A Unified Approach to Shape Model Fitting and Non-rigid Registration

Non-rigid registration and shape model fitting are the central problems in any shape modeling pipeline. Even though the goal is in both problems to establishing point-to-point correspondence between two objects, their algorithmic treatment is usually very different. In this paper we present an approach that allows us to treat both problems in a unified algorithmic framework. We use the well known formulation of non-rigid registration as the problem of fitting a Gaussian process model, whose covariance function favors smooth deformations. We compute a low rank approximation of the Gaussian process using the Nystrom method, which allows us to formulate it as a parametric fitting problem of the same form as shape model fitting. Besides simplifying the modeling pipeline, our approach also lets us naturally combine shape model fitting and non-rigid registration, in order to reduce the bias in statistical model fitting, or to make registration more robust. As our experiments on 3D surfaces and 3D CT images show, the method leads to a registration accuracy that is comparable to standard registration methods.