Multiple-point statistics (MPS) is a useful approach to reconstruct three-dimensional models in the macroscopic or microscopic field. Extracting spatial features for three-dimensional reconstruction from two-dimensional training images (TIs), and characterizing non-stationary features with directional ductility are two key issues in MPS simulation. This study presents a step-wise MPS-based three-dimensional structures reconstruction algorithm with the sequential process and hierarchical strategy based on two-dimensional images. An extension method is proposed to construct three-dimensional TIs. With a sequential simulation process, an initial guess at the coarsest scale is simulated, in which hierarchical strategy is used according to the characteristics of TIs. To obtain a more refined realization, an expectation-maximization like iterative process with global optimization is implemented. A concrete example of chondrite micro-structure simulation, in which one scanning electron microscopy (SEM) image of the Heyetang meteorite is used as TI, shows that the presented algorithm can simulate complex non-stationary structures.

多点统计（MPS）是在宏观或微观领域重建三维模型的有用方法。从二维训练图像（TI）中提取用于三维重建的空间特征，并利用方向延性来表征非平稳特征是MPS仿真中的两个关键问题。该研究提出了一种基于MPS的逐步三维结构重建算法，该算法具有基于二维图像的顺序过程和分层策略。提出了一种扩展方法来构造三维TI。通过顺序仿真过程，可以模拟最粗略的初始猜测，其中根据TI的特性使用分层策略。为了获得更完善的实现，实现了期望最大化，例如带有全局优化的迭代过程。以球眼陨石的一个扫描电子显微镜（SEM）图像作为TI的球粒陨石微结构模拟的一个具体例子表明，该算法可以模拟复杂的非平稳结构。