改进的Fisher鉴别分析两步算法研究及其在人脸识别中的应用
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摘要
随着计算机技术、图像处理技术的飞速发展，人脸识别(Face Recognition)技术已成为世界和平、国家安全、社会稳定等层面备受关注的研究热点，并逐步形成一门重要的生物特征识别技术。特别是20世纪90年代以来，以主成分分析(PrincipalComponent Analysis, PCA)和线性鉴别分析(Linear Discriminant Analysis, LDA)为代表的子空间方法的进一步研究，有力地促进了人脸识别技术的发展，使得人脸识别技术在防恐、反恐、刑事侦查、机要管理等方面得以广泛应用，并成为刑侦领域不可或缺的重要手段和基准方法。本文通过研究主成分分析与Fisher鉴别分析这两类子空间方法的现有算法与关键问题，寻找两者之间的切合点、研究新算法，旨在提取出不失表征性同时具有较强鉴别力的人脸识别特征。主要工作如下：
围绕人脸图像样本镜像对称特性在主成分分析中的应用展开研究，鉴于人脸呈现出相对严格的关于正面中心垂直线的镜像对称特性，利用镜像图像作为一类人脸虚拟样本，扩大了训练样本容量，克服了人脸姿态、视角、旋转等因素的影响。在深入分析现有的对称主成分分析算法的基础上，针对核对称主成分分析(Kernel basedSymmetrical PCA, KSPCA)算法存在的核函数选取范围类型局限、缺乏特定样本具体分析能力等问题进行研究与改进，提出了基于插值核方法的广义核对称主成分分析(Generalized KSPCA, GKSPCA)算法。
研究了Fisher鉴别分析中鉴别准则的推广、鉴别向量集的正交性、统计不相关性等关键问题，针对现有的两步算法存在鉴别向量类型与个数受限、鉴别特征维数受限及统计相关性的问题，基于在表征空间中提取鉴别特征的算法思想，提出了两种改进的核Fisher鉴别分析两步算法，即WKPCA+LDA与GKSPCA+SLDA。其中，WKPCA即白化的核主成分分析(Whitened Kernel based PCA)，SLDA即基于Fisher对称零空间鉴别准则的LDA。WKPCA+LDA中，提出了NLUSODVs(Non-LinearUncorrelated Space based Optimal Discriminant Vectors)及其一般化求解方法，实现了在非线性统计不相关约束空间(WKPCA子空间)中求解Fisher最佳鉴别向量集的极值问题，在不失一般性的前提下，尽可能地提取出鉴别力更强且更有利于人脸识别的鉴别特征。GKSPCA+SLDA中，推广应用了两级对称准则(镜像奇偶对称表征准则与Fisher对称零空间鉴别准则)，旨在增加鉴别向量的类型与个数，同时，增加鉴别特征的维数，使人脸识别特征的表征力与鉴别力同时实现趋大化。人脸识别实验中，分析了鉴别向量的求解方法及特征选择策略对识别性能的影响，比较了两种改进算法相对于其它传统算法的优势。
提出了图像增强新算法，结合Fisher鉴别分析改进算法使人脸识别更加准确快捷。
针对Fisher鉴别分析中的多种双向二维线性算法，包括双向两步算法及双向组合算法，通过人脸识别实验展开讨论，分析了双向投影矩阵的求解方法及特征选择策略对识别性能的影响，同时，从实验中验证了规律性。
Along with the rapid development of computer technology and image processingtechnology, face recognition technology has become a concerned research focus in areassuch as world peace, state security and social stability, and has gradually formed animportant technology of biological characteristics identification. Especially since the1990s, the further research of principal component analysis (PCA) and linear discriminantanalysis (LDA), which are the representative of subspace method, has effectivelypromoted the development of face recognition technology. As a result, face recognitiontechnology is widely used in areas such as prevention of terrorism, anti-terrorism, criminalinvestigation, code management, and is becoming an indispensable important means and abenchmark method in criminal investigation field. This paper focuses on finding therelevant points between the two kinds of subspace methods through the study on theexisting algorithms and key problems of them. It is designed to extract mostdiscriminating facial features without loss of expressive power, and to put forward somenew effective algorithms. The main works of this article are as follows:
The research spreads around the application of the mirror symmetry characteristic offacial image sample in principal component analysis. Face presents a relatively strictcharacteristic of mirror symmetry about front center vertical line. The use of mirrorimages as a class of virtual face samples can expand the size of training sample set andovercome the impact of factors such as facial pose, visual angle, and rotation changes. Onthe basis of deep analysis of existing symmetrical PCA algorithms, existing problems ofkernel based symmetrical PCA (KSPCA) algorithm are studied and improved, such as thelimitation of selection type of kernel function, the lack of concrete analysis ability aimingat specific samples, and so on. And a generalized kernel based symmetrical PCA(GKSPCA) algorithm is proposed, which is based on the interpolation kernel method.
