ij n j j iλλλTherefore,μλλμλλλλ−−==+−−==+−==−=−∑∑∑∑∑∑======io ni ii n i iio n i ii ni in i ij n j ji C C C C C C C C Z Z E Z Z Var 100101001011020*00*0)0()0(2)0(2])[()][Note: The error variance of SK is given by0100*)0(][i ni iC C Z Z Var ∑=−=−λQuestion: Is the error variance of OK smaller than SK?2. O rdinary Kriging Using Variogram•The relationship between C ij and γij ()[][][][]{}[][][][])()0(2212122222222ij ij j i ji j j i i j i ij h C C C m Z Z E m Z E Z Z E Z E Z E Z Z E Z E Z Z E −=−=+−−=−=+−=−=σγi.e.,ij ij C C −=)0(γ or ij ij C C γ−=)0(• OK equations using γijNow, replacing C ij in the following equations with γij),...,1(10n k C C ko kj n j j==+∑=μλwe have),...,1()0(])0([10n k C C kokj n j j =−=+−∑=γμγλor),...,1()0()0(10n k C C kokj n j j =−=+−∑=γμγλor),...,1(10n k kokj n j j ==−∑=γμγλAbove system should solved together with∑==ni i 101λWe can write above system in matrix notationγ λ0 = γ0 where⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=01...11.............1...1111nn n n γγγγγ ⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−=μλλλn 0100... ⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=1...0100n γγγ• OK Estimation Error using γijμγλμγλμλ−==−−−==−−=−∑∑∑===io n i iio ni iio ni iC C C C Y Y Var 1010100*])0([)0()0()][3.Example: In your text, an example of how OK works is given for a data set of 7sample values. As an even smaller example to illustrate the mechanics of OK, suppose we consider just a subset of 3 of these 7 points, as given in the following, and want to predict the value of V at the new location (65, 137)Z2=696*Z1=477* Z0*Z3=227*Sample x y Z dij1 61 139 477 4.472 63 140 696 3.613 64 129 227 8.06where the distance between them areThe OK equations are:1330201030333012011020302220211010133012201110=++=+++=+++=+++λλλμλλλμλλλμλλλC C C C C C C C C C C C n nor⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛10111111302010302010333231232221131211C C C C C C C C C C C C μλλλThe covariance function or theoretical model used in the text is the exponential model with nugget,⎪⎩⎪⎨⎧>⎟⎠⎞⎜⎝⎛−=+=0exp 0)(110h if L h C h if C C h CSuppose for this small example that the nugget effect C1 is 0, the range is 10/3, and the sill is C(0) is 10, compute the coefficient matrix⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛011111036.044.0136.01011.5144.011.5100111111333231232221131211C C C C C C C C Cand⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛180.039.361.21302010C C CThe OK equations⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛180.039.361.2011111036.044.0136.01011.5144.011.510302010μλλλSolve this system of linear equations with MATLAB, we obtain⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛44.230.043.027.0302010μλλλ• Compare