A Family of Directional Relation Models for Extended Objects

In this paper, we introduce a family of expressive models for qualitative spatial reasoning with directions. The proposed family is based on the cognitive plausible cone-based model. We formally define the directional relations that can be expressed in each model of the family. Then, we use our formal framework to study two interesting problems: computing the inverse of a directional relation and composing two directional relations. For the composition operator, in particular, we concentrate on two commonly used definitions, namely, consistency-based and existential composition. Our formal framework allows us to prove that our solutions are correct. The presented solutions are handled in a uniform manner and apply to all of the models of the family.     

Reasoning about cardinal directions between extended objects

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a relation model, known as the cardinal direction calculus (CDC), for representing direction relations between connected plane regions. The CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking the consistency of complete networks of basic CDC constraints, and proves that reasoning with the CDC is in general an NP-complete problem. For a consistent complete network of basic CDC constraints, our algorithm returns a ‘canonical’ solution in cubic time. This cubic algorithm is also adapted to check the consistency of complete networks of basic cardinal constraints between possibly disconnected regions.     

Computing and managing cardinal direction relations

Qualitative spatial reasoning forms an important part of the commonsense reasoning required for building intelligent geographical information systems (GIS). Previous research has come up with models to capture cardinal direction relations for typical GIS data. In this paper, we target the problem of efficiently computing the cardinal direction relations between regions that are composed of sets of polygons and present two algorithms for this task. The first of the proposed algorithms is purely qualitative and computes, in linear time, the cardinal direction relations between the input regions. The second has a quantitative aspect and computes, also in linear time, the cardinal direction relations with percentages between the input regions. Our experimental evaluation indicates that the proposed algorithms outperform existing methodologies. The algorithms have been implemented and embedded in an actual system, CARDIRECT, that allows the user to 1) specify and annotate regions of interest in an image or a map, 2) compute cardinal direction relations between them, and 3) pose queries in order to retrieve combinations of interesting regions.     

Reasoning about cardinal directions between extended objects: The NP-hardness result

The cardinal direction calculus (CDC) proposed by Goyal and Egenhofer is a very expressive qualitative calculus for directional information of extended objects. Early work has shown that consistency checking of complete networks of basic CDC constraints is tractable, while reasoning with the CDC in general is NP-hard. This paper shows, however, that if some constraints are unspecified, then consistency checking of incomplete networks of basic CDC constraints is already intractable. This draws a sharp boundary between the tractable and intractable subclasses of the CDC. The result is achieved by a reduction from the well-known 3-SAT problem.     

一种基于真实物体的主方向关系的合成算法

使用基于真实物体的方向关系模型,通过一系列的定义和定理,研究了一种基于真实物体的主方向关系的合成方法。在此基础上,提出了一种新的合成算法,该算法能够更有效地合成真实物体间更为复杂的主方向关系。     

Fuzzy semantics for direction relations between composite regions

This paper proposes a model that combines qualitative spatial reasoning with fuzzy semantic typing to derive direction relations between two composite regions in a spatial configuration. It extends Goyal and Egenhofer’s direction relation model, initially proposed for simple regions, towards composite regions. A fuzzy semantics typing qualifies the overall direction relations of two composite regions. We introduce flexible fuzzy measures that allow for both a qualitative and metric study of direction relation similarities.     

基于矩阵的原子方向关系合成

方向关系是空间关系研究的重要领域,应用十分广泛。因此,空间数据库中对方向关系的研究越来越引起人们的注意。本文在分析和研究了文[6]提出的方向关系模型的基础上,对该模型做了进一步扩展,提出了一种用关系矩阵表示方向关系的新方法,并对原子方向关系的合成进行了深入研究,提出了不同于传统理论中使用原子方向关系合成表来求解的新的基于矩阵运算的原子方向关系的合成方法。     

原子方向与基本方向关系合成方法的研究

随着空间数据库技术的不断发展,基于方向关系的空间推理越来越引起人们的注意,作为空间推理的一部分方向关系合成的研究应运而生。文章使用方向关系矩阵表示物体MBR(MinimumBoundingBox)之间方向关系模型,通过一系列方向关系矩阵的性质和运算的定义、定理,提出了原子方向关系与基本方向关系合成问题的求解方法,并证明其正确性。     

基于MBR的主方向关系一致性检验

定性的空间推理在地理信息系统、人工智能、数据库及多媒体等领域中的应用越来越引起人们的注意.空间推理的基础理论以及相应算法也在不断地创新和发展.方向关系推理是空间推理研究领域的重要分支,利用区间代数及矩形代数理论,以物体的极小边界盒(minimum bounding rectangle,简称MBR)为模型,提出了一种基于MBR的主方向关系与矩形代数关系相结合的推理方法.利用该方法,可以将矩形代数良好的计算性质应用于空间方向关系推理中,实现了矩形代数与基于MBR主方向关系的相互转换方法、主方向关系合成及求反方法、主方向关系中凸(convex)关系判定方法及方向关系一致性检验算法.