FaceRec tutorial explanation

Question

I try to do this face recognition example, with Eigenfaces. And cannot understand what these functions subspaceProject() and subspaceReconstruct() actually do. I tried to search on http://docs.opencv.org/ but there was not any link to description.

Could you explain me what this part of the code actually do?

Mat evs = Mat(W, Range::all(), Range(0, num_components));
Mat projection = subspaceProject(evs, mean, images[0].reshape(1,1));
Mat reconstruction = subspaceReconstruct(evs, mean, projection);
    // Normalize the result:
reconstruction = norm_0_255(reconstruction.reshape(1, images[0].rows));

I mean what these functions do, what kind of cv::Mat they return ?

Answer 1

subspaceProject() will basically give you a dimensionality reduction.

projection = (images[0] - mean) * evs

Subtracting the mean ensures that the images approximate a subspace. Presumably evs is the truncated right singular vectors.

and for subspaceReconstruct()

reconstruction = projection * transpose(evs) + mean

The reconstruction is just the reverse of the projection, except since evs is truncated, it can not be perfect.

See PCA