with the Inverse distanceAbove results or the weights we obtained with OK do not seem very interesting until they are compared with the strictly inverse distance-based weights as given in the table below:Weights (Inverse Distance)Weights (Kriging)Distance to estimation point 10.36 0.27 4.47 20.45 0.43 3.61 3 0.20 0.30 8.10Note: Point 1 is much closer to the point (than Point 3) we want to estimate, yet has a smaller kriging weight.Can you explain this apparent reversal in the ranks of the weights with OK?• The Z 0 is given by496227*30.0696*43.0477*27.0330220110*0==++==++=Z Z Z Z λλλ• The Estimation Error16.544.280.0*30.039.3*43.061.2*27.010)0()][100*0=+−−−==−−=−∑=μλio ni iC C Z Z Varand the standard deviation is 2.27.。
transform的relabel, tolabel, colorize方法
transform的relabel, tolabel, colorize方法【原创实用版4篇】目录（篇1）1.介绍 transform 模块2.详述 relabel 方法3.详述 tolabel 方法4.详述 colorize 方法5.总结正文（篇1）1.介绍 transform 模块在深度学习领域，尤其是计算机视觉领域，数据预处理非常重要。
其中，transform 模块是 Pillow 库中一个非常实用的工具，可以帮助我们对图像进行各种变换，如缩放、旋转、翻转等。
这使得我们可以在不同的模型训练过程中使用同一张图像，从而提高训练效果。
2.详述 relabel 方法relabel 方法是 transform 模块中的一个方法，主要作用是对图像中的标签进行重新标记。
在进行数据增强时，我们可能会对原始图像进行各种变换，导致原始标签与变换后的图像不再匹配。
这时，relabel 方法就可以派上用场，它会自动根据变换后的图像生成新的标签。
这样，在训练过程中，模型就可以根据新的标签进行学习，从而提高模型的泛化能力。
3.详述 tolabel 方法tolabel 方法是 transform 模块中的另一个方法，它的主要作用是将图像中的像素坐标转换为标签坐标。
在实际应用中，我们常常需要对图像中的某一区域进行特定的操作，如裁剪、缩放等。
这时，我们可以使用tolabel 方法将图像中的像素坐标转换为对应的标签坐标，从而实现对特定区域的操作。
4.详述 colorize 方法colorize 方法是 transform 模块中的一个非常有趣的方法，它可以将灰度图像转换为彩色图像。
这个方法在 Pillow 库中是通过将灰度图像与一个调色板进行映射实现的。
这样，我们可以将原本单调的灰度图像转换为丰富多彩的彩色图像，从而提高图像的观赏性。
5.总结总的来说，transform 模块中的 relabel、tolabel 和 colorize 方法为我们在图像处理过程中提供了很大的便利。
罗氏应变应力公式手册
罗氏应变应力公式手册ε=σ/E其中，ε表示应变，σ表示应力，E表示弹性模量。
弹性模量是材料的一种力学性质，它衡量了材料在受到力的作用下发生形变的能力。
弹性模量越大，材料在受到力的作用下发生的形变越小，说明材料越刚性。
相反，弹性模量越小，材料在受到力的作用下发生的形变越大，说明材料越柔软。
ν = -ε_lateral / ε_longitudinal其中，ν 表示泊松比，ε_lateral 表示横向应变，ε_longitudinal 表示纵向应变。
泊松比描述了材料在受到力的作用时的横向变化情况。
当材料受到压缩时，泊松比是正值；当材料受到拉伸时，泊松比是负值。
泊松比越大，材料在受到外力作用时的横向变化越明显。
除了哈克定律和泊松比公式，罗氏应变应力公式还可以通过材料的代表性模型来计算应变和应力的关系。
常见的代表性模型包括胡克模型和麦克斯韦模型。
胡克模型将材料看作是由弹簧和几何高度连接的颗粒组成，它认为应变是与应力成正比的。
σ=kε其中，σ表示应力，ε表示应变，k表示材料的弹簧常数。
麦克斯韦模型是胡克模型的扩展，它考虑到材料在受到外力作用时的滞后效应。
麦克斯韦模型的公式为：σ = kε + β(dε / dt)其中，σ 表示应力，ε 表示应变，k 表示材料的弹簧常数，β 表示材料的阻尼系数，dε / dt 表示应变的时间导数。
通过以上公式和模型，我们可以计算材料在受到力的作用时产生的应变和应力。
这些公式不仅适用于均匀材料，也适用于各种复杂材料和结构。
它们为材料力学的研究和应用提供了重要的理论基础。
在工程实践中，我们可以通过罗氏应变应力公式手册来查阅和使用这些公式和模型。
手册通常会包含各种材料的弹性模量、泊松比、弹簧常数和阻尼系数的数值，以及具体计算步骤和例题。
通过手册，我们可以快速准确地计算出材料在受力下的应变和应力，为工程设计和应用提供参考。
自适应分形矢量量化编码
自适应分形矢量量化编码
洪喜勇;陈贺新
【期刊名称】《长春工业大学学报（自然科学版）》
【年(卷),期】2001(022)004
【摘要】提出了一种自适应分形矢量量化编码方法.对图像进行自适应四叉树分割,并构造粗糙的均值图像.误差图像进行分形矢量量化编码时,使用设计的自适应二维维纳数字滤波器,对收缩的均值图像进行滤波后,可构造好的码书.实验证明,本方法码书不需外部训练,解码不需要迭代,可以改善重建图像的视觉质量,使压缩比和PSNR 都有明显提高.
