基于维数约简的区域协方差矩阵及其在人脸识别中的应用

发布时间：2018-06-15 12:30

本文选题：区域协方差矩阵 + 二维Gabor小波变换　；参考：《云南财经大学》2017年硕士论文

【摘要】：随着现代科学技术的发展与创新,越来越多的学者加入了人脸识别的研究领域。因为协方差矩阵具有旋转不变性的特征,一些学者提出了一些基于Gabor特征的区域协方差矩阵的人脸识别方法:一种方法为获取人脸图像的区域协方差矩阵并通过区域协方差矩阵的广义特征值距离来进行人脸识别,但是该方法并未对区域协方差矩阵进行降维,由于对数据进行Gabor小波变换得到的特征矩阵维数很大,再求得的区域协方差矩阵维数依然很大,很容易陷入维数灾难问题,造成图像识别率下降;另一种方法为改进的一种方法,在上述方法的基础上,对区域协方差矩阵进行近似联合对角化,再通过广义特征值距离来实现人脸识别,该方法由于将协方差矩阵降维成近似对角化矩阵,降维过多,可能造成图像信息损失过多,从而影响人脸识别的识别率。本文从二维人脸数据库出发,将人脸数据库分为五个区域,通过二维Gabor小波变换获取人脸图像的特征信息。为了验证增加Gabor特征后人脸识别的有效性,提出了7种不同的特征映射函数,再分别计算出不同映射下的区域协方差矩阵。针对上面两种方法存在的缺陷,本文提出三种基于降维的区域协方差矩阵的人脸识别方法,即基于二维主成分分析的欧式距离分类法、基于二维主成分分析的马氏距离分类法和基于二维主成分分析的广义特征值距离分类法。由于二维主成分分析方法可以利用图像矩阵直接构造图像的散布矩阵,不需要像主成分分析那样在特征提取之前需要把图像矩阵转化为对应的向量,经过二维主成分分析降维后的区域协方差矩阵,有利于提取出重要的脸部特征进行人脸识别,既提取了图像的重要信息,又不会造成维数灾难,提高了人脸识别的识别率。本文为了验证所提方法在人脸识别上有效性,在未降维的区域协方差矩阵人脸识别方法上利用欧式距离分类法、马氏距离分类法和广义特征值分类法来进行人脸识别,将未降维的这三种区域协方差矩阵方法、基于区域协方差矩阵近似联合对角化的人脸识别方法和基于降维的三种人脸识别方法分别应用在ORL,YALE,PIE和FERET四种人脸数据库中。通过验证发现增加Gabor的特征映射函数,人脸识别率更高,基于降维的三种区域协方差矩阵的人脸识别方法的识别率要比未降维的区域协方差矩阵的的人脸识别方法和基于区域协方差矩阵的近似联合对角化的人脸识别方法的人脸识别率更高。
[Abstract]:With the development and innovation of modern science and technology, more and more scholars have joined the research field of face recognition. Because the covariance matrix has the characteristics of rotation invariance, some scholars have put forward some face recognition methods based on the Gabor characteristic area covariance matrix: one method is to obtain the regional covariance moment of the face image. The array is used for face recognition through the generalized eigenvalue distance of the regional covariance matrix, but the method does not reduce the dimension of the regional covariance matrix. The dimension of the feature matrix is very large because of the Gabor wavelet transform to the data, and the dimension of the regional covariance matrix is still very large, so it is easy to fall into the dimension disaster problem. The rate of image recognition is reduced; another method is an improved method. On the basis of the above method, the region covariance matrix is approximately combined diagonalization, and then the face recognition is realized through the generalized eigenvalue distance. This method reduces the covariance matrix into an approximate diagonalization matrix and reduces the dimension of the image, which may cause the image information. In this paper, we divide the face database into five regions and obtain the feature information of the face image by two-dimensional Gabor wavelet transform. In order to verify the effectiveness of the face recognition after increasing the Gabor features, 7 different feature mapping functions are proposed. The region covariance matrix under different mappings is calculated. Aiming at the defects of the above two methods, this paper proposes three face recognition methods based on the reduced dimension of the regional covariance matrix, namely, the Euclidean distance classification based on the two-dimensional principal component analysis, the martensitic distance classification method based on the two-dimensional principal component analysis and the two-dimensional principal component analysis. The generalized eigenvalue distance classification method, because the two-dimensional principal component analysis method can make use of the image matrix to directly construct the scattered matrix of the image, and do not need to transform the image matrix into the corresponding vector before the feature extraction, like the principal component analysis, and analyze the regional covariance matrix after the two-dimensional principal component analysis. Taking out important facial features for face recognition, it not only extracts the important information of the image, but also does not cause the dimension disaster, and improves the recognition rate of face recognition. In order to verify the effectiveness of the proposed method in face recognition, the Euclidean distance classification method and the martensitic distance are used in the face recognition method of the Undimensionality of the regional covariance matrix. The classification method and the generalized eigenvalue classification method are used to carry out face recognition. The three regional covariance matrix methods, which are non dimensionality reduction, are applied to four face databases, ORL, YALE, PIE and FERET, based on the area covariance matrix approximate joint diagonalization face recognition and the three face recognition methods based on dimensionality reduction. The face recognition rate is higher by adding the feature mapping function of Gabor. The recognition rate of face recognition method based on the three regional covariance matrix based on dimensionality reduction is higher than the face recognition method of the area covariance matrix of the Undimensionality and the approximate joint diagonalization of the face recognition method based on the area covariance matrix.
【学位授予单位】：云南财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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