Discrete combinatorial geometry
Discrete combinatorial geometry
复制标题
离散组合几何
DOI：
10.1016/s0031-3203(97)00001-0
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
A. Ichikawa
中科院分区：
文献类型：
--
作者：
Y. Kenmochi;A. Imiya;A. Ichikawa
在计算机视觉中，最终目标之一是从测量数据确定我们真实的世界中的三维物体的几何特性。作为测量的原始数据和几何属性之间的中间表达，我们需要一种在计算机中表示对象的方法。对于对象表示，只使用有限精度数的几何是必要的，因为在计算机中我们只能操纵有限精度数。在本文中，我们开发了一个新的几何，我们称之为离散组合几何，由于有限精度数的空间的离散性，应用经典组合几何的基本定义。利用离散组合几何，我们介绍了一种新的方法来表示曲线，曲面和物体的计算机。我们还表明，我们的新表示是基于这样一个事实，即曲面的边界由曲线和对象的边界由曲面组成。
In computer vision, one of the ultimate aims is the determination of geomettric properties of 3-dimensional objects in our real world from measured data. As an expression intermediate between measured raw data and geometric properties, we need a method of representing objects in computers. For the object representations, geometry which uses only finite-precision numbers is necessary because in computers we can only manipulate finite-precision numbers. In this paper, we develop a new geometry, which we call discrete combinatorial geometry due to the discreteness of the space of finite-precision numbers, applying fundamental definitions of classical combinatorial geometry. Using discrete combinatorial geometry, we introduce a new method for representing curves, surfaces and objects in computers. We also show that our new representation is based on the fact that the boundary of a surface consists of curves and the boundary of an object consists of surfaces.