We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm. Our methodology initiates with the computational determination of the Convex Hull vertices within the point cloud, followed by a systematic selection of optimal line segments, strategically chosen for their likelihood of intersecting internal void regions. We then utilize Delaunay triangulation in conjunction with Voronoi diagrams to ascertain the initial points for the construction of the maximal internal curve envelope by adopting a pseudo-recursive approach for higher-order void identification. In each iteration, the existing collection of maximal internal curve envelope points serves as a basis for identifying additional candidate points. This iterative process is inherently self-converging, ensuring progressive refinement of the void's shape with each successive computation cycle. The mathematical robustness of this method allows for an efficient convergence to a stable solution, reflecting both the geometric intricacies and the topological characteristics of the voids within the point cloud. Our findings introduce a method that aims to balance geometric accuracy with computational practicality. The approach is designed to improve the understanding of void shapes within point clouds and suggests a potential framework for exploring more complex, multi-dimensional data analysis.

翻译：我们提出了一种新方法，用于识别和表征二维点分布中的空洞形状。该方法整合了德劳内三角剖分、沃罗诺伊图以及最小距离评分算法。具体步骤包括：首先计算点云中凸包顶点的位置，系统性地选取最有可能与内部空洞区域相交的最优线段；随后结合德劳内三角剖分与沃罗诺伊图，采用伪递归方法确定初始点并构建最大内部曲线包络，以实现高阶空洞识别。在每次迭代中，以现有最大内部曲线包络点集为基础识别候选新点，该迭代过程具有自收敛特性，确保随着计算轮次递增逐步精确化空洞形状。该方法具备数学严谨性，可在收敛至稳定解的同时，准确反映点云中空洞的几何复杂度与拓扑特征。实验表明，该方法在几何精度与计算实用性之间取得了平衡，有助于深化对点云空洞形状的理解，并为探索更复杂的多维数据分析提供了潜在框架。