  The free-form deformation model can represent a wide range of non-rigid
deformations by manipulating a control point lattice over the image. However,
due to a large number of parameters, it is challenging to fit the free-form
deformation model directly to the deformed image for deformation estimation
because of the complexity of the fitness landscape. In this paper, we cast the
registration task as a multi-objective optimization problem (MOP) according to
the fact that regions affected by each control point overlap with each other.
Specifically, by partitioning the template image into several regions and
measuring the similarity of each region independently, multiple objectives are
built and deformation estimation can thus be realized by solving the MOP with
off-the-shelf multi-objective evolutionary algorithms (MOEAs). In addition, a
coarse-to-fine strategy is realized by image pyramid combined with control
point mesh subdivision. Specifically, the optimized candidate solutions of the
current image level are inherited by the next level, which increases the
ability to deal with large deformation. Also, a post-processing procedure is
proposed to generate a single output utilizing the Pareto optimal solutions.
Comparative experiments on both synthetic and real-world images show the
effectiveness and usefulness of our deformation estimation method.
