Closed-Form Alignment of Active Surface Models Using Splines

We propose a new formulation of the active surface model in 3D. Instead of aligning a shape dictionary through the similarity transform, we consider more flexible affine transformations and introduce an alignment method that is unbiased in the sense that it implicitly constructs a common reference shape. Our formulation is expressed in the continuous domain and we provide an algorithm to exactly implement the framework using spline-based parametric surfaces. We test our model on real 3D MRI data. A comparison with the classical active shape model shows that our method allows us to capture shape variability in a dictionary in a more precise way.