提出二维二值图像中简化点的新拓扑表征方法
Topological numbers and their use to characterize simple points for 2D binary images
- 用单邻域定义两个拓扑数表征简化点
- 拓扑数可准确识别简化点，且揭示最多16种配置
- 适合图像细化算法设计与拓扑保持研究
本文将原先用于3D二值图像高效表征简化点的两个拓扑数，适配至2D二值图像场景。不同于3D情况，二维情形仅需一个邻域即可定义这两个拓扑数。我们通过两个拓扑数或两者间关联的单一拓扑数来刻画简化点。将拓扑数方法与基于Hilditch交叉数和Yokoi数的方法进行对比，并指出简化点对应的可能配置数量为16，这代表了并行删除简化点的细化算法在保持拓扑不变性下所能处理的最大局部配置上限（实际是否可达取决于删除策略）。
原文摘要 · Abstract (English)
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).
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