Of the many uses for singular value decomposition, one that I found to be most interesting was face recognition. Efficient and accurate facial recognition has been a problem for computer scientists and the like for many years. Because faces can take on completely different looks under different lighting or angles there is great difficulty in accurate facial recognition. Due to this innate difficulty, researchers have yet to reach the level of human facial recognition over the past 20 years. However, there are a multitude of algorithms and strategies currently available that come close under restricted circumstances. Here I present a few in summary.

There are a number of algorithms that require many photos of a person in order to ‘prime’ their algorithm for accuracy. With a multitude of photos, geometrical models can be made along with very detailed feature recognition. 3D morphable models are common in the facial recognition field. First, a generic model of the human face is needed along with sample photos of the desired person. A bunch of intermediate photos are then created from the original samples, which are then used to stretch and skew the 3D model to match key features such as nose or eye location.

However, many photos are not always available in the real world. It is often the case that only a driver’s license or passport are available (unless you have access to their facebook photos…) under which circumstances these facial recognition algorithms lack in accuracy. Linear Discriminant Analysis (LDA) is an example of this. LDA requires a minimum of two photos in order to compare facial feature variations. It does so by first creating a matrix of the image where each pixel is representative of a feature. It then measures the variation between the two photos of the same person and comparing those values to the variation of the person/photo in question along with principal component analysis (PCA). A common solution to this situation involves combining the original image linearly with a derived image gotten by perturbation of the singular values of original image matrix and then performing PCA (PC^2 A). Although we haven’t yet reached the level of facial recognition equivalent to those of humans, current algorithms and strategies are nonetheless impressive.

http://en.wikipedia.org/wiki/Principal_components_analysis
http://en.wikipedia.org/wiki/Linear_discriminant_analysis
http://ieeexplore.ieee.org/iel5/9515/30163/01384878.pdf?arnumber=1384878
http://cs.nju.edu.cn/zhouzh/zhouzh.files/publication/appmathcomp05.pdf