【总页数】5页(P46-50)
【作者】洪喜勇;陈贺新
【作者单位】吉林大学信息学院,;吉林大学信息学院,
【正文语种】中文
【中图分类】TN919.81
【相关文献】
1.改进的分形矢量量化编码 [J], 洪喜勇;陈贺新
2.基于矢量量化的层次分形编码方法 [J], 印鉴;魏思兵
3.基于矢量量化的图象分形压缩编码 [J], 沈建军;涂丹;沈振康
4.基于小波近似的分形矢量量化图像编码方法 [J], 洪喜勇
5.基于自适应小波变换和矢量量化的图像压缩编码 [J], 王雪梅;何南忠
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聚合物流变学全套公式
1克罗内克尔符号九个分量2、哈密顿算符用于矢量运算时3、应力张量应力张量是应力状态的数学表示。
数学上应力为二阶张量，三维空间中需九个分量（三个正应力分量和六个剪应力分量）来确定。
用应力张量形式表示为其中， 第一个下标表示力的作用面的法线方向，第二个下标表示力作用的方向，如σxy 表示作用在与x 垂直的平面上的应力分量，方向指向y 。
当i=j 时，表示应力方向与外法线方向相同，称为应力张量的法向分量， σxx σyy σzz 分别垂直于与x 、y 、z 垂直的平面上。
当i≠j 时，表示应力分量作用在相应面的切线方向上，称为剪切分量，如σxy σyz σzx 。
按照Caucky 应力定律，在平衡时物体受的合外力和合外力矩等于0，所以平衡时应力张量为对称张量，只有6个独立分量。
三个法向应力分量和三个剪切应力分量。
1()0()ij i j i j e e i j δ=⎧==⎨≠⎩ 111213212223313233100010001δδδδδδδδδ⎡⎤⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦123123i i e e e e x x x x ∂∂∂∂∇=++=∂∂∂∂ i i i i e x ∇=∇∂∇=∂ 其中，0lim s Fs δδσδ→=xx xy xz yx yy yz zx zy zz σσσσσσσσσ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦......xx xy xz yy yz zz σσσσσσ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦4、全导数形式的连续性方程5、 为全微分-偏微分关系算符,也叫实质微分算符.其中, 左边表示的函数称:随体导数,指物理量随着流体质元一起运动时所发生的变化率,或者是当流体的微元体积上的一点在dt 时间内从进入微元体积的空间位置(x,y,z)移动到离开微元体积的的空间位置(x+dx,y+dy,z+dz)时,物理量随时间的变化率. 它由两部分组成,一是物理量的局部变化,即在空间一个固定点上随时间的变化,由场的不稳定性引起;二是物理量的对流变化,即由于流体质点的运动,从一点转移到另一点时所发生的变化,由空间位置变化引起的变化,为对流导数,由场的不均匀性引起. 适用于牛顿或非牛顿\可压缩或不可压缩流体6、动量方程其他形式的动量方程（1）（2）....d V V V V divV dt ρρρρρρ=-∇-∇+∇=-∇=- 流体的质量散度，反映了流动场中某一瞬间区的流量发散程度 (410)x y z D v v v Dt t x y z ∂∂∂∂=+++-∂∂∂∂.(228)dv g dtρσρ=∇+-.()..(229)dv P g dt P ggradP div g ρδτρδτρτρ=∇-++=-∇+∇+=-++-yx x xx zx x dv P g dt x x y z τττρρ∂⎛⎫∂∂∂=-++++ ⎪∂∂∂∂⎝⎭y xy yy zy y dv P g dt y x y z τττρρ∂∂∂⎛⎫∂=-++++ ⎪∂∂∂∂⎝⎭yz xz z zz z dv P g dt z x y z τττρρ∂⎛⎫∂∂∂=-++++ ⎪∂∂∂∂⎝⎭（3）在x 方向在y 方向在z 方向式中左边括号中是流场中某微团的加速度,即随流导数,由两部分组成,第一项是表示速度随时间的变化率,是局部加速度,其余三项是随空间坐标变化,是迁移加速度. 