III: Small: A Theory of Topological Relations for Compound Spatial Objects

覆盖不完整的空间数据集合会产生带有空洞和分隔的区域，而这些区域通常无法通过内插来填充。地球传感器网络通常会产生这样的配置，随着传感器群体的激增，现在迫切需要向用户提供更好的信息技术和认知上可信的方法，以搜索或比较可能不完整的可用空间数据集。这些研究的目的是增进对具有空洞和/或分离的空间区域的定性空间关系的认识。核心活动是研究具有空洞区域的拓扑空间关系和具有分离区域的拓扑空间关系之间的相互作用，以解决既具有空洞又具有分离特征的潜在的复杂构型。讨论了这样一组拓扑关系的三个特征：在允许区分空洞和分离区域的显著特征的粒度上对一组合理的关系进行形式化，同时提供机会以有意义和一致的方式将其推广到更粗的关系；放松这种关系，使得最相似关系的确定直接遵循应用的方法论；从这种关系的组合中定性地推断新的信息以识别不一致，并从个体关系中提取不直接可用的信息。假设将关系形式化与合理的相似性和组合推理相结合，为有效地表达完整区域和具有分离的区域的拓扑关系建模提供了关键的见解。拓扑空间关系的结果理论突出了有空洞区域的关系和有分离区域的关系之间的平行关系，当这些区域嵌入到球面上时，这种平行关系最为明显，而这些规律的某些部分往往隐藏在通常的平面嵌入中。由于拓扑关系是定性的空间描述，它们更接近于人们自己的推理，所以更好地理解复合空间对象的关系将对定性空间推理产生分支，而不需要绘制图形描述来进行推理。它还为语言结构以自然语言空间配置进行交流奠定了基础，最终导致了会说话的地图。这种孔洞和分离区域之间的拓扑关系理论的直接影响是对地球传感器网络收集的数据集的查询和推理。有关详细信息，请参阅项目网页：URL：http://www.spatial.maine.edu/~max/holesAndParts.html

Spatial data collections with an incomplete coverage yield regionswith holes and separations that often cannot be filled byinterpolation. Geosensor networks typically generate suchconfigurations, and with the proliferation of sensor colonies,there is now an urgent need to provide users with better informationtechnologies of cognitively plausible methods to search for orcompare available spatial data sets that may be incomplete. Theobjective of the investigations is to advance knowledge aboutqualitative spatial relations for spatial regions with holesand/or separations.The core activity is the study of the interplay between topologicalspatial relations with holed regions and topological spatial relationswith separated regions to address the potentially complexconfigurations that feature both holes and separations. Threecharacteristics of such a set of topological relations are addressed:the formalization of a sound set of relations at a granularity thatallows for the distinction of the salient features of holed andseparated regions, while offering the opportunity to generalize tocoarser relations in a meaningful and consistent way; the relaxation ofsuch relations so that the determination of the most similar relationsfollows immediately from the applied methodology; and the qualitativeinference of new information from the composition of such relations toidentify inconsistencies and to drawn information that is notimmediately available from individual relations.The hypothesis is that combining the relation formalization with soundsimilarity and composition reasoning yields critical insights for asufficiently expressive, common approach to modeling topologicalrelations for holed regions and regions with separations. The resultingtheory of topological spatial relations highlights a parallelismbetween relations with holed regions and regions with separations,which is most apparent when these regions are embedded on thesurface of the sphere, while some parts of these regularities are oftenhidden in the usual planar embedding.Since topological relations are qualitative spatial descriptions, theycome close to people's own reasoning, so that a better understanding ofthe relations for compound spatial objects will have ramifications forqualitative spatial reasoning, without a need for drawing graphicaldepictions to make inferences. It also lays the foundation forlinguistic constructs to communicate in natural language spatialconfigurations, ultimately leading to talking maps. An immediate impactof this theory of topological relations between holed and separatedregions is on the querying and reasoning about dataset that aregathered by geosensor networks.For further information see the project web page:URL: http://www.spatial.maine.edu/~max/holesAndParts.html