CARL: A Framework for Equivariant Image Registration
图像配准估计估计在成对图像之间的空间对应关系。这些估计通常通过深度网络的数值优化或回归来获得。具有这种估计器的一个良好特性是对输入图像的一对图像之间的对应关系保持不变。具体来说，估计器应对输入图像的变形保持等价。在本文中，我们仔细分析了在多级深度配准网络中实现所需等价性的愿望。根据这些分析，我们1）引入了$[U,U]$等价性（网络对输入图像相同变形保持等价性）和$[W,U]$等价性（输入图像可以经历不同的变形）；2）证明了在适当的分层配准设置中，如果第一步具有$[W,U]$等价性，其他步骤具有$[U,U]$等价性，那么总体$[W,U]$等价性是足够的；3）证明了常见的位移预测网络只表现出$[U,U]$等价性（平移）而不是更强大的$[W,U]$等价性；4）通过结合坐标注意机制和位移预测修复层（CARL），实现了多级$[W,U]$等价性。总体而言，我们的方法在多个3D医学图像配准任务中获得了出色的实际配准性能，并且比现有的无监督方法在具有挑战性的腹部配准问题中表现更好。
Image registration estimates spatial correspondences between a pair of images. These estimates are typically obtained via numerical optimization or regression by a deep network. A desirable property of such estimators is that a correspondence estimate (e.g., the true oracle correspondence) for an image pair is maintained under deformations of the input images. Formally, the estimator should be equivariant to a desired class of image transformations. In this work, we present careful analyses of the desired equivariance properties in the context of multi-step deep registration networks. Based on these analyses we 1) introduce the notions of $[U,U]$ equivariance (network equivariance to the same deformations of the input images) and $[W,U]$ equivariance (where input images can undergo different deformations); we 2) show that in a suitable multi-step registration setup it is sufficient for overall $[W,U]$ equivariance if the first step has $[W,U]$ equivariance and all others have $[U,U]$ equivariance; we 3) show that common displacement-predicting networks only exhibit $[U,U]$ equivariance to translations instead of the more powerful $[W,U]$ equivariance; and we 4) show how to achieve multi-step $[W,U]$ equivariance via a coordinate-attention mechanism combined with displacement-predicting refinement layers (CARL). Overall, our approach obtains excellent practical registration performance on several 3D medical image registration tasks and outperforms existing unsupervised approaches for the challenging problem of abdomen registration.
https://arxiv.org/abs/2405.16738
https://arxiv.org/pdf/2405.16738.pdf