Eigenface Analysis Results:

By looking at a few sample images, one can distinguish among the images with approximately 70-80 principle components. Below are the reproduced images for 2 images V₁ and V₂.

 Different amount of padding were tested. The result of the reconstruction error vs. number of eigenfaces is shown below.

As can be seen from the graph (and the table below), the number of eigenfaces required for reconstructing the image is increased as the level of padding is increased in the images. Since the number of pixels around the image, which are not face pixels, has increased, it will take more components to reconstruct the approximate original image. Although the difference might be less if all the images had the same background, but this is not the case here, since all the images have quite different backgrounds. The original padding will have a 1.39E+07 reconstruction error with only 41 vectors. In comparison the 1.5 padding around the images will have approximately the same reconstruction error but with 67 vectors. Similar statements can be made for the other padding tested.

The images in this section were constrained to the images with “full” smiles meaning smiles with teeth showing! The number of eigenfaces for which the error in reproducing the original image is less than 10%, is approximately 13 eigenfaces.

Comparison of the first five eigenfaces of the original set images with the constrained set of images can be seen below:

My set of images all had smiles in them and the "smile" can clearly be seen in the set of constrained eigenfaces. Sample Image:

The filter I used for this section is the Gradient Anisotropic Diffusion Image Filter. The filter smoothes the image without blurring away the sharp boundaries. Although this may seem unnecessary for some of the images, but it will smooth and reduce noise in the images that need it. Thus this will give us less variability in the images. The filter was run with a time step of 0.125, 5 iterations and with a conductance of 3. The result can be seen in the graph below.

Smoothing the images will cause a decrease in the amount of PCs needed for reconstructing the image. This can clearly be seen in the graph above.

Some images before and after the smoothing filter:

Comparison of the first 6 eigenfaces for with and without the filter:

Comparison of the reprojection error for V0 with and without a filter: