本文選題：區(qū)域協(xié)方差矩陣 + 二維Gabor小波變換　； 參考：《云南財經(jīng)大學》2017年碩士論文

【摘要】：隨著現(xiàn)代科學技術(shù)的發(fā)展與創(chuàng)新,越來越多的學者加入了人臉識別的研究領(lǐng)域。因為協(xié)方差矩陣具有旋轉(zhuǎn)不變性的特征,一些學者提出了一些基于Gabor特征的區(qū)域協(xié)方差矩陣的人臉識別方法:一種方法為獲取人臉圖像的區(qū)域協(xié)方差矩陣并通過區(qū)域協(xié)方差矩陣的廣義特征值距離來進行人臉識別,但是該方法并未對區(qū)域協(xié)方差矩陣進行降維,由于對數(shù)據(jù)進行Gabor小波變換得到的特征矩陣維數(shù)很大,再求得的區(qū)域協(xié)方差矩陣維數(shù)依然很大,很容易陷入維數(shù)災(zāi)難問題,造成圖像識別率下降;另一種方法為改進的一種方法,在上述方法的基礎(chǔ)上,對區(qū)域協(xié)方差矩陣進行近似聯(lián)合對角化,再通過廣義特征值距離來實現(xiàn)人臉識別,該方法由于將協(xié)方差矩陣降維成近似對角化矩陣,降維過多,可能造成圖像信息損失過多,從而影響人臉識別的識別率。本文從二維人臉數(shù)據(jù)庫出發(fā),將人臉數(shù)據(jù)庫分為五個區(qū)域,通過二維Gabor小波變換獲取人臉圖像的特征信息。為了驗證增加Gabor特征后人臉識別的有效性,提出了7種不同的特征映射函數(shù),再分別計算出不同映射下的區(qū)域協(xié)方差矩陣。針對上面兩種方法存在的缺陷,本文提出三種基于降維的區(qū)域協(xié)方差矩陣的人臉識別方法,即基于二維主成分分析的歐式距離分類法、基于二維主成分分析的馬氏距離分類法和基于二維主成分分析的廣義特征值距離分類法。由于二維主成分分析方法可以利用圖像矩陣直接構(gòu)造圖像的散布矩陣,不需要像主成分分析那樣在特征提取之前需要把圖像矩陣轉(zhuǎn)化為對應(yīng)的向量,經(jīng)過二維主成分分析降維后的區(qū)域協(xié)方差矩陣,有利于提取出重要的臉部特征進行人臉識別,既提取了圖像的重要信息,又不會造成維數(shù)災(zāi)難,提高了人臉識別的識別率。本文為了驗證所提方法在人臉識別上有效性,在未降維的區(qū)域協(xié)方差矩陣人臉識別方法上利用歐式距離分類法、馬氏距離分類法和廣義特征值分類法來進行人臉識別,將未降維的這三種區(qū)域協(xié)方差矩陣方法、基于區(qū)域協(xié)方差矩陣近似聯(lián)合對角化的人臉識別方法和基于降維的三種人臉識別方法分別應(yīng)用在ORL,YALE,PIE和FERET四種人臉數(shù)據(jù)庫中。通過驗證發(fā)現(xiàn)增加Gabor的特征映射函數(shù),人臉識別率更高,基于降維的三種區(qū)域協(xié)方差矩陣的人臉識別方法的識別率要比未降維的區(qū)域協(xié)方差矩陣的的人臉識別方法和基于區(qū)域協(xié)方差矩陣的近似聯(lián)合對角化的人臉識別方法的人臉識別率更高。
[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.
【學位授予單位】：云南財經(jīng)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP391.41

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