Represent input image in PCA

We need to take a picture of the users face and represent it in term of all the eigenfaces W

Inputs

1. Matrix W of eigenfaces computed in #1
2. Mean mu found in #1

Outputs

1. a vector x which represents the input face in the PCA subspace

Procedure

1. Create function to take an image from computer camera (opencv can do this)
2. Create a function to open a pre-existing image
3. turn image into a flat vector y
4. compute x = Wy + mu
5. return value

Input Image

• Function that loads an input image from file and formats it
• Function that takes a user's picture using the default camera
  • Add frame to to help user position face in image

Image Functions

• Need a function that can display an input image to screen
• Need a function to save an image to file

Formatting images

We need to take a input face image data set and turn it into a format that can be turned into a
eigenfaces

Input

1. file location string

Output

1. a matrix M containing N vectors of M length (M = product of image dimensions)

Procedure

1. load images from input file
   1. Inputs can be found here:
      1. http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html
      2. http://vision.ucsd.edu/content/yale-face-database
      3. http://vision.ucsd.edu/~leekc/ExtYaleDatabase/ExtYaleB.html
   2. Images will probably come in a specific format so you may need to figure out how to open them
2. Make each image a flat vector
3. Append each image vector to a Matrix M
4. Return matrix M

Need a function to display eigenfaces.
The problem is that the eigenfaces are normalize and contain negative values.
These values need to be remapped to [0-255]

• find the largest and smallest values in the vector
• subtract the smallest value from all values in the vector
• divide all values by the range between the smallest and largest values
  • this puts the values between [0,1]
• multiply all the values by 255
  • putting them in the range from [0,255]

We need a function that stores projections into a file format so that they can be retrieved later. These projections need to saved in a key:value format since we need to know which face they belong too.

Need a function that compares projections to find the closest one.

Projections are 1xN arrays where N is the number of component eigenfaces that it's been projected upon.

Constructing a PCA subspace

We need to have a function that takes a Matrix of vectors and computes an input `k' largest eigenvectors and stores them into some data format (probaby a txt file).

Inputs

1. matrix M of flat image vectors (n vectors of m length)
2. k (integer) of largest eignenvectors
3. filename for subspace output

Outputs

1. Matrix W of eignevectors

Procedure

1. compute the mean of the vectors in M
2. calculate the covariance matrix S using the mean and the vectors in M
3. compute the eigenvalues and eigenvectors of S
4. sort eigenvectors by eigenvalue
5. save k largest eigenvectors into some file format for further use
6. add file to gitignore
7. check numpy for an ideal format to use

Custom images (taken via webcam) are not able to be represented using eigenfaces. Some possible reasons for this problem are:

• The lighting in the picture is too different
• The training set has inadequate variance to represent my face
• The features are not sensitive to beards
• Something else?

Possible solutions to this problem:

• Acquire a bigger and broader data set
• change the lighting in the room of the picture
• Shave
• ?

Need a function to scale images down to make taking small face pictures easier. The function would take an input rows and columns and scale the image down to that size. This function can then be added to create_image to scale down the taken image.

Subspace Loader

A function in pca.py which will load a subspace from a file. It will output the subspace W as well as it's mean mu, and it's image size.