Spatial transformation of motion and deformation fields using nonrigid registration

In this paper, we present a technique that can be used to transform the motion or deformation fields defined in the coordinate system of one subject into the coordinate system of another subject. Such a transformation accounts for the differences in the coordinate systems of the two subjects due to misalignment and size/shape variation, enabling the motion or deformation of each of the subjects to be directly quantitatively and qualitatively compared. The field transformation is performed by using a nonrigid registration algorithm to determine the intersubject coordinate system mapping from the first subject to the second subject. This fixes the relationship between the coordinate systems of the two subjects, and allows us to recover the deformation/motion vectors of the second subject for each corresponding point in the first subject. Since these vectors are still aligned with the coordinate system of the second subject, the inverse of the intersubject coordinate mapping is required to transform these vectors into the coordinate system of the first subject, and we approximate this inverse using a numerical line integral method. The accuracy of our numerical inversion technique is demonstrated using a synthetic example, after which we present applications of our method to sequences of cardiac and brain images.