Constructing Data-Driven Optimal Representations for Iterative Pairwise Non-rigid Registration

Non-rigid registration of a pair of images depends on the generation of a dense deformation field across one of the images. Such deformation fields can be represented by the deformation of a set of knotpoints, interpolated to produce the continuous deformation field. This paper addresses the question of how best to choose the knotpoints of such a representation based on all of the available image information. These knotpoints are not landmarks, they can be positioned anywhere in the images, and do not necessarily correspond to any image feature. We use an iterative, data-driven algorithm for the selection of knotpoints, and a novel spline that interpolates smoothly between knotpoints. The algorithm produces a low-dimensional representation of the deformation field that can be successively refined in a multi-resolution manner. We demonstrate the properties of the algorithm on sets of 2D images and discuss the extension of the algorithm to 3D data.