人体检测博士论文.ppt
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1、2019/9/8,LPP,UDP and Their Relationship,讲解人: 谢术富,2019/9/8,相关文章,LPP Xiaofei He, Partha Niyogi, “Locality Preserving Projections”, NIPS 2003. Xiaofei He, Shuicheng Yan, Yuxiao Hu, Partha Niyogi, and Hong-Jiang Zhang, Fellow, IEEE, “Face Recognition Using Laplacianfaces”, IEEE TPAMI 27(3), 2005. UDP Ji
2、an Yang, David Zhang, Senior Member, IEEE, Jing-yu Yang, and Ben Niu, “Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Applications to Face and Palm Biometrics”, IEEE TPAMI 29(4), 2007. Relationship Weihong Deng, Jiani Hu, Jun Guo, Honggang Zhang, and Chuang Zhang,
3、 Comments on “Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Application to Face and Palm Biometrics”, IEEE TPAMI 2008.,2019/9/8,Outline,Locality Preserving Projection (LPP) Unsupervised Discriminant Projection (UDP) Comments on LPP and UDP,2019/9/8,Face Recogniti
4、on Using Laplacianfaces,PCA LDA Locality Preserving Projection(LPP) Statistical view of LPP Theoretical analysis of LPP, PCA and LDA Manifold ways or Visual Analysis Experimental Results,2019/9/8,作者的相关信息,He Xiaofei第一作者 Professor of computer science, Zhejiang University, China 简历 2000, Zhejiang Unive
5、rsity, China, BS. 2005, University of Chicago, PhD. 20052007, Yahoo Research Labs, research scientist. 2007Now, Zhejiang University, Professor. 研究方向 Locality Preserving Projections (LPP) and Manifold Learning Information Retrieval Web Search and Mining Face Representation and Recognition 论文著作 Journa
6、l: 11, Conference: 35. He Xiaofei et al., “Face Recognition Using Laplacianfaces”, IEEE TPAMI 2005 27(3),引用次数: 222. 个人主页: http:/people.cs.uchicago.edu/xiaofei/,2019/9/8,作者的相关信息,Yan ShuiCheng第二作者 I am currently Assistant Professor (助理教授) at Department of Electrical and Computer Engineering, National
7、University of Singapore. 简历 1999, Applied Mathematics Department, School of Mathematical Sciences, Peking University, BS. 2004, Applied Mathematics Department, School of Mathematical Sciences, Peking University, Ph.D. 研究方向 Activity and event detection in images and videos Subspace learning and manif
8、old learning Generic object recognition and categorization Biometrics Medical image analysis 论文 Journal: 34, Conference: 66. Yan Shuicheng et al., “Graph Embedding and Extensions: A General Framework for Dimensionality Reduction”, IEEE TPAMI 2007.引用次数:63. 个人主页: http:/www.ece.nus.edu.sg/stfpage/eleya
9、ns/,2019/9/8,作者的相关信息,Yuxiao Hu(胡宇晓) 第三作者 简历 1999, Department of Computer Science and Technology, Tsinghua University, BS. 2001, Department of Computer Science and Technology, Tsinghua University, MS. 20012003, Microsoft Research Asia, Assistant Researcher. 2003Now, Image Formation and Processing Gro
10、up (IFP) in University of Illinois at Urbana-Champaign, Ph.D. 研究方向 Camera/Microphone Array for Dynamic 3D Face Data Collection Building Large Scale 3D Face Database for Face Analysis 3D Face Reconstruction and Recognition Face Detection, Alignment and Recognition User Attention Tracking in Large Dis
11、play 个人主页: http:/www.ifp.uiuc.edu/hu3/,2019/9/8,作者的相关信息,Partha Niyogi I am Professor in the Computer Science and Statistics departments at the University of Chicago. 研究方向 Machine Learning and Information Extraction. The Human Language System. 论文 M Belkin, P Niyogi, “Laplacian Eigenmaps for Dimension
