Parametric spatial transformation models have been successfully applied to
image registration tasks. In such models, the transformation of interest is
parameterized by a fixed set of basis functions as for example B-splines. Each
basis function is located on a fixed regular grid position among the image
domain, because the transformation of interest is not known in advance. As a
consequence, not all basis functions will necessarily contribute to the final
transformation which results in a non-compact representation of the
transformation. We reformulate the pairwise registration problem as a recursive
sequence of successive alignments. For each element in the sequence, a local
deformation defined by its position, shape, and weight is computed by our
recurrent registration neural network. The sum of all local deformations yield
the final spatial alignment of both images. Formulating the registration
problem in this way allows the network to detect non-aligned regions in the
images and to learn how to locally refine the registration properly. In
contrast to current non-sequence-based registration methods, our approach
iteratively applies local spatial deformations to the images until the desired
registration accuracy is achieved. We trained our network on 2D magnetic
resonance images of the lung and compared our method to a standard parametric
B-spline registration. The experiments show, that our method performs on par
for the accuracy but yields a more compact representation of the
transformation. Furthermore, we achieve a speedup of around 15 compared to the
B-spline registration.

采用递归对齐的方式，使用循环注册神经网络计算每个元素的局部变形，最终的空间对齐由所有局部变形的总和得到；使用该方法可以检测图像中非对齐的区域并学习如何适当地进行本地注册。在用于肺部磁共振图像的实验中，该方法与当前标准的参数化 B 样条配准方法相比，准确性不相上下，但给出了更紧凑的变换表示，并且加速了约 15 倍。