Multi-objective optimization for deformable image registration: proof of concept

In this work we develop and study a methodology for deformable image registration that overcomes a drawback of optimization procedures in common deformable image registration approaches: the use of a single combination of different objectives. Because selecting the best combination is well-known to be non-trivial, we use a multiobjective optimization approach that computes and presents multiple outcomes (a so-called Pareto front) at once. The approach is inherently more powerful because not all Pareto-optimal outcomes are necessarily obtainable by running existing approaches multiple times, for different combinations. Furthermore, expert knowledge can be easily incorporated in making the final best-possible decision by simply looking at (a diverse selection of) the outcomes illustrating both the transformed image and the associated deformation vector field. At the basis of the optimization methodology lies an advanced, model-based evolutionary algorithm that aims to exploit features of a problem’s structure in a principled manner via probabilistic modeling. Two objectives are defined: 1) maximization of intensity similarity (normalized mutual information) and 2) minimization of energy required to accomplish the transformation (a model based on Hooke’s law that incorporates elasticity characteristics associated with different tissue types). A regular grid of points forms the basis of the transformation model. Interpolation extends the correspondence as found for the grid to the rest of the volume. As a proof of concept we performed tests on a 2D axial slice of a CT scan of a breast. Results indicate plausible behavior of the proposed methodology that innovatively combines intensity-based and model-based registration criteria with state-of-theart adaptive computation techniques for multi-objective optimization in deformable image registration.