Some key problems of Fisher discriminant analysis are studied, including thepromotion of discriminant criterion, and orthogonal and statistically uncorrelated set ofdiscriminant vectors. In view of problems of the existing two-phase algorithms, includingthe limitation of types and numbers of discriminant vector and dimensions of discriminant feature, and statistical correlation of discriminant feature, two new two-phase kernel basedFisher discriminant analysis algorithms are proposed based on the algorithm ideaabout“extraction of discriminant features in the expressive space”, includingWKPCA+LDA and GKSPCA+SLDA. Among them, WKPCA namely is whitened kernelbased PCA, and SLDA namely is LDA based on Fisher symmetrical null spacediscriminant criterion. In WKPCA+LDA algorithm, the non-linear uncorrelated spacebased optimal discriminant vectors (NLUSODVs) and its generalized solution method areput forward. The WKPCA+LDA algorithm can realize that the extremal problem of Fisheroptimal discriminant vectors solved in the non-linear statistically uncorrelated constraintspace (WKPCA subspace). Under the premise without loss of generality, theWKPCA+LDA algorithm can extract more discriminating features as many as possible,which are more conducive to face recognition. In GKSPCA+SLDA algorithm, thetwo-stage symmetrical criterion is promoted and applied, which is aimed to increase thetype and number of discriminant vectors and the dimension of discriminant features, thusto achieve the maximization of expressive and discriminating power of face recognitionfeatures. In face recognition experiments, the influences of solving methods and selectionstrategies of discriminant vectors on recognition performance are analyzed, and comparedwith traditional algorithms, advantages of the two new algorithms are raised.
New algorithms of image enhancement are put forward, which combined with thenew Fisher discriminant analysis algorithms will make face recognition much moreaccurate and quicker.
Various two-directional two-dimensional linear algorithms of Fisher discriminantanalysis are discussed through face recognition experiments, including two-directionaltwo-phase algorithms and two-directional combined algorithms. The influences of solvingmethods of two-directional projection matrixs and feature selection strategies onrecognition performance are analyzed. At the same time, the regularities are verified byexperiments.
围绕人脸图像样本镜像对称特性在主成分分析中的应用展开研究，鉴于人脸呈现出相对严格的关于正面中心垂直线的镜像对称特性，利用镜像图像作为一类人脸虚拟样本，扩大了训练样本容量，克服了人脸姿态、视角、旋转等因素的影响。在深入分析现有的对称主成分分析算法的基础上，针对核对称主成分分析(Kernel basedSymmetrical PCA, KSPCA)算法存在的核函数选取范围类型局限、缺乏特定样本具体分析能力等问题进行研究与改进，提出了基于插值核方法的广义核对称主成分分析(Generalized KSPCA, GKSPCA)算法。
研究了Fisher鉴别分析中鉴别准则的推广、鉴别向量集的正交性、统计不相关性等关键问题，针对现有的两步算法存在鉴别向量类型与个数受限、鉴别特征维数受限及统计相关性的问题，基于在表征空间中提取鉴别特征的算法思想，提出了两种改进的核Fisher鉴别分析两步算法，即WKPCA+LDA与GKSPCA+SLDA。其中，WKPCA即白化的核主成分分析(Whitened Kernel based PCA)，SLDA即基于Fisher对称零空间鉴别准则的LDA。WKPCA+LDA中，提出了NLUSODVs(Non-LinearUncorrelated Space based Optimal Discriminant Vectors)及其一般化求解方法，实现了在非线性统计不相关约束空间(WKPCA子空间)中求解Fisher最佳鉴别向量集的极值问题，在不失一般性的前提下，尽可能地提取出鉴别力更强且更有利于人脸识别的鉴别特征。GKSPCA+SLDA中，推广应用了两级对称准则(镜像奇偶对称表征准则与Fisher对称零空间鉴别准则)，旨在增加鉴别向量的类型与个数，同时，增加鉴别特征的维数，使人脸识别特征的表征力与鉴别力同时实现趋大化。人脸识别实验中，分析了鉴别向量的求解方法及特征选择策略对识别性能的影响，比较了两种改进算法相对于其它传统算法的优势。
提出了图像增强新算法，结合Fisher鉴别分析改进算法使人脸识别更加准确快捷。
针对Fisher鉴别分析中的多种双向二维线性算法，包括双向两步算法及双向组合算法，通过人脸识别实验展开讨论，分析了双向投影矩阵的求解方法及特征选择策略对识别性能的影响，同时，从实验中验证了规律性。
