OpenImaj Tutorial and EigenFaces

Question

I do not know if this is a relevant forum, but I have been following this tutorial here:

http://www.openimaj.org/tutorial/eigenfaces.html

For some reason it is not clear enough for me. There are some things I do not understand. It says at one point,

The first step in implementing an Eigenfaces recogniser is to use the training images to learn the PCA basis which we'll use to project the images into features we can use for recognition. The EigenImages class needs a list of images from which to learn the basis (i.e. all the training images from each person), and also needs to know how many dimensions we want our features to be (i.e. how many of the eigenvectors corresponding to the biggest eigenvalues to keep):

The it goes writing this code:

List<FImage> basisImages = DatasetAdaptors.asList(training);
int nEigenvectors = 100;
EigenImages eigen = new EigenImages(nEigenvectors);
eigen.train(basisImages);

So I do not get it. What exactly is the train() method training? From what I got it is just applying PCA right? In my mind training is always associated with a perceptron for example or another neural network or an algorithm with parameters.

Also I need some help understanding Exercise 13.1.1,

13.1.1. Exercise 1: Reconstructing faces

An interesting property of the features extracted by the Eigenfaces algorithm (specifically from the PCA process) is that it's possible to reconstruct an estimate of the original image from the feature. Try doing this by building a PCA basis as described above, and then extract the feature of a randomly selected face from the test-set. Use the EigenImages#reconstruct() to convert the feature back into an image and display it. You will need to normalise the image (FImage#normalise()) to ensure it displays correctly as the reconstruction might give pixel values bigger than 1 or smaller than 0.

In the examples there is some code that already extracts the features:

    Map<String, DoubleFV[]> features = new HashMap<String, DoubleFV[]>();
    for (final String person : training.getGroups()) {
        final DoubleFV[] fvs = new DoubleFV[nTraining];

        for (int i = 0; i < nTraining; i++) {
            final FImage face = training.get(person).get(i);
            fvs[i] = eigen.extractFeature(face);
        }
        features.put(person, fvs);
    }

So if I just call this:

eigen.reconstruct(fvs[i]).normalise() -> returns an image I can display, which looks like a normal face but it is really small in dimensions (is that normal?).

Should do it ?

Thanks.

Answer 1

For the first question

PCA has two stages:

1. Learning ("training") a linear transform that projects data into a lower-dimensional space. This is done in such a way that the first axis (the principal axis) in the transformed space is in the direction of highest variance in the "training" data; the second axis is in the direction of most variance at right-angles to the first axis; and so on.
2. Applying the learnt transform to data ("projecting" the data) in order to reduce its dimensionality.

Most descriptions of PCA that you'll find assume that you've got some data and you just want to reduce its dimensionality. More specifically, it is assumed that the data in the two steps is the same. This doesn't have to be the case however; you can perform step 1 on a representative sample of data to learn the transform and then apply step 2 to different data (although for the results to be meaningful this data should be from the same population).

In the case of Eigenfaces you learn the PCA transform from some or all of your "training" face data and then project all of the training data with the transform and train a supervised classifier. When you want to test the system, you use the learned PCA transform to project a previously unseen data item into the lower-dimensional space and then pass it to the classifier.

For the second question

eigen.reconstruct(fvs[i]).normalise() is the correct approach. The reconstructed image will have the same dimensions as all the images used for training/testing (a limitation of the Eigenfaces approach is that all inputs must have the same size). In the case of the tutorial, the AT&T face dataset consists of relatively low resolution images (92x112 pixels).