Extended Hausdorff distance for spatial objects in GIS
Extended Hausdorff distance for spatial objects in GIS
复制标题
GIS 中空间对象的扩展豪斯多夫距离
DOI：
10.1080/13658810601073315
复制
发表时间：
2007-01-01
影响因子：
5.7
通讯作者：
Xiaoyong, C.
中科院分区：
文献类型：
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作者：
Min, D.;Zhilin, L.;Xiaoyong, C.
距离是空间科学中的一个基本概念。空间距离是衡量空间物体之间相对位置、表示相邻物体之间相似程度的一个非常重要的参数。事实上，空间距离在邻域分析、结构相似性度量、图像（或对象）匹配、聚类分析等许多领域中发挥着重要作用。本文对现有的空间物体间距离计算模型进行了评估并指出了其存在的问题；然后，引入豪斯多夫距离的概念作为不同类型空间对象的度量指标。通过引入分位数，该距离被扩展为统一表示，从而产生扩展的豪斯多夫距离。事实上，所谓扩展豪斯多夫距离，实际上是一种以最小距离、豪斯多夫距离、中位豪斯多夫距离为特征的度量。前两者可用于测量离散度，最后一个可用于测量空间对象之间距离分布的集中趋势。已经提出了一种称为 ε-buffer 的方法来计算中值 Hausdorff 距离。最后，讨论了潜在的应用。
Distance is a fundamental concept in spatial sciences. Spatial distance is a very important parameter to measure the relative positions between spatial objects and to indicate the degree of similarity between neighbouring objects. Indeed, spatial distance plays an important role in many areas such as neighbourhood analysis, structural similarity measure, image (or object) matching, clustering analysis, and so on. In this paper, existing computational models for the distance between spatial objects are evaluated and their problems pointed out; then, the concept of the Hausdorff distance is introduced as a metric indicator for different types of spatial objects. This distance is extended to a uniform representation by the introduction of the quantile, leading to the extended Hausdorff distance. Indeed, the so‐called extended Hausdorff distance is, in fact, a kind of metric characterized by the minimum distance, the Hausdorff distance, and the median Hausdorff distance. The first two can be used for measuring the dispersion and the last one for measuring the central tendency of the distance distribution between spatial objects. A method termed the ε‐buffer has been proposed for the computation of the median Hausdorff distance. Finally, potential applications are discussed.