论文标题
内侧轴等体轮廓
Medial Axis Isoperimetric Profiles
论文作者
论文摘要
最近提出的作为评估几何紧凑性的稳定手段，平面域的等值剖面测量的最小周边是刻有规定面积从0到域面积变化所需的最小周边。尽管此配置文件已被证明对于评估地理分区的属性很有价值，但现有的计算算法取决于积极的近似值，并且在计算上仍然昂贵。在本文中，我们提出了一种近似等级轮廓的实用方法，并表明对于满足“厚颈”条件的域，我们的近似值是准确的。对于更一般的领域，我们表明我们的界限仍然在保守的制度内，否则是上限。我们的方法基于内侧轴的遍历，该轴会产生有效且稳健的结果。我们将技术与最新近似值与各种域上的等速度概况进行了比较，并且比以前可以实现的范围明显更紧密。
Recently proposed as a stable means of evaluating geometric compactness, the isoperimetric profile of a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain. While this profile has proven valuable for evaluating properties of geographic partitions, existing algorithms for its computation rely on aggressive approximations and are still computationally expensive. In this paper, we propose a practical means of approximating the isoperimetric profile and show that for domains satisfying a "thick neck" condition, our approximation is exact. For more general domains, we show that our bound is still exact within a conservative regime and is otherwise an upper bound. Our method is based on a traversal of the medial axis which produces efficient and robust results. We compare our technique with the state-of-the-art approximation to the isoperimetric profile on a variety of domains and show significantly tighter bounds than were previously achievable.
