Volume-preserving correction for image registration using free-form deformations

Registration of an image non-rigidly to another one causes deformations, which generally do not preserve the initial volume. Volume preservation is however indispensable for observing tumors in medical images. This paper presents the correction of B-spline based registration to preserve the volume in observed regions. In contrast to other approaches, our solution is not obtained through energy minimization, but by calculating the correction parameters for the deformation directly. Especially for high resolution image data this strategy is very efficient in terms of computational expenses. We derive a closed form solution to optimize the registration with respect to the compression at a single point and then extend the problem to multiple points. Finally we prove also that the correction terms do not have any significant influence on the registration quality.