用邻域序列逼近正方形网格中的欧氏圆
Approximating the Euclidean circle in the square grid using neighbourhood sequences
摘要：
距离测量是数字几何和数字图像处理中的一个重要课题。由于我们对几何的自然理解，我们认为离给定点等远的点的集合是一个欧几里得圆。利用数字网格上的经典邻域关系，我们得到了与欧几里得圆有很大不同的圆。在本文中，我们研究了不同的方法近似的欧几里得圆的正方形网格，考虑可能的动机以及。我们比较周长，面积，曲线和非紧性为基础的近似，并检查其实现使用邻域序列。我们还提供了一个表格，总结了我们的结果，并可用于开发应用程序时，支持邻域序列。
英文摘要：
Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the classical neighbourhood relations on digital grids, we get circles that greatly differ from the Euclidean circle. In this paper we examine different methods of approximating the Euclidean circle in the square grid, considering the possible motivations as well. We compare the perimeter-, area-, curve- and noncompactness-based approximations and examine their realization using neighbourhood sequences. We also provide a table which summarizes our results, and can be used when developing applications that support neighbourhood sequences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
