This paper is addressing the problem of realigning broken
objects without correspondences. We consider linear transformations between
the object fragments and present the method through 2D and 3D
affine transformations. The basic idea is to construct and solve a polynomial
system of equations which provides the unknown parameters of the
alignment. We have quantitatively evaluated the proposed algorithm on
a large synthetic dataset containing 2D and 3D images. The results show
that the method performs well and robust against segmentation errors.
We also present experiments on 2D real images as well as on volumetric
medical images applied to surgical planning.