On covering a digital disc with concentric circles in Z2
On covering a digital disc with concentric circles in Z2
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关于Z2中用同心圆覆盖数字光盘
DOI：
10.1016/j.tcs.2013.07.036
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
B. Bhattacharya
中科院分区：
文献类型：
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作者：
Sahadev Bera;Partha Bhowmick;Peer Stelldinger;B. Bhattacharya
数字圆和数字盘满足许多奇异的各向异性特性，理解这些特性对于解决图像分析和计算机图形学中的各种问题至关重要。在本文中，我们研究的基本属性缺席像素出现，而覆盖数字光盘与同心数字圆。我们提出，第一次，这些像素的数学表征数论和数字几何的基础上。有趣的是，缺席发生在众多，我们表明，他们的计数随半径的平方变化。利用最小抛物线和最大抛物线的概念导出了这些缺席者的数量。利用这一抛物线特征，我们得到了一个像素是一个盘缺席的充分必要条件，并得到了缺席的几何性质。提出了一种定位缺席者的算法。我们发现，缺席像素的光盘像素的总数的比率接近一个常数，随着半径的增加。测试结果证实了我们的理论研究结果。
Digital circles and digital discs satisfy many bizarre anisotropic properties, understanding of which is essential for solving various problems in image analysis and computer graphics. In this paper we study the underlying properties ofabsentee pixelsthat appear while covering a digital disc with concentric digital circles. We present, for the first time, a mathematical characterization of these pixels based on number theory and digital geometry. Interestingly, the absentees occur in multitude, and we show that their count varies quadratically with the radius. The notion ofinfimum parabolaandsupremum parabolahas been used to derive the count of these absentees. Using thisparabolic characterization, we derive a necessary and sufficient condition for a pixel to be adisc absentee, and obtain the geometric properties of the absentees. An algorithm to locate the absentees is presented. We show that the ratio of the absentee pixels to the total number of disc pixels approaches a constant with increasing radius. Test results have been furnished to substantiate our theoretical findings.