Deformable image registration by multi-objective optimization using a dual-dynamic transformation model to account for large anatomical differences

Some of the hardest problems in deformable image registration are problems where large anatomical differences occur between image acquisitions (e.g. large deformations due to images acquired in prone and supine positions and (dis)appearing structures between image acquisitions due to surgery). In this work we developed and studied, within a previously introduced multi-objective optimization framework, a dual-dynamic transformation model to be able to tackle such hard problems. This model consists of two non-fixed grids: one for the source image and one for the target image. By not requiring a fixed, i.e. pre-determined, association of the grid with the source image, we can accommodate for both large deformations and (dis)appearing structures. To find the transformation that aligns the source with the target image we used an advanced, powerful model-based evolutionary algorithm that exploits features of a problem's structure in a principled manner via probabilistic modeling. The actual transformation is given by the association of coordinates with each point in the two grids. Linear interpolation inside a simplex was used to extend the correspondence (i.e. transformation) as found for the grid to the rest of the volume. As a proof of concept we performed tests on both artificial and real data with disappearing structures. Furthermore, the case of prone-supine image registration for 2D axial slices of breast MRI scans was evaluated. Results demonstrate strong potential of the proposed approach to account for large deformations and (dis)appearing structures in deformable image registration.