Eigenface

Eigenfaces are a set of eigenvectors derived from the covariance matrix of the probability distribution of the high-dimensional vector space of possible faces of human beings. These eigenvectors are used in the computer vision problem of human face recognition.
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Eigenfaces.png
Some eigenfaces.

In layperson's terms, 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. One person's face might be made up of 10% from face 1, 24% from face 2 and so on. This means that if you want to record someone's face for use by face recognition software you can use far less space than would be taken up by a digitised photograph.

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 (say m×n), and then treated as mn-dimensional vectors whose components are the values of their pixels. The eigenvectors of the covariance matrix of the statistical distribution of face image vectors are then extracted.

Since the eigenvectors belong to the same vector space as face images, they can be viewed as if they were m×n pixel face images: hence the name eigenfaces.

Viewed in this way, the principal eigenface looks like a bland androgynous average human face. Some subsequent eigenfaces can be seen to correspond to generalized features such as left-right and top-bottom asymmetry, or the presence or lack of a beard. Other eigenfaces are hard to categorize, and look rather strange.

When properly weighted, eigenfaces can be summed together to create an approximate gray-scale rendering of a human face. Remarkably few eigenvector terms are needed to give a fair likeness of most people's faces, so eigenfaces provide a means of applying data compression to faces for identification purposes.

to do: handling variations in facial expression and lighting conditions

References

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy