A feature extraction method: Principal Component Analysis (PCA)
Ok, it sounds like you are trying to do eigenfaces, right?

In that case, you have to think of your face images as points in a very high-dimensional space. For example, if your images are 32x32, then the space has 32 * 32 = 1024 dimensions.  Operating in so many dimensions is very difficult, because distances between points become almost meaningless.  With so many dimensions any point is very far away from any other point, even if the two points represent the same face.

That's why you want to reduce the dimensionality, and PCA is one way to do it. If you go from 1024 dimensions to, say, 10, then the distances will become more meaningful, which fits in with your idea of "highlight their similarities and differences".  However, PCA by itself will not tell you of any patterns in your data, beyond the directions of greatest variance.  PCA will project your data into a lower-dimensional space with decorrelated axes, but you have to do more work to actually discover the patterns in the data, such as train a classifier, or run a clustering algorithm.

Now, to understand what happens to the edges and transitions from light to dark, you have to display your eigenvectors as images and look at them. You will see that you don't really preserve the precise edge information, but you do keep course-level information about light and dark areas.