A frequently investigated problem in various applications of binary image processing is to ensure the topology preservation of image operators. Although the literature primarily focuses on 2D and 3D pictures that are sampled on the conventional square and cubic grids, respectively, some alternate structures such as the body-centered cubic grid and the face-centered cubic grid have also attracted remarkable scientific interest. This work examines the topology preservation on the 3D body-centered cubic grid. A simple object point in a binary picture has the property that the deletion of that single point preserves the topology. As the first result of this paper, some easily visualized characterizations of simple points are presented. It is well-known that the simultaneous deletion of a set of simple points may not preserve the topology. The author also managed to state a sufficient condition for topology preserving operators that deletes a number of object points at a time. In addition, two examples for so-called subfield-based reductions are presented, and their topological correctness is verified with the help of the new sufficient condition.

二值图像处理的各种应用中经常研究的一个问题是确保图像算子的拓扑保存。尽管文献主要集中在分别在常规方形和立方网格上采样的 2D 和 3D 图片，但体心立方网格和面心立方网格等一些替代结构也引起了极大的科学兴趣。这项工作检查了 3D 体心立方网格上的拓扑保留。二值图像中的一个简单目标点具有删除该单个点保留拓扑结构的特性。作为本文的第一个结果，提出了一些简单点的易于可视化的表征。众所周知，同时删除一组简单点可能不会保留拓扑。作者还设法陈述了一次删除多个对象点的拓扑保留算子的充分条件。此外，还给出了两个所谓的基于子场的约简的例子，并在新的充分条件的帮助下验证了它们的拓扑正确性。