由于ρ是单位体积的质量,所以左边相当于力,是惯性力项,反映单位时间单位体积内流体动量的增量.• 右边第一项是静压力项,反映静压力对动量的影响;• 第二项是粘性力项,反映流体粘性对动量的影响;• 第三项是重力项,反映重力对动量的影响.• 可见, 惯性力=静压力+粘性力+重力.• 任何流体都适用.• 由于高分子流体的粘度很大,重力常忽略不计.影响流体的流动主要是压力和粘弹力.流动形式可区分为:压力流和拖曳流.7、能量方程流动场中普通的能量守恒方程yx x x x x xx zx x y z x v v v v P v v v g t x y z x x y z τττρρ∂⎛⎫⎛⎫∂∂∂∂∂∂∂+++=-++++ ⎪ ⎪∂∂∂∂∂∂∂∂⎝⎭⎝⎭y y y y xy yt zy x y z y v v v v P v v v g t x y z y x y z τττρρ∂∂∂∂∂∂∂⎛⎫⎛⎫∂+++=-++++ ⎪ ⎪∂∂∂∂∂∂∂∂⎝⎭⎝⎭yz xz z z z z zz x y z z v v v v P v v v g t x y z z x y z τττρρ∂⎛⎫⎛⎫∂∂∂∂∂∂∂+++=-++++ ⎪ ⎪∂∂∂∂∂∂∂∂⎝⎭⎝⎭...(.).E Ev q v g v tρρσρ∂=-∇-∇+∇+∂()()().....(232)v dT P c T P v q v P v dt T P T v q v T ρρρττ⎡⎤∂⎛⎫=--∇-∇+∇-∇⎢⎥ ⎪∂⎝⎭⎢⎥⎣⎦⎡⎤∂⎛⎫=-∇-∇+∇-⎢⎥ ⎪∂⎝⎭⎢⎥⎣⎦：：用于求温度分布的能量守恒方程式中左边是单位时间内某一点温度的变化,对于不可压缩高聚物流体,此项可忽略不计.第二项是由热传导引起的温度变化,第三项是由机械功变为热能引起的温度变化.8、牛顿流体的本构方程9、幂律流体的本构方程 y x z v x y z y y x x z xx yy zz xy y x z y x z z xz yz q q q T T T T P c v v v T t x y z x y z T v v v v v x y z y x v v v x y z v v v v z x z y ρρττττττ⎡⎤∂⎛⎫⎛⎫∂∂∂∂∂∂∂⎛⎫+++=-++-⎢⎥ ⎪ ⎪ ⎪∂∂∂∂∂∂∂∂⎝⎭⎢⎥⎝⎭⎝⎭⎣⎦⎧∂∂⎡⎤⎛⎫∂∂∂+++++ ⎪⎢⎥∂∂∂∂∂∂⎛⎫∂∂⎣⎦⎝⎭+++ ⎪∂∂∂∂⎛⎫∂∂∂⎝⎭⎛⎫+++ ⎪ ⎪∂∂∂∂⎝⎭⎝⎭(454)⎫⎪⎪⎪⎪-⎨⎬⎪⎪⎪⎪⎩⎭x yx v r y τηη∂==∂ {}1n kr r τ-=-。
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4. λ1 > 0 and λ2 > 0?
Parameters: Gaussian std. dev, window size, threshold
CSE152, Spr 11 Intro Computer Vision CSE152, Spr 11 Intro Computer Vision
What to do with edges?
Picking KLH Particles in Stage 1
Zhu et al., IEEE Transactions on Medical Imaging, In press, 2003
CSE152, Spr 11 Intro Computer Vision CSE152, Spr 11 Intro Computer Vision
– Y = f(x, a1,a2,…ap) – Or g(x,y,a1,a2,…ap) = 0 – a1, a2, … ap are the parameters – The parameter space is p-dimensional – The accumulating array is LARGE!
