In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation. The induced loss function enjoys a more benign landscape than its Euclidean counterpart and Bayesian optimization is employed for computation. Numerical experiments show improved accuracy and efficiency over existing algorithms on the alignment of real protein molecules. In the context of aligning heterogeneous pairs, we illustrate a potential need for new distance functions.

翻译：本文提出了一种在三维物体以密度图表示时的对齐算法，其研究动机源于低温电子显微镜的应用场景。该算法通过最小化刚性变换后密度图之间的1-Wasserstein距离来实现对齐。与欧几里得距离对应的损失函数相比，该诱导损失函数具有更优的景观特性，并采用贝叶斯优化进行计算。数值实验表明，在真实蛋白质分子的对齐任务中，该算法相较于现有方法具有更高的准确性和效率。针对异质配对的对齐场景，本文揭示了新距离函数潜在的开发需求。