Singular Value Decomposition, Eigenfaces, and 3D Reconstructions

Singular value decomposition (SVD) is one of the most important and useful factoriza- tions in linear algebra. We describe how SVD is applied to problems involving image processing—in particular, how SVD aids the calculation of so-called eigenfaces, which pro- vide an efficient representation of facial images in face recognition. Although the eigenface technique was developed for ordinary grayscale images, the technique is not limited to these images. Imagine an image where the different shades of gray convey the physical three- dimensional structure of a face. Although the eigenface technique can again be applied, the problem is finding the three-dimensional image in the first place. We therefore also show how SVD can be used to reconstruct three-dimensional objects from a two-dimensional video stream.