Week 4 - Face Recognition Walkthrough

This week, we were able to advance on the face recognition component of the biometric recognition project. The steps for the MATLAB algorithm (pseudocode) are given below. In addition, we have decided on a fingerprint scanner and advanced with minutiae analysis of fingerprinting and Fourier analysis of voice.

1. Create a test database. Take a picture and convert it into grayscale to reduce the number of channels (R, G, B).

2. Then, reduce into a 1-D vector because all images share this property (R^m).

3. Add every "reshaped" vector to a matrix known as the "test" matrix of dimensions mxn concatenating vertically.

4. Taking this mxn matrix, take the mean along every row and output a column vector averaging every pixel in all 20 images.

5. Creating a new matrix, known as the SCATTER MATRIX, every individual column is subtracted by the mean vector (R^m) evaluated before.

6. The SCATTER MATRIX has dimensions mxn.

7. Because the SCATTER MATRIX is not necessarily square, it can be multiplied by its transpose to create a square matrix. It is known that the maximum number of eigenvalues for a mxn matrix (non-square) is min(m-1, n-1). Therefore, new eigenvalues will not be generated just because the square matrix with larger dimensions is chosen.

8. The objective is to make the process minimally computationally expensive. Because m is the number of pixels and n is the number of images, left-transposition yields nxm x mxn = nxn matrix. Right-transposition yields mxn x nxm = mxm, which is considerably larger than nxn. Therefore, nxn is the best choice.

9. After finding the eigenvalues and eigenvectors of nxn, the eigenfaces is a measure of how much faces differ from the mean face based on the data set. These eigenfaces are not unique to the faces used to compile them, but will be projected onto the original images themselves to determine how “different” an image is from others.

10. Once the eigenfaces have been computed, this matrix has at most nx(n-1) dimensions.

11. Once the eigenface matrix has been obtained (it has only numerical value and is in the eigenspace), it can be projected into imagespace by multiplying into the original grayscale matrix of pixels. This process has essentially extracted the principal components, hence the name PCA, that are unique to individuals such as the hairline, where the nose is, where the mouth is, etc. The background details become trivial because they are averaged with the mean face (a green-screen would be ideal and will be implemented in the final design).

12. The scatter of the test image will be obtained by subtracting from the mean of all images in the database. Multiplying by the eigenface matrix yields a “feature vector” that contains the principal component details.

13. The total Euclidean distance in imagespace between the projected test image and the training images is computed for every image. The image with smallest scatter when compared to the appropriate image is the best match!