In GIS, spatial analysis is based on the use of spatial operations such as testing the spatial relations between features. Often, such tests are invalidated by errors in datasets. It is a very common experience that two bordering regions which should obey the topological relation “meet” fall instead in the “overlap” category. The situation is exacerbated when applying topological operators to regions that come from different datasets, where resolution and error sources are different. Despite the problem being quite common, up to now no standard approach has been defined to deal with spatial relations affected by errors of various origins. Referring to topological relations, we define a model to extend the eight Egenhofer relations between two simple regions: we call them homological relations (H‐relations). We discuss how exact topological relations can be extracted from observed relations and discuss the case of irregular tessellations, where errors have the most impact on vector data. In the proposed case study within the domain of geographic crowdsourced data, we propose algorithms for identifying homological regions and obtaining a corrected tessellation. This methodology can be considered as a step for quality control and the certification of irregular tessellations.

中文翻译：

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同源关系：不规则镶嵌认证的方法

在GIS中，空间分析基于对空间操作的使用，例如测试要素之间的空间关系。通常，此类测试会因数据集错误而失效。一个非常普遍的经验是，两个应遵循拓扑关系“相遇”的边界区域落在“重叠”类别中。当将拓扑运算符应用于来自不同数据集的区域时，情况更加恶化，其中分辨率和错误来源不同。尽管该问题非常普遍，但迄今为止，尚未定义任何标准方法来处理受各种起源误差影响的空间关系。关于拓扑关系，我们定义一个模型来扩展两个简单区域之间的八个Egenhofer关系：我们称它们为同源关系（H关系）。我们讨论了如何从观察到的关系中提取确切的拓扑关系，并讨论了不规则镶嵌的情况，其中不规则误差对矢量数据的影响最大。在地理众包数据领域内的拟议案例研究中，我们提出了用于识别同源区域并获得校正的细分的算法。这种方法可以被认为是质量控制和不规则方格花纹认证的步骤。