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，其研究动机源于冷冻电子显微镜的应用需求。该算法基于刚性变换后密度图之间1-Wasserstein距离的最小化。相较于欧几里得距离，该损失函数具有更平缓的优化地形，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，该算法在精度和效率上均优于现有方法。针对异质性配对对齐场景，我们揭示了开发新距离函数的潜在需求。