  We present an efficient approach of Finite Element Method (FEM)-based
nonrigid image registration, in which the spatial transformation is constructed
using truncated hierarchical B-splines (THB-splines). The image registration
framework minimizes an energy functional using an FEM-based method and thus
involves solving a large system of linear equations. This framework is carried
out on a set of successively refined grids. However, due to the increased
number of control points during subdivision, large linear systems are generated
which are generally demanding to solve. Instead of using uniform subdivision,
an adaptive local refinement scheme is carried out, only refining the areas of
large change in deformation of the image. By incorporating the key advantages
of THB-spline basis functions such as linear independence, partition of unity
and reduced overlap into the FEM-based framework, we improve the matrix
sparsity and computational efficiency. The performance of the proposed method
is demonstrated on 2D synthetic and medical images.