12、ality Reduction and Data Representation”, Neural Computation 2003.引用次数: 591. 个人主页: http:/people.cs.uchicago.edu/niyogi/,2019/9/8,作者的相关信息,HongJiang Zhang Managing Director, Microsoft Advanced Technology Center 简历 Zhengzhou University, Bachelor Technical University of Denmark(丹麦技术大学), Ph.D 研究方向 media
13、computing video and image content analysis, representation, retrieval and browsing Paper Automatic partitioning of full-motion video, Readings in Multimedia Computing and Networking, 2001.引用次数:915. Content based video indexing and retrieval, Multimedia IEEE, 1994.引用次数: 402. 个人主页: http:/ propose an a
14、ppearance-based face recognition method called the Laplacianface approach. By using Locality Preserving Projections (LPP), the face images are mapped into a face subspace for analysis. Different from Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) which effectively see only
15、 the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the
16、 face manifold. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. Theoretical analysis shows that PCA, LDA, and LPP can be obtained from different graph models. We compare the proposed Laplacianface approach with Eigenf
17、ace and Fisherface methods on three different face data sets. Experimental results suggest that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition.,2019/9/8,摘要,我们提出了一种基于表观的人脸识别方法-拉普拉斯脸(Laplacianface). 通过局部保持投影,人脸图像被映射到一个子空间进行分析.不同于
18、基于人脸空间欧式结构的PCA和LDA,LPP找到一个嵌入来保持局部信息,从而得到一个最好的探测到人脸流形结构的人脸子空间. Laplacianfaces是对人脸流形上的Laplace Beltrami 算子的特征函数的最优线性近似.在这种情况下,由光照,表情和姿态的变化所产生的多余变化被减少或去除.理论分析表明, PCA, LDA和LPP可以由不同的图模型产生. 在三个不同的数据集合上我们比较了Laplacianface, Eigenface和Fisherface. 实验结果表明, Laplacianface提供了更好的表示,在人脸识别上有更低的错误率.,2019/9/8,相关背景知识介绍,P
19、CA Matthew Turk and Alex Pentland, “Eigenfaces for Recognition,” Journal of Cognitive Neuroscience 3(1), pp.7186, 1991. LDA Peter N. Belhumeur, Joo P.Hespanha, and David J.Kriegman, “Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection,” IEEE TPAMI 19(7), pp.711720, 1997.,2
20、019/9/8,PCA,目标: 提取方差最大的子空间 n个d-维样本x1,x2,xn,变换W将样本xi变换为yi: yi=WT*xi 输出:数据协方差矩阵的特征值(从大到小排序)所对应的特征向量w1,w2,wk. 特点 与分类目标无关,只能够最大程度地对原始数据进行重构. PCA是一种非常有效的线性降维方法.,2019/9/8,LDA,目标: 选择判别性最强的方向. 假定n个d-维样本x1,x2,xn属于l类,优化目标: m:所有样本平均值,ni:第i类样本数目, 第i类的第j个样本,SB:类间散度矩阵,Sw:类内散度矩阵. 由于类内散度矩阵的奇异(n-ld)问题,先对数据利用PCA降维至低于
21、n-l维,再利用LDA进行降维(FisherFace). 特点: LDA是一种非常有效的线性判别分析方法,在模式识别领域被广泛地采用. 同PCA不同, LDA会选择那些分类能力比较强的投影轴.,2019/9/8,PCA vs. LDA,2019/9/8,LPP,动机 PCA和LDA保持数据的全局结构,而保持局部结构在一些实际应用中也非常重要. LPP的目标是保持数据内在的局部结构. 优化目标(如果样本点在原始空间距离 很小,那么在投影后它们的距离也很小): Sij反映原始空间点的距离度量,构成邻接矩阵,可通过 -近邻或者k近邻定义,若xi和xj越接近,则Sij值越大.,2019/9/8,LPP
22、,通过推导(展开),可得: L:拉普拉斯矩阵. D:反映了数据点的重要性,值越大表示该点越重要(值越大,该点离其他样本点的距离之和越小,该点则越有可能成为其他样本点组成cluster的中心). 增加约束: 对W的值做限制,因为目标是求最小值,保证W的解唯一. 保持数据点的重要性:在原始空间中,若数据点为cluster中心,则在投影空间中也尽可能保持是投影后cluster中心(如果样本X做过中心化处理,YDYT相当于加权的协方差矩阵).,2019/9/8,LPP,最终优化目标: 求解通过广义特征值分解得到解,选择特征值(从小到大排序)对应的特征向量: 这与 等价!,2019/9/8,LPP:从统
23、计观点来看,欲使线性变换w能够在L2意义上最好地保留分布的局部结构,则对任意两个随机变量x,y: 若定义:z=x-y, 则: 若定义指示函数Sij, 则有推导:,d代表Sij中非0项的数目,这里用1/d近似z的概率,2019/9/8,LPP与PCA,当拉普拉斯矩阵L定义为 ,XLXT等价于数据的协方差矩阵(I为单位阵,n为样本点数目,e为每行值为1的列向量). 此时, 即数据的协方差矩阵. S矩阵在LPP中有重要作用: 若保留全局结构,则取k(或 )为无穷大并选择最大特征值所对应的特征向量. 若保留局部结构,则取 足够小并选择最小特征值对应的特征向量.,2019/9/8,LPP与PCA,PCA
24、,LPP,PCA,LPP,判别能力比较(长的线段表示找到的第一维投影方向),对Outlier点的抗干扰能力(长的线段表示找到的第一维投影方向),2019/9/8,LPP与LDA,假定有l类数据,第i类包含ni个样本点,m(i)代表第i类的平均向量,x(i)代表第i类的随机向量,定义X=(x1,x2,xn), SB可以推导为: LDA保留判别信息和数据的整体几何结构. LDA可以由LPP推导出来.,2019/9/8,LPP用于人脸表示,1,PCA降维: 去掉特征值小的主成分,在实验中保留98%的能量,避免XDXT奇异问题. 2,构建最近邻图:利用k近邻确定近邻点. 3,选择权重(Hot Kern
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