Unifying Characterization of Deformable Registration Methods Based on the Inherent Parameterization

In this paper, we propose to characterize some of the most common deformable registration methods in a unified way, based on their parameterization. In contrast to traditional classifications, we do not apply this characterization only to standard 'parametric' methods such as B-Spline Free-form deformations, but extend it to 'non-parametric' methods, that is, the variational approach with explicitly defined regularization energy, and the Demons method. To this end, we consider parameterizations by linear combinations of arbitrary basis functions. For the variational approach we utilize the tensor product piecewise linear bases, as used for linear interpolation. For the fluid demons method, we demonstrate that this approach can be seen an inherently parameterized by densely located Gaussian basis functions. Stating the inherent parameterization of these approaches allows a clear distinction between these methods. This point of view opens new possible ways of relating the different methods to each other.     «

In this paper, we propose to characterize some of the most common deformable registration methods in a unified way, based on their parameterization. In contrast to traditional classifications, we do not apply this characterization only to standard 'parametric' methods such as B-Spline Free-form deformations, but extend it to 'non-parametric' methods, that is, the variational approach with explicitly defined regularization energy, and the Demons method. To this end, we consider parameterizations...     »