If we have the previously mentioned set of images, we can generate a statistical model of shape variation. Since the labeled points on an object describe the shape of that object, we firstly align all the sets of points into a coordinate frame using Procrustes Analysis, if required, and represent each shape by a vector, x. Then, we apply Principal Component Analysis (PCA) to the data. We can then approximate any example using the following formula:
x = x + Ps bs