Chapter 5 PCA ALGORITHM
5.1 Eigen faces Approach
Extract relevant information in a face image [Principal Components] and encode that information in a suitable data structure. For recognition take the sample image and encode it in the same way and compare it with the set of encoded images. In mathematical terms we want to find eigen vectors and eigen values of a covariance matrix of images. Where one image is just a single point in high dimensional space [n * n] , where n * n are the dimensions of a image . There can be many eigen vectors for a covariance matrix but very few of them are the principle one's. Though each eigen vector can be used for finding different amount of variations among the face image. But we are only interested in principal eigen vectors because these can account for substantial variations among a bunch of images. They can show the most significant relationship between the data dimensions.
Eigenvectors with highest eigen values are the principle component of the Image set. We may lose some information if we ignore the components of lesser significance. But if the eigen values are small then we won't lose much. Using those set of eigen vectors we can construct eigenfaces .