# eigenface

Some eigenfaces from AT&T Laboratories Cambridge.
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 facial recognition technology that worked. 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

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 persons face.

## Use in facial recognition

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.

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: [1] or the wiki article eigen sign language

## References

eigenvector of the transformation and the blue vector is not. Since the red vector was neither stretched nor compressed, its eigenvalue is 1. All vectors with the same vertical direction - i.e., parallel to this vector - are also eigenvectors, with the same eigenvalue.
Computer vision is the science and technology of machines that see.

As a scientific discipline, computer vision is concerned with the theory and technology for building artificial systems that obtain information from images.
A facial recognition system is a computer application for automatically identifying or verifying a person from a digital image or a video frame from a video source. One of the ways to do this is by comparing selected facial features from the image and a facial database.
A facial recognition system is a computer application for automatically identifying or verifying a person from a digital image or a video frame from a video source. One of the ways to do this is by comparing selected facial features from the image and a facial database.
MIT Media Laboratory Professor Alex (Sandy) Pentland is a pioneer in wearable computers, health systems, smart environments, and technology for developing countries. He is one of the most-cited computer scientists in the world.
eigenvector of the transformation and the blue vector is not. Since the red vector was neither stretched nor compressed, its eigenvalue is 1. All vectors with the same vertical direction - i.e., parallel to this vector - are also eigenvectors, with the same eigenvalue.
In statistics and probability theory, the covariance matrix is a matrix of covariances between elements of a vector. It is the natural generalization to higher dimensions of the concept of the variance of a scalar-valued random variable.
probability distribution that assigns a probability to every subset (more precisely every measurable subset) of its state space in such a way that the probability axioms are satisfied.
dimension (Latin, "measured out") is a parameter or measurement required to define the characteristics of an object—i.e., length, width, and height or size and shape.
In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. More formally, a vector space is a set on which two operations, called (vector) addition and (scalar) multiplication, are
SET may stand for:
• Sanlih Entertainment Television, a television channel in Taiwan
• Secure electronic transaction, a protocol used for credit card processing,

pixel (short for picture element, using the common abbreviation "pix" for "pictures") is a single point in a graphic image. Each such information element is not really a dot, nor a square, but an abstract sample.
Principal components analysis (PCA) is a technique used to reduce multidimensional data sets to lower dimensions for analysis. Depending on the field of application, it is also named the discrete Karhunen-Loève transform, the Hotelling transform or
In statistics and probability theory, the covariance matrix is a matrix of covariances between elements of a vector. It is the natural generalization to higher dimensions of the concept of the variance of a scalar-valued random variable.
Principal components analysis (PCA) is a technique used to reduce multidimensional data sets to lower dimensions for analysis. Depending on the field of application, it is also named the discrete Karhunen-Loève transform, the Hotelling transform or
Symmetry in common usage generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance; such that it reflects beauty or perfection.
Graphology is the study and analysis of handwriting especially in relation to human psychology. The term is sometimes incorrectly used to refer to forensic document examination.
Lip reading, also known as lipreading, speech reading, or speechreading, is a technique of understanding speech by visually interpreting the movements of the lips, face and tongue with information provided by the context, language, and any residual hearing.
Speaker recognition, or voice recognition is the task of recognizing people from their voices. Such systems extract features from speech, model them and use them to recognize the person from his/her voice.
Medical imaging refers to the techniques and processes used to create images of the human body (or parts thereof) for clinical purposes (medical procedures seeking to reveal, diagnose or examine disease) or medical science
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
Digital photography, as opposed to film photography, uses electronic devices to record and capture the image as binary data. As such, the images can be displayed, printed, stored, manipulated, transmitted and archived using various kinds of digital technology, including personal
A facial recognition system is a computer application for automatically identifying or verifying a person from a digital image or a video frame from a video source. One of the ways to do this is by comparing selected facial features from the image and a facial database.
3D computer graphics (in contrast to 2D computer graphics) are graphics that utilize a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images.
Computer animation is the art of creating moving images via the use of computers. It is a subfield of computer graphics and animation. Increasingly it is created by means of 3D computer graphics, though 2D computer graphics are still widely used for low bandwidth and faster
Craniofacial anthropometry is a technique used in physical anthropology comprising precise and systematic measurement of the bones of the human skull. Among its more important applications are: forensics, facial reconstruction, and paleoanthropology.