Editing Eigenface (section)

== History ==

The eigenface approach began with a search for a low-dimensional representation of face images. Sirovich and Kirby showed that [[principal component analysis]] could be used on a collection of face images to form a set of basis features.<ref name="Kirby1987" /> 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 chosen 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 the ''K'' "features" or eigenfaces: Face image<sub>1</sub> = (23% of E<sub>1</sub>) + (2% of E<sub>2</sub>) + (51% of E<sub>3</sub>) + ... + (1%  E<sub>n</sub>).

In 1991 M. Turk and A. Pentland expanded these results and presented the eigenface method of face recognition.<ref name="Turk1991a" /> In addition to designing a system for automated face recognition using eigenfaces, they showed a way of calculating the [[eigenvectors]] of a [[covariance matrix]] such that computers of the time could 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.<ref>{{cite book | last1=Yambor | first1=Wendy S. | last2=Draper | first2=Bruce A. | last3=Beveridge | first3=J. Ross | title=Empirical Evaluation Methods in Computer Vision | series=Series in Machine Perception and Artificial Intelligence | volume=50 | chapter=Analyzing PCA-based Face Recognition Algorithms: Eigenvector Selection and Distance Measures | publisher=WORLD SCIENTIFIC | year=2002 | pages=39–60 | issn=1793-0839 | doi=10.1142/9789812777423_0003 | isbn=978-981-02-4953-3 | chapter-url=https://www.cs.colostate.edu/evalfacerec/papers/eemcvcsu.pdf}}</ref> Multiple manifold approaches were also used to build sets of eigenfaces for different subjects<ref>{{cite conference | last1=Belhumeur | first1=P.N. | last2=Kriegman | first2=D.J. | title=What is the set of images of an object under all possible lighting conditions? | journal=Proc. IEEE Conference on Computer Vision and Pattern Recognition. | year=1996 | pages=270–277 | doi=10.1109/cvpr.1996.517085| isbn=0-8186-7259-5 }}</ref><ref>{{Cite book | doi=10.1007/978-3-642-23878-9_58|chapter = Eigenlights: Recovering Illumination from Face Images|title = Intelligent Data Engineering and Automated Learning - IDEAL 2011| volume=6936| pages=490–497|series = Lecture Notes in Computer Science|year = 2011|last1 = Burnstone|first1 = James| last2=Yin| first2=Hujun| isbn=978-3-642-23877-2}}</ref> and different features, such as the eyes.<ref>{{cite conference | last1=Moghaddam | first1=B. | last2=Wahid | first2=W. | last3=Pentland | first3=A. | date=1998 | title=Beyond eigenfaces: probabilistic matching for face recognition | journal=Proc. Third IEEE International Conference on Automatic Face and Gesture Recognition | pages=30–35 | doi=10.1109/afgr.1998.670921| isbn=0-8186-8344-9 }}</ref>