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

不完全覆盖的空间数据收集产生的区域有孔洞和分隔，通常无法通过插值填充。地理传感器网络通常会产生这样的配置，随着传感器群体的扩散，现在迫切需要为用户提供更好的信息技术，即认知上合理的方法来搜索或比较可能不完整的可用空间数据集。调查的目的是提高对具有孔和/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穴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，以解决具有空穴和分离特征的潜在复杂配置。本文讨论了这种拓扑关系的三个特征：在一定的粒度上形式化一组可靠的关系，这种关系允许区分有孔和分离区域的显著特征，同时提供了以有意义和一致的方式推广到更粗的关系的机会；放宽这种关系，以便从所采用的方法中立即确定最相似的关系；从这些关系的组成中对新信息进行定性推断，以识别不一致之处，并从单个关系中提取不能立即获得的信息。假设是，将关系形式化与声音相似性和组合推理相结合，可以为充分表达的通用方法提供关键见解，从而为有孔区域和有分离的区域建模拓扑关系。由此产生的拓扑空间关系理论强调了带孔区域和带分离区域之间的关系的相似性，当这些区域嵌入到球体表面时，这种相似性最为明显，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，因此它们更接近于人们自己的推理，因此更好地理解复合空间对象的关系将对定性空间推理产生影响，而不需要绘制图形描述来进行推理。它还为以自然语言空间结构进行交流的语言结构奠定了基础，最终导致说话地图。这种空穴和分离区域之间的拓扑关系理论的直接影响是对地理传感器网络收集的数据集的查询和推理。欲了解更多信息，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