  Recent successes in deep learning based deformable image registration (DIR)
methods have demonstrated that complex deformation can be learnt directly from
data while reducing computation time when compared to traditional methods.
However, the reliance on fully linear convolutional layers imposes a uniform
sampling of pixel/voxel locations which ultimately limits their performance. To
address this problem, we propose a novel approach of learning a continuous warp
of the source image. Here, the required deformation vector fields are obtained
from a concatenated linear and non-linear convolution layers and a learnable
bicubic Catmull-Rom spline resampler. This allows to compute smooth deformation
field and more accurate alignment compared to using only linear convolutions
and linear resampling. In addition, the continuous warping technique penalizes
disagreements that are due to topological changes. Our experiments demonstrate
that this approach manages to capture large non-linear deformations and
minimizes the propagation of interpolation errors. While improving accuracy the
method is computationally efficient. We present comparative results on a range
of public 4D CT lung (POPI) and brain datasets (CUMC12, MGH10).
