Homological relations: A methodology for the certification of irregular tessellations

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.