图像配准是计算机视觉领域的一类重要问题, 对于两幅定义域相同的图像, 图像配准的目标是求一个图像定义域上的变换场, 使得其中一幅图像复合上该变换场尽可能接近另一 幅图像, 同时保持原图像的一些关键特征. 由于图像配准能够获取图像的像素级形变, 致使其广泛应用于医学图像和遥感图像处理, 在无监督分割、比对多期相图像差异等问题中有 着许多研究和应用成果.

传统的图像配准方法一般基于变分模型, 这些方法以数学理论作为支撑, 在模型的可解 释性、稳定性、几何性质的描述方面具有优势, 然而其高额的时间消耗导致其在许多实际应用中举步维艰. 随着卷积神经网络在计算机视觉领域大放异彩, 越来越多的研究者开始关注基于深度学习的图像配准方法. 尽管这些方法取得了非常优秀的配准效果, 然而配准后的图像细节提升、配准变换的拓扑保持能力仍然具有挑战性. 此外, 许多基于深度学习的配准方法采取几乎相同的网络结构, 即使一些工作使用注意力机制重构网络结构, 这些注意力机制往往也面临过度依赖经验以及加入人类主观偏见的问题. 面对这些配准方法中存在的问题, 本文的主要工作包括以下两方面：

为了提升图像配准的细节精度, 本文考察了卷积网络中配准残差的高维特征分布, 并用混合分布模型对这些高维特征进行描述, 以此得到可解释注意力机制. 该注意力机制对偏差场高维特征的残差进行加权, 使得网络具备自适应寻找关键区域的能力, 增强图像配准细节. 具体来说, 使用卷积和激活层将原始图像映射到高维特征空间, 进而使用具有混合分布先验的变分模型构建高维特征空间中的数值迭代算法, 最后使用算法展开技术(unrolling technique) 将数值算法展开为卷积神经网络, 本文中将该卷积网络命名为混合分布 U 形网络 (MDUnet).

为了使配准变换场的微分同胚性不依赖于训练数据分布, 本文利用变分模型构建数值迭代算法, 并以无参数迭代层的形式加入网络结构, 实现非数据依赖的微分同胚约束. 除此之外, 本文还从数值计算角度分析了现有损失函数约束项的局限性, 并提出计算高效且使得微分同胚约束更有效的雅各比行列式计算方式.

Image registration is an important problem in the field of computer vision. For two images with the same domain, the goal of image registration is to find a transformation field on the image domain, which makes one image, after being transformed by the field, as similar as possible to the other image while maintaining some key features of the original image. Due to the ability of image registration to obtain pixel-level deformations, it has been widely used in medical image and remote sensing image processing, as well as in unsupervised segmentation, comparison of multitemporal phase images, and other problems, which have yielded many research and application achievements.

Traditional image registration methods are generally based on variational models, which are supported by mathematical theories and have advantages in interpretability, stability, and description of geometric properties. However, their high time consumption makes it difficult to be applied in many practical applications. With the convolutional neural network making significant strides in the field of computer vision, more and more researchers have begun to focus on deep learningbased image registration methods. Although these methods have achieved very good registration results, the challenges of improving the detailed accuracy of registered images and maintaining the topological preservation ability of registration transformations still exist. In addition, many deep learning-based registration methods adopt almost the same network structure. Even some works use attention techniques to reconstruct the network structure, these attention techniques often face the problems of excessive dependence on experience and adding human subjective bias. In view of these problems existing in the registration methods, the main work of this paper includes the following two aspects:

To improve the detail accuracy of image registration, this paper examines the highdimensional feature distribution of the registration residuals in convolutional networks and describes these high-dimensional features using a mixture distribution model to obtain an interpretable attention technique. The attention technique weights the residual of the high-dimensional IIfeature of the displacement field, enabling the network to have the ability to adaptively search for key regions and enhance the detail of image registration. Specifically, the original image is mapped to a high-dimensional feature space using convolutional and activation layers, and then a numerical iterative algorithm is constructed in the high-dimensional feature space using a variational model with a mixture distribution prior. Finally, the numerical algorithm is unrolled into a convolutional neural network using the unrolling technique, and the convolutional network is named the mixture distribution U-shaped network (MDUnet) in this paper.

To make diffeomorphism of registration transformation field independent of the training data distribution, this paper uses a variational model to construct a numerical iterative algorithm and adds it to the network structure in the form of a non-parameter iterative layer, realizing a non-data dependent diffeomorphism constraint. In addition, this paper analyzes the limitations of existing loss function constraint terms from a numerical calculation perspective and proposes a Jacobian determinant calculation method that is computationally efficient and makes the diffeomorphism constraint more effective.