Conclusions and Discussion

We have presented a new fluid deformation algorithm with variable viscosity for the registration of images containing structures with variable deformability. Results show the algorithm reduces the deformation of selected regions. The hierarchical strategy (registration within Gaussian scale space) was not optimal for the 3D case since it preferred initial registration at the strongest boundaries which were the (non-homologous) outer boundaries. We suggest instead a model-based hierarchy, using initial registration by an (automated) C-MTQ with rigid vertebrae, followed by MF3 for more localised deformations.

Inhomogeneities in deformability can be extended to include anisotropies in the constraint parameters, such that there are preferential directions of deformation. Anisotropies in ease of deformation are common in physical tissue such as muscle. Adapting the mathematical representation of the deformation of a physical medium to allow anisotropies is more complex than only allowing for isotropic inhomogeneities; we leave such a possibility for future research. Another possible amendment to the fluid registration is to supply pre-determined uniform and constant but non-zero velocities within regions defined as independently moving to allow rigid-body transformations within an overall fluid deformation.