Face recognition by using Eigenfaces and Machine learning techniques
To make algorithms capable of facial recognition have always been human fantasy. Different approach were tried to do the same. In this section i will discuss face recognition by forming eigenfaces which is implementation and discussion of algorithm developed by M.Turf and A.Petland.
The effort to apply PCA in data containing images as the column of a matrix results in formation of eigenfaces. In simple terms we have removed the redun- dant information common in all the images and bring out those information that are important for their recognition.
1st step in removing the redundancy of the data is substracting the common mean image from each training image. Mean image is the image formed by taking a simple average of all the images we have. If training images are α 1 , α 2 , ..., α m where each α i is a column vector of dimention N^2 corresponding to each N × N dimention training image. then the average image or the mean image can be defined as:-
The substraction of average image from each image was done to remove the features that are common to all the images.
Now our next aim is to find the eigenfaces which can be mathematically interpreated as the principal components. To find eigenfaces we form covariance matrix.
This would give C to be a N^2 ×N^2 matrix which would mean having to calculate N^2 eigenvectors with each eigenvector having dimention N^2 × 1. So if we have 60pixel × 60pixel images our covariance matrix C would be 3600 × 3600 matrix. This would require us to calculate 3600 eigenvectors which is computationaly a nightmare. So to solve this problem we reduce the dimention of the data that we have. That is mapping the data in lower dimention. This is done by defining
thus reducing the dimention of C from N 2 × N 2 to m × m. Now once we have the covariance matrix we can easily find out m corre- sponding eigenvectors, which would give us our eigenfaces.
Next phase is the recognition part in which test image is first represented as the weighted sum of eigenfaces. This new weight W of the test image is then compared with each of the weights of training images and the distance is calculated. Minimmum distance corresponds to the most similar image.
Further i have triained a neural network model to find the threshold that should result in the classifaction between the face corresponding to the least distance and the option image not present in training set. THANK YOU
