AAM search and fitting

With our fresh, new combined shape and texture model, we have found a nice way to describe how a face could change not only in shape, but also in appearance. Now, we want to find which set of p shape and λ appearance parameters will bring our model as close as possible to a given input image I(x). We could naturally calculate the error between our instantiated model and the given input image in the coordinate frame of I(x), or map the points back to the base appearance and calculate the difference there. We are going to use the latter approach. This way, we want to minimize the following function:

In the preceding equation, S0 denotes the set of pixels x is equal to (x,y)T that lie inside the AAMs base mesh, A0(x) is our base mesh texture, Ai(x) is appearance images from PCA, and W(x;p) is the warp that takes pixels from the input image back to the base mesh frame.

Several approaches have been proposed for this minimization through years of studying. The first idea...