Now that one has a collection of eigenface vectors, a question that may arise is, what next? Well, a sighted person can fairly easily recognize a face based on a rough reconstruction of an image using only a limited number of eigenfaces. However, reconstruction of non-face images is not so successful.

Poor Non-Face Reconstruction |
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Given that the initial objective is a face recognition system, eigenfaces happen to be a fairly easy, computationally economical, and successful method to determine if a given face is a known person, a new face, or not a face at all. A set of eigenface vectors can be thought of as linearly independent basis set for the face space. Each vector lives in its own dimension, and a set of M eigenfaces will yield an M dimensional space.

It should also be noted that the eigenfaces represent the principal components of the face set. These principal components are very useful in simplifying the recognition process of a set of data. To make it simpler, suppose we had a set of vectors that represented a person’s weight and height. Projecting a given person onto these vectors would then yield that person’s corresponding weight and height components. Given a database of weight and height components, it would then be quite easy to find the closest matches between the tested person and the set of people in the database.

A similar process is used for face recognition with eigenfaces. First take all the mean subtracted images in the database and project them onto the face space. This is essentially the dot product of each face image with one of the eigenfaces. Combining vectors as matrices, one can get a weight matrix (M*N, N is total number of images in the database)

An incoming image can similarly be projected onto the face space. This will yield a vector in M dimensional space. M again is the number of used eigenfaces. Logically, faces of the same person will map fairly closely to one another in this face space. Recognition is simply a problem of finding the closest database image, or mathematically finding the minimum Euclidean distance between a test point and a database point.

Due to overall similarities in face structure, face pixels follow an overall “face” distribution. A combination of this distribution and principal component analysis allows for a dimensional reduction, where only the first several eigenfaces represent the majority information in the system. The computational complexity becomes extremely reduced, making most computer programs happy. In our system, two techniques were used for image recognition.