Along with the rapid development of computer technology and image processingtechnology, face recognition technology has become a concerned research focus in areassuch as world peace, state security and social stability, and has gradually formed animportant technology of biological characteristics identification. Especially since the1990s, the further research of principal component analysis (PCA) and linear discriminantanalysis (LDA), which are the representative of subspace method, has effectivelypromoted the development of face recognition technology. As a result, face recognitiontechnology is widely used in areas such as prevention of terrorism, anti-terrorism, criminalinvestigation, code management, and is becoming an indispensable important means and abenchmark method in criminal investigation field. This paper focuses on finding therelevant points between the two kinds of subspace methods through the study on theexisting algorithms and key problems of them. It is designed to extract mostdiscriminating facial features without loss of expressive power, and to put forward somenew effective algorithms. The main works of this article are as follows:
The research spreads around the application of the mirror symmetry characteristic offacial image sample in principal component analysis. Face presents a relatively strictcharacteristic of mirror symmetry about front center vertical line. The use of mirrorimages as a class of virtual face samples can expand the size of training sample set andovercome the impact of factors such as facial pose, visual angle, and rotation changes. Onthe basis of deep analysis of existing symmetrical PCA algorithms, existing problems ofkernel based symmetrical PCA (KSPCA) algorithm are studied and improved, such as thelimitation of selection type of kernel function, the lack of concrete analysis ability aimingat specific samples, and so on. And a generalized kernel based symmetrical PCA(GKSPCA) algorithm is proposed, which is based on the interpolation kernel method.
Some key problems of Fisher discriminant analysis are studied, including thepromotion of discriminant criterion, and orthogonal and statistically uncorrelated set ofdiscriminant vectors. In view of problems of the existing two-phase algorithms, includingthe limitation of types and numbers of discriminant vector and dimensions of discriminant feature, and statistical correlation of discriminant feature, two new two-phase kernel basedFisher discriminant analysis algorithms are proposed based on the algorithm ideaabout“extraction of discriminant features in the expressive space”, includingWKPCA+LDA and GKSPCA+SLDA. Among them, WKPCA namely is whitened kernelbased PCA, and SLDA namely is LDA based on Fisher symmetrical null spacediscriminant criterion. In WKPCA+LDA algorithm, the non-linear uncorrelated spacebased optimal discriminant vectors (NLUSODVs) and its generalized solution method areput forward. The WKPCA+LDA algorithm can realize that the extremal problem of Fisheroptimal discriminant vectors solved in the non-linear statistically uncorrelated constraintspace (WKPCA subspace). Under the premise without loss of generality, theWKPCA+LDA algorithm can extract more discriminating features as many as possible,which are more conducive to face recognition. In GKSPCA+SLDA algorithm, thetwo-stage symmetrical criterion is promoted and applied, which is aimed to increase thetype and number of discriminant vectors and the dimension of discriminant features, thusto achieve the maximization of expressive and discriminating power of face recognitionfeatures. In face recognition experiments, the influences of solving methods and selectionstrategies of discriminant vectors on recognition performance are analyzed, and comparedwith traditional algorithms, advantages of the two new algorithms are raised.
New algorithms of image enhancement are put forward, which combined with thenew Fisher discriminant analysis algorithms will make face recognition much moreaccurate and quicker.
Various two-directional two-dimensional linear algorithms of Fisher discriminantanalysis are discussed through face recognition experiments, including two-directionaltwo-phase algorithms and two-directional combined algorithms. The influences of solvingmethods of two-directional projection matrixs and feature selection strategies onrecognition performance are analyzed. At the same time, the regularities are verified byexperiments.
引文
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