【作者】 马中伟；

【导师】 韩向春；

【作者基本信息】 燕山大学 ， 计算机应用技术， 2010， 硕士

【摘要】 定性空间推理是空间数据库和地理信息系统应用研究中必不可少的组成部分,而随着定性空间推理研究的深入,方向关系与拓扑关系等多种空间关系组合推理成为了定性空间推理的研究热点。目前已有的方向关系与拓扑关系组合的模型和推理方法都存在缺陷和不足,更缺少方向关系与拓扑关系组合网络一致性检验的专门研究。因此,本文对方向关系与拓扑关系的组合推理和一致性检验进行了研究和探索。首先,基于井字投影模型,结合区间代数和矩形代数理论,提出了空间对象拓扑关系投影区间矩形代数的表示方法,实现了空间对象方向关系和拓扑关系的统一表示。其次,考虑到组合推理的灵活性,引入了方向关系和拓扑关系的取反运算,基于拓扑与方向间的相互依赖关系,给出了方向关系与拓扑关系的交互表,进而得到了矩形基本方向关系、非矩形基本方向关系及多基本方向关系与拓扑关系组合的推理算法,并给出了推理算法的正确性证明和示例验证。通过对上述三种算法进行分析,给出了方向关系与拓扑关系同质和异质组合推理的通用算法和该算法的正确性证明。最后,本文对空间对象井字投影模型中的凸关系进行详细分析,给出了空间对象方向关系与拓扑关系组合中凸关系的判断方法和异质约束判断方法,结合凸关系网络定理和路径一致性算法,提出了方向关系与拓扑关系组合网络一致性检验的算法,并对算法进行了复杂性分析和理论性证明,最后,根据算法进行了实验设计,对实验结果进行了详细分析,验证了算法的正确性。更多还原

【Abstract】 Qualitative spatial reasoning is an absolutely necessary part of the study about the application of spatial database and Geography Information System. With the deepening of qualitative spatial reasoning, reasoning with topological relations, cardinal direction relations etc multi-aspect spatial information has become the focus of qualitative spatial reasoning. The current model and the approaches of heterogeneous composition reasoning of all kinds of direction relations with topological relations have some kind of disadvantages, in addition, the specific studies in consistency checking of the combinatory networks of direction relation and topological. So this paper carries on studies and explores in the direction relation with topological relation combine reasoning and consistency checking.First of all, based on projection model and combined the rectangle algebra, this paper will propose approaches of rectangle algebra of projective intervals for topological relations of spatial object, having the united rectangle algebra expressing of direction relations and topological relations.Secondly, taking the flexibility of heterogeneous complex reasoning into account, this paper will introduce inverse to direction relations and topological relations. Based on the Interdependence of direction relations and topological relations, interaction table for direction relations and topological relations will be given. Based on the above-mentioned study, the accurate heterogeneous composition reasoning of rectangular basic direction relations and non-rectangular basic direction relations respectively with the topology relations are solved, and the correctness of the reasoning and example application will also be given. Three algorithms above are analyzed in detail, the common composition reasoning algorithm of direction relations and topological relations is provided. Finally, convex relations in the projection model of intersecting parallels are analyzed in detail. The judging method of convex relations and heterogeneous restraint in composition with direction relation and topological relation is provided. This method and algorithm of consistency checking for the combinatory networks of direction relation and topological are proposed by combining the convex relation network theorem and path consistency checking algorithm, as well as the corresponding correctness proof and analysis of complexity are given. At the end of the paper, the experiment is designed based on the algorithm. The experimental result shows that the algorithm is correct.更多还原