Unifying Characterization of Deformable Registration Methods Based on the Inherent Parametrization

We propose to characterize deformable registration methods in a unified way, based on their parametrization. In contrast to traditional classifications, we do not apply this characterization only to standard “parametric” methods such as B-Spline Free-form deformations, but we explicitly include elastic and fluid-type “non-parametric” methods, such as the classic variational approach, and the fluid demons method. To this end, we consider parametrizations by linear combinations of arbitrary basis functions. While for the variational approach we simply utilize piecewise linear bases, for the fluid demons method we provide a new interpretation by showing that it can be seen as inherently parametrized by densely located Gaussian basis functions. Furthermore, we show that the semi-implicit discretization of the variational approach can be seen as steepest descent, with a displacement parametrized by densely located bases, based on Green’s functions corresponding to the regularization. This provides a further connection to the demons approaches. The proposed characterization is widely applicable and provides a simple and intuitive way of relating some of the arguably most commonly used methods to each other.