Three-dimensional (3D) digital images are helpful in studying the physical properties of a medium. Moreover, reconstructing a 3D image from a two-dimensional (2D) image via computer-mathematical modeling is an important process. Based on the relationship between cascaded grids, an ingenious cascaded polymorphic method is proposed in this work to reconstruct a 3D image from a 2D image. By using the cascaded polymorphic method, a patch can be copied directly into a reconstruction grid by matching the patterns between cascaded grids; the polymorphism of the templates correspond to the grid size. To improve the reconstruction performance further, the non-edge region expansion strategy for a layer and the non-edge region replication strategy for adjacent layers were also proposed. A core sample and building material were selected as the test materials, and several effective measurements were used as quantitative means. To display the reconstruction effect intuitively, 2D reconstruction experiments were also performed along with the 3D experiment. The results show that the reconstruction speed is significantly improved using the cascaded polymorphic method, and the morphological features of the 3D reconstruction are clearly promoted.

三维 (3D) 数字图像有助于研究介质的物理特性。此外，通过计算机数学建模从二维 (2D) 图像重建 3D 图像是一个重要的过程。基于级联网格之间的关系，本文提出了一种巧妙的级联多态方法来从 2D 图像重建 3D 图像。通过使用级联多态方法，可以通过匹配级联网格之间的模式将补丁直接复制到重建网格中；模板的多态性对应于网格大小。为了进一步提高重构性能，还提出了一层非边缘区域扩展策略和相邻层非边缘区域复制策略。选取岩心样品和建筑材料作为试验材料，并使用了几种有效的测量方法作为定量手段。为了直观地展示重建效果，在3D实验的同时还进行了2D重建实验。结果表明，采用级联多态方法重建速度显着提高，3D重建的形态特征得到明显提升。