Given a set of points $S\in {\mathbb{R}}^2$, reconstruction is a process of identifying the boundary edges that best approximates the set of points. In general, the set of points can either be derived from only the boundaries of the curves (called as boundary sample) or can be derived from both boundary and interior of the curves (called as dot pattern). Most of the existing algorithms focus towards reconstruction from only boundary samples, termed as curve reconstruction. Unfortunately many of them don't reconstruct when the input is of dot pattern type (called as shape reconstruction). In this paper, we propose an input-independent non-parametric algorithm for reconstruction that works for both dot patterns as well as boundary samples. The algorithm starts with computing the Delaunay triangulation of the given point set. An edge between a pair of triangles is marked for removal when the circumcenters lie on the same side of the edge. Further, we also propose additional criterion for removing edges based on characterizing a triangle by the distance between its circumcenter and incenter. To maintain a manifold output, a degree constraint is employed. The proposed approach requires only a single pass to capture both inner and outer boundaries irrespective of the number of objects/holes. Moreover, the same criterion has been employed for both inner and outer boundary detection. The experiments show that our approach works well for a variety of inputs such as multiple components, multiple holes etc. Extensive comparisons with state-of-the-art methods for various kinds of point sets including varying the sampling density and distribution show that our algorithm is either better or on par with them. Theoretical discussions on the algorithm have also been presented using ϵ-sampling and r-sampling. Limitations of the algorithm are also discussed.

给定一点 $\mathrm{小号}\in {\mathbb{[R}}^2$重建是确定最接近点集的边界边的过程。通常，点集可以仅从曲线的边界导出（称为边界样本），也可以从曲线的边界和内部导出（称为点图案）。现有的大多数算法都集中于仅从边界样本进行重建，这称为曲线重建。不幸的是，当输入为点模式类型时，它们中的许多都无法重构（称为形状重构）。在本文中，我们提出了一种与输入无关的非参数重建算法，该算法适用于点图案和边界样本。该算法开始于计算给定点集的Delaunay三角剖分。当外接点位于边缘的同一侧时，标记一对三角形之间的边缘以将其删除。此外，我们还提出了附加标准，该标准基于通过三角形的外接心和内心之间的距离来表征三角形来消除边缘。为了保持歧管输出，采用度约束。所提出的方法只需要一次通过就可以捕获内部和外部边界，而与对象/孔的数量无关。而且，对于内部和外部边界检测都采用了相同的标准。实验表明，我们的方法适用于多种输入，例如多个组件，多个孔等。与各种点集的最新技术进行了广泛的比较，包括改变采样密度和分布，这表明我们的算法是更好的或与之相当。关于算法的理论讨论也已经使用ϵ采样和r采样。还讨论了该算法的局限性。