In this paper, we adapt the two topological numbers, which have been proposed to efficiently characterize simple points in specific neighborhoods for 3D binary images, to the case of 2D binary images. Unlike the 3D case, we only use a single neighborhood to define these two topological numbers for the 2D case. Then, we characterize simple points either by using the two topological numbers or by a single topological number linked to another one condition. We compare the characterization of simple points by topological numbers with two other ones based on Hilditch crossing number and Yokoi number. We also highlight the number of possible configurations corresponding to a simple point, which also represents the maximum limit of local configurations that a thinning algorithm operating by parallel deletion of simple (individual) points may delete while preserving topology (limit usually not reachable, depending on the deletion strategy).

翻译：本文针对二维二值图像，对已提出的用于三维二值图像特定邻域中高效表征简单点的两个拓扑数进行了适应性调整。与三维情况不同，在二维情形中我们仅采用单一邻域来定义这两个拓扑数。随后，我们通过使用这两个拓扑数，或通过关联另一条件的单一拓扑数来表征简单点。我们将基于拓扑数的简单点表征方法与基于Hilditch交叉数和Yokoi数的另外两种表征方法进行了比较。同时，我们重点分析了对应简单点的可能构型数量，该数量也代表了采用并行删除简单（单个）点操作的细化算法在保持拓扑结构前提下可删除的局部构型最大极限（该极限通常无法达到，具体取决于删除策略）。