Diffeomorphic statistical shape models

We describe a method of constructing parametric statistical models of shape variation which can generate continuous diffeomorphic (non-folding) deformation fields. Traditional statistical shape models are constructed by analysis of the positions of a set of landmark points. Here, we describe an algorithm which models parameters of continuous warp fields, constructed by composing simple parametric diffeomorphic warps. The warps are composed in such a way that the deformations are always defined in a reference frame. This allows the parameters controlling the deformations to be meaningfully compared from one example to another. A linear model is learnt to represent the variations in the warp parameters across the training set. This model can then be used to generalise the deformations. Models can be built either from sets of annotated points, or from unlabelled images. In the latter case, we use techniques from non-rigid registration to construct the warp fields deforming a reference image into each example. We describe the technique in detail and give examples of the resulting models.