We present a generalization of the convolution based
variational image registration approach, in which different
regularizers can be implemented by conveniently exchanging
the convolution kernel, even if it is nonseparable
or nonstationary. Nonseparable kernels pose a challenge because
they cannot be efficiently implemented by separate
1D convolutions. We propose to use a low-rank tensor decomposition
to efficiently approximate nonseparable convolution.
Nonstationary kernels pose an even greater challenge
because the convolution kernel depends on, and needs to
be evaluated for, every point in the image. We propose to
pre-compute the local kernels and efficiently store them in
memory using the Tucker tensor decomposition model. In
our experiments we use the nonseparable exponential kernel
and a nonstationary landmark kernel. The exponential kernel
replicates desirable properties of elastic image registration,
while the landmark kernel incorporates local prior knowledge
about corresponding points in the images.We examine
the trade-off between the computational resources needed
and the approximation accuracy of the tensor decomposition
methods. Furthermore, we obtain very smooth displacement
fields even in the presence of large landmark displacements.