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] Eigenfaces is the name given to a set of eigenvectors when they are used in the computer vision problem of human face recognition.〔Ruiz-del-Solar, J and Navarrete, P.''Eigenspace-based face recognition: a comparative study of different approaches'', 2005〕 The approach of using eigenfaces for recognition was developed by Sirovich and Kirby (1987) and used by Matthew Turk and Alex Pentland in face classification.〔Turk, Matthew A and Pentland, Alex P. '' Face recognition using eigenfaces''. Computer Vision and Pattern Recognition, 1991. Proceedings , Computer Society Conference on 1991〕 The eigenvectors are derived from the covariance matrix of the probability distribution over the high-dimensional vector space of face images. The eigenfaces themselves form a basis set of all images used to construct the covariance matrix. This produces dimension reduction by allowing the smaller set of basis images to represent the original training images. Classification can be achieved by comparing how faces are represented by the basis set. == History == The Eigenface approach began with a search for a low-dimensional representation of face images. Sirovich and Kirby (1987) showed that Principal Component Analysis could be used on a collection of face images to form a set of basis features. These basis images, known as Eigenpictures, could be linearly combined to reconstruct images in the original training set. If the training set consists of ''M'' images, principal component analysis could form a basis set of ''N'' images, where ''N < M''. The reconstruction error is reduced by increasing the number of eigenpictures, however the number needed is always less than ''M''. For example if you need to generate a number of N eigenfaces for a training set of M face images, you can say that each face image can be made up of "proportions" of all this K "features" or eigenfaces : Face image1 = (23% of E1) + (2% of E2) + (51% of E3)+...+(1% En). In 1991 M. Turk and A. Pentland expanded these results and presented the Eigenface method of face recognition.〔Turk, Matthew A and Pentland, Alex P. ''Face recognition using eigenfaces''. Computer Vision and Pattern Recognition, 1991. Proceedings , Computer Society Conference on 1991〕 In addition to designing a system for automated face recognition using eigenfaces, they showed a way of calculating the eigenvectors of a covariance matrix in such a way as to make it possible for computers at that time to perform eigen-decomposition on a large number of face images. Face images usually occupy a high-dimensional space and conventional principal component analysis was intractable on such data sets. Turk and Pentland's paper demonstrated ways to extract the eigenvectors based on matrices sized by the number of images rather than the number of pixels. Once established, the eigenface method was expanded to include methods of preprocessing to improve accuracy.〔Draper, Bruce A. and Yambor, Wendy S and Beveridge, J Ross. ''Analyzing pca-based face recognition algorithms: Eigenvector selection and distance measures''. 2002.〕 Multiple manifold approaches were also used to build sets of eigenfaces for different subjects〔Belhumeur, and Kriegman, D. ''What is the set of images of an object under all possible lighting conditions?''. Proceedings '96, 1996 Computer Society Conference on Computer Vision and Pattern Recognition, 1996〕〔Burnstone J and Yin H. ''Eigenlights: Recovering Illumination From Face Images''. Conf Proceedings on IDEAL 2011.〕 and different features, such as the eyes.〔Moghaddam, B and Wahid, W and Pentland, A. ''Beyond eigenfaces: probabilistic matching for face recognition''. Third International Conference on Automatic Face and Gesture Recognition, 1998. Proceedings〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Eigenface」の詳細全文を読む スポンサード リンク
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