An algorithm is proposed for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The algorithm produces a mesh whose boundary is proved to be homeomorphic to the object surface. In addition, it provides a guaranteed dihedral angle bound of up to $19.47^{\circ }$ for the output tetrahedra. Moreover, it allows for user-specified guaranteed bounds on the distance between the boundaries of the mesh and the boundaries of the materials. It produces a small number of mesh elements that comply with these guarantees, and is compatible in performance with other software. The algorithm offers all of the following properties: bounded dihedral angles, customized two-sided Hausdorff distance, topological faithfulness, a small number of elements, and run-time performance. The experimental evaluation on synthetic and real medical data illustrates the efficiency and effectiveness of the method.

提出了一种生成多材料图像三维非结构化四面体网格的算法。该算法产生一个网格，其边界被证明与物体表面同胚。此外，它还提供了一个有保证的二面角界限，最高可达$19.47^{\circ }$为输出四面体。此外，它允许用户指定网格边界和材料边界之间距离的保证边界。它生成少量符合这些保证的网格元素，并且在性能上与其他软件兼容。该算法提供以下所有属性：有界二面角、自定义两侧 Hausdorff 距离、拓扑忠实度、少量元素和运行时性能。对合成和真实医学数据的实验评估说明了该方法的效率和有效性。