Hough transform algorithm
• Typically use a different parameterization
– d is the perpendicular distance from the line to the origin – θ is the angle this perpendicular makes with the x axis – Why?
⎡ ∑ I 2 x C ( x, y ) = ⎢ I Iy ⎢ ∑ x ⎣
∑ I I ⎤ ⎥ ∑ I ⎥ ⎦
x y 2 y
So, to detect corners
• • • • • Filter image with a Gaussian. Compute the gradient everywhere. Move window over image and construct C over the window. Use linear algebra to find λ1 and λ2.
• R, θ representation of line • Maximum accumulator value is 6
CSE152, Spr 11 Intro Computer Vision
2
Hough Transform for Curves
(Generalized Hough Transform) The H.T. can be generalized to detect any curve that can be expressed in parametric form:
Image Accumulator
Hough Transform: “Noisy line”
Image Accumulator
• R, θ representation of line • Maximum accumulator value is 4
CSE152, Spr 11 Intro Computer Vision
• Accurately fitting parametric curves (e.g., lines) to grouped edge points.
CSE152, Spr 11
Intro Computer Vision
CSE152, Spr 11
Intro Computer Vision
1
Finding lines in an image
Intro Computer Vision
CSE152, Spr 11
Intro Computer Vision
CSE152, Spr 11
Line fitting cont.
2. Substitute d back into E where where n=(a b)T. 3. Minimize E=nTUTUn=nTSn with respect to a, b subject to the constraint nTn = 1. Note that S is given by
y b
Finding lines in an image
y (x0,y0) b
(m0,b0) x m
x
m
image space
Hough space
image space
Hough space
Connection between image (x,y) and Hough (m,b) spaces
• A line in the image corresponds to a point in Hough space • To go from image space to Hough space:
CSE152, Spr 11
Intro Computer Vision
TEM Image of Keyhole Limpet Hemocyanin with detected particles
3D Maps of KLH
(a)
(b)
(c)
(d)
FIG. Three-dimensional maps of KLH at a resolution of 23.5 Å reconstructed using particles extracted either manually or automatically as described in the text. (a), (b) The side- and top- view of a 3D map reconstructed from a set of 1042 manually selected particle images. (c), (d) The side- and top- view of a 3D map from a set of automatically extracted 1243 particle images.
3
Line Fitting
Line Fitting
Given n points (xi, yi), estimate parameters of line axi + byi - d = 0 subject to the constraint that a2 + b 2 = 1 Problem: minimize
CSE152, Spr 11
Intro Computer Vision
CSE152, Spr 11
Intro r Vision
Corner Detection
What is region like if: 1. λ1 = 0?
2. λ2 = 0?
€ 3. λ1 = 0 and λ2 = 0?
Announcements
• Assignment 2: Due today • Midterm: Thursday, May 5 in class
Generalized Hough Transform, line fitting
Introduction to Computer Vision CSE 152 Lecture 11a
Cost Function: Sum of squared distances between each point and the line
with respect to (a,b,d). 1. Minimize E with respect to d: Where is the mean of the data points
CSE152, Spr 11 Intro Computer Vision
Example: Finding circles
Equation for circle is (x – xc)2 + (y – yc)2 = r2 Where the parameters are the circle’s center (xc, yc) and radius r. Three dimensional generalized Hough space.
Intro Computer Vision
• R, θ representation of line • Maximum accumulator value is 20
CSE152, Spr 11 Intro Computer Vision
Hough Transform: Random points
– given a set of points (x,y), find all (m,b) such that y = mx + b
Connection between image (x,y) and Hough (m,b) spaces
• A line in the image corresponds to a point in Hough space • To go from image space to Hough space:
If they are both big, we have a corner.
1. Let e(x,y) = min(λ1(x,y), λ2(x,y))
2. (x,y) is a corner if it’s local maximum of e(x,y) and e(x,y) > τ
Hough Transform: 20 colinear points
Image Accumulator
•
Basic Hough transform algorithm
1. Initialize H[d, θ]=0 ; H is called accumulator array 2. for each edge point I[x,y] in the image for θ = 0 to 180