Realigning 2D and 3D Object Fragments without Correspondences

This paper addresses the problem of simultaneous estimation of different linear deformations, resulting in a global non-linear transformation, between an original object and its broken fragments. A general framework is proposed without using correspondences, where the solution of a polynomial system of equations directly provides the parameters of the alignment. We quantitatively evaluate the proposed algorithm on a large synthetic dataset containing 2D and 3D images, where linear (rigid-body and affine) transformations are considered. We also conduct an exhaustive analysis of the robustness against segmentation errors and the numerical stability of the proposed method. Moreover, we present experiments on 2D real images as well as on volumetric medical images.