A statistical deformation prior for non-rigid image and shape registration

Non-rigid registration is central to many problems in computer vision and medical image analysis. We propose a registration algorithm which is regularized by prior knowledge in the form of a statistical deformation model. This model is obtained from previous registrations performed on a set of noise-free training examples given by images, or shapes represented by level set functions. Contrary to similar approaches, our method does not strictly constrain the result to lie in the span of the statistical model but rather uses the model for Tikhonov regularization. Therefore, our method can be used to reduce the influence of noise and artifacts even when the model contains only a few typical examples. This automatically gives rise to a bootstrapping strategy for building statistical models from noisy data sets requiring only a limited number of high quality examples. We demonstrate the effectiveness of the approach on synthetic and medical images.