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Eigenfaces are a set of eigenvectors used in the computer vision problem of human face recognition. The approach of using eigenfaces for recognition was developed by Matthew Turk and Alex Pentland beginning in 1987, and is considered the first successful example of facial recognition technology.[How to reference and link to summary or text] These eigenvectors are derived from the covariance matrix of the probability distribution of the high-dimensional vector space of possible faces of human beings.

## Eigenface generation Edit

To generate a set of eigenfaces, a large set of digitized images of human faces, taken under the same lighting conditions, are normalized to line up the eyes and mouths. They are then all resampled at the same pixel resolution. Eigenfaces can be extracted out of the image data by means of a mathematical tool called principal component analysis (PCA). Here are the steps involved in converting an image of a face into eigenfaces:

1. Prepare a training set. The faces constituting the training set T should be already prepared for processing.
2. Subtract the mean. The average matrix A has to be calculated and subtracted from the original in T. The results are stored in variable S.
3. Calculate the covariance matrix.
4. Calculate the eigenvectors and eigenvalues of this covariance matrix.
5. Choose the principal components.

There will be a large number of eigenfaces created before step 5, and far fewer are really needed. Select from them those that have the highest eigenvalues. For instance, if we are working with a 100 x 100 image, then this system will create 10,000 eigenvectors. Since most individuals can be identified using a database with a size between 100 and 150, most of the 10,000 can be discarded, and only the most important should remain.

The eigenfaces that are created will appear as light and dark areas that are arranged in a specific pattern. This pattern is how different features of a face are singled out to be evaluated and scored. There will be a pattern to evaluate symmetry, if there is any style of facial hair, where the hairline is, or evaluate the size of the nose or mouth. Other eigenfaces have patterns that are less simple to identify, and the image of the eigenface may look very little like a face.

The technique used in creating eigenfaces and using them for recognition is also used outside of facial recognition. This technique is also used for handwriting analysis, lip reading, voice recognition and medical imaging. Therefore, some do not use the term eigenface, but prefer to use 'eigenimage'.

Basically, eigenfaces are a set of "standardized face ingredients", derived from statistical analysis of many pictures of faces. Any human face can be considered to be a combination of these standard faces. For example, your face might be composed of 10% from eigenface 1, 55% from eigenface 2, and even -3% from eigenface 3. The values connecting a face to an eigenface can be anywhere from 100% to -100%, the higher the value, the closer the face is to that eigenface. Remarkably, it does not take many eigenfaces summed together to give a fair likeness of most faces. Also, because a person's face is no longer recorded by a digital photograph, but instead as just a list of values (one value for each eigenface in the database used), much less space is taken for each person's face.

## Use in facial recognition Edit

Facial recognition was the source of motivation behind the creation of eigenfaces. For this use, eigenfaces have advantages over other techniques available, such as the system's speed and efficiency. Using eigenfaces is very fast, and able to functionally operate on lots of faces in very little time. Unfortunately, this type of facial recognition does have a drawback to consider: trouble recognizing faces when they are viewed with different levels of light or angles. For the system to work well, the faces need to be seen from a frontal view under similar lighting. Face recognition using eigenfaces has been shown to be quite accurate. By experimenting with the system to test it under variations of certain conditions, the following correct recognitions were found: an average of 96% with light variation, 85% with orientation variation, and 64% with size variation. (Turk & Pentland 1991, p. 590)

To complement eigenfaces, another approach has been developed called eigenfeatures. This combines facial metrics (measuring distance between facial features) with the eigenface approach. Another method, which is competing with the eigenface technique uses 'fisherfaces'. This method for facial recognition is less sensitive to variation in lighting and pose of the face than the method using eigenfaces.

Research that applies similar eigen techniques to sign language images has also been made. More can be read here: http://www.geigel.com/signlanguage/index.php or the wiki article eigen sign language

## References Edit

• M. Turk and A. Pentland (1991). Eigenfaces for recognition. Journal of Cognitive Neuroscience 3 (1): 71–86.
• A. Pentland, B. Moghaddam, T. Starner, O. Oliyide, and M. Turk. (1993). "Template:Citeseer". Technical Report 245, M.I.T Media Lab.