ABSTRACT

This paper explores a class of qualitative-geometric relations between disjoint regions, embedded in the surface of a sphere or in the plane. These relations combine topological information about the configuration of the regions themselves as well as of the geometric Voronoi regions surrounding them. The method uses maptrees to construct a rigorous and exhaustive framework for n-ary relations between ensembles of regions. The resulting uniquely defined relations are akin to the verbal spatial relation ‘surrounds,’ in one common interpretation. The paper provides an exhaustive formal classification of such extended spatial relations between up to three regions. A further exhaustive computational exploration of up to seven regions in the sphere also provides an algorithm to enumerate all possible configurations. The results demonstrate how the approach can be used to provide fine-grained and salient descriptions of qualitative-geometric relations for complex scenes involving ensembles of multiple regions.

摘要

本文探讨了嵌入球体表面或平面中的不相交区域之间的一类定性几何关系。这些关系结合了有关区域本身以及周围几何Voronoi区域的配置的拓扑信息。该方法使用maptrees为n构建严格而详尽的框架区域合奏之间的一元关系。在一种常见的解释中，得到的唯一定义的关系类似于言语空间关系“周围”。本文对多达三个区域之间的这种扩展空间关系进行了详尽的形式分类。对球体内多达七个区域的进一步穷举计算探索还提供了一种枚举所有可能配置的算法。结果表明，该方法如何用于为涉及多个区域的集合的复杂场景提供定性-几何关系的细粒度和显着描述。