Multimodal image alignment is the process of finding spatial correspondences between images formed by different imaging techniques or under different conditions, to facilitate heterogeneous data fusion and correlative analysis. The information-theoretic concept of mutual information (MI) is widely used as a similarity measure to guide multimodal alignment processes, where most works have focused on local maximization of MI, which typically works well only for small displacements. This points to a need for global maximization of MI, which has previously been computationally infeasible due to the high run-time complexity of existing algorithms. We propose an efficient algorithm for computing MI for all discrete displacements (formalized as the cross-mutual information function (CMIF)), which is based on cross-correlation computed in the frequency domain. We show that the algorithm is equivalent to a direct method while superior in terms of run-time. Furthermore, we propose a method for multimodal image alignment for transformation models with few degrees of freedom (e.g., rigid) based on the proposed CMIF-algorithm. We evaluate the efficacy of the proposed method on three distinct benchmark datasets, containing remote sensing images, cytological images, and histological images, and we observe excellent success-rates (in recovering known rigid transformations), overall outperforming alternative methods, including local optimization of MI, as well as several recent deep learning-based approaches. We also evaluate the run-times of a GPU implementation of the proposed algorithm and observe speed-ups from 100 to more than 10,000 times for realistic image sizes compared to a GPU implementation of a direct method. Code is shared as open-source at github.com/MIDA-group/globalign.

多模态图像对齐是寻找不同成像技术或不同条件下形成的图像之间的空间对应关系，以促进异构数据融合和相关分析的过程。互信息 (MI) 的信息论概念被广泛用作指导多模态对齐过程的相似性度量，其中大多数工作都集中在 MI 的局部最大化上，这通常仅适用于小位移。这表明需要全局最大化 MI，由于现有算法的高运行时复杂性，这在以前在计算上是不可行的。我们提出了一种有效的算法来计算所有离散位移的 MI（形式化为交叉互信息函数（CMIF）），它基于在频域中计算的互相关。我们表明该算法等效于直接方法，但在运行时间方面具有优势。此外，我们提出了一种基于所提出的 CMIF 算法的具有少量自由度（例如，刚性）的变换模型的多模态图像对齐方法。我们评估了所提出的方法在三个不同的基准数据集上的有效性，包括遥感图像、细胞学图像和组织学图像，并且我们观察到出色的成功率（在恢复已知的刚性变换方面），总体上优于替代方法，包括局部优化MI，以及最近的几种基于深度学习的方法。我们还评估了所提出算法的 GPU 实现的运行时间，并观察了从 100 到超过 10 的加速，与直接方法的 GPU 实现相比，真实图像尺寸的 000 倍。代码在 github.com/MIDA-group/globalign 上作为开源共享。