This method tries to find the principal component of the distribution of faces, or the eigenvectors of the covariance matrix of the set of face images. These eigenvectors can be considered as a set of features which together characterize the variation between face images. By referring to a well-known theory in pattern recognition, we know that each of the images in the training set can be represented exactly in terms of a linear combination of the eigenfaces. If we use only some eigenvectors that have the largest eigenvalues, we can approximate and represent the most significant variation within the image set. So we find the eigenvectors of the smaller matrix .
P is smaller that the number of pixels in each image.
Once we obtain the M eigenvectors, we select only K . And I have tested on 15 faces front-viewed, smiling faces of the same group of people. And they can be recognized. Also, one interesting point for using eigenfaces method is that some images which are not complete can still be reconstructed and recognized in eigenspaces. Some examples will be shown in the demo day.