Areas of Same Cardinal Direction

Cardinal directions, such as North, East, South, and West, are the foundation for qualitative spatial reasoning, a common field of GIS, Artificial Intelligence, and cognitive science. Such cardinal directions capture the relative spatial direction relation between a reference object and a target object, therefore, they are important search criteria in spatial databases. The projection-based model for such direction relations has been well investigated for point-like objects, yielding a relation algebra with strong inference power. The Direction Relation Matrix defines the simple region-to-region direction relations by approximating the reference object to a minimum bounding rectangle. Models that capture the direction between extended objects fall short when the two objects are close to each other. For instance, the forty-eight contiguous states of the US are colloquially considered to be South of Canada, yet they include regions that are to the North of some parts of Canada. This research considers the cardinal direction as a field that is distributed through space and may take on varying values depending on the location within a reference object. Therefore, the fundamental unit of space, the point, is used as a reference to form a point-based cardinal direction model. The model applies to capture the direction relation between point-to-region and region-to-region configurations. As such, the reference object is portioned into areas of same cardinal direction with respect to the target object. This thesis demonstrates there is a set of 106 cardinal point-to-region relations, which can be normalized by considering mirroring and 90° rotations, to a subset of 22 relations. The differentiating factor of the model is that a set of base relations defines the direction relation anywhere in the field, and the conceptual neighborhood graph of the base relations offers the opportunity to exploit the strong inference of point-based direction reasoning for simple regions of arbitrary shape. Considers the tiles and pockets of same cardinal direction, while a coarse model provides a union of all possible qualitative direction values between a reference region and a target region

A study of spatial data models and their application to selecting information from pictorial databases

People have always used visual techniques to locate information in the space surrounding them. However with the advent of powerful computer systems and user-friendly interfaces it has become possible to extend such techniques to stored pictorial information. Pictorial database systems have in the past primarily used mathematical or textual search techniques to locate specific pictures contained within such databases. However these techniques have largely relied upon complex combinations of numeric and textual queries in order to find the required pictures. Such techniques restrict users of pictorial databases to expressing what is in essence a visual query in a numeric or character based form. What is required is the ability to express such queries in a form that more closely matches the user's visual memory or perception of the picture required. It is suggested in this thesis that spatial techniques of search are important and that two of the most important attributes of a picture are the spatial positions and the spatial relationships of objects contained within such pictures. It is further suggested that a database management system which allows users to indicate the nature of their query by visually placing iconic representations of objects on an interface in spatially appropriate positions, is a feasible method by which pictures might be found from a pictorial database. This thesis undertakes a detailed study of spatial techniques using a combination of historical evidence, psychological conclusions and practical examples to demonstrate that the spatial metaphor is an important concept and that pictures can be readily found by visually specifying the spatial positions and relationships between objects contained within them

Trends and concerns in digital cartography

CISRG discussion paper ;

Cognitive assessment of topological movement Patterns and direction turns: An influence of scale

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.Spatial relations are considered as one of the most unique aspects of spatial or geographical information and have linked the space and natural language. Many spatial relations represent distance (topological relations) and directional relations. This research discusses the role of topology for the conceptualization of different movement and furthermore to assess the influence of two different scales of spaces on cognitive classes through human subject tests. Two experiments are conducted with two different scales. Each experiment was performed by 20 participants. Experiments were fully based on the grouping paradigm. Grouping task enable to categorize the movement entities into groups and establish the cognitive categories or classes. Entities or movement patterns within a class are assumed to similar to one another but different from the entities in other classes. It is believed that the two scales of space are quite distinct in the ways people see and think about them in their mind (Downs and Stea, 1977). To assess the influence of scale on the cognitive classes, two different scales are assumed i. e bike and city and bike and park. Similarity measure and category construction of different movement patterns are assessed using both scales. All movement patterns were designed through conceptual neighborhood graph. The result of this experiment shows that different movement patterns are distinguished by the topological relations. This study not also presents the importance of the topology for conceptualization and perception of different movement patterns but also the influence of scale to distinguish the different movement pattern and to build cognitive classes. The main finding of this study is that the grouping behavior of Non- tangential proper part is found to be different in both scales. Direction relations are also an important aspect of spatial relations. Human beings use different angular information in their environment and derive information. This study not also assesses the conceptualization of different direction turns but also examine the category construction influenced by the two different scales. This research discusses the category construction of direction turns created in both scales. The results shows that human perceive different angular information and deduce this information. It is also examined that cognitive classes constructed remain same in both scale. Furthermore, linguistic description is also evaluated in this research but not in much detail. Verbal labeling of the groups participant created also gives the idea about the human perception about the two different scales

A survey of qualitative spatial representations

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

A query processing system for very large spatial databases using a new map algebra

Dans cette thèse nous introduisons une approche de traitement de requêtes pour des bases de donnée spatiales. Nous expliquons aussi les concepts principaux que nous avons défini et développé: une algèbre spatiale et une approche à base de graphe utilisée dans l'optimisateur. L'algèbre spatiale est défini pour exprimer les requêtes et les règles de transformation pendant les différentes étapes de l'optimisation de requêtes. Nous avons essayé de définir l'algèbre la plus complète que possible pour couvrir une grande variété d'application. L'opérateur algébrique reçoit et produit seulement des carte. Les fonctions reçoivent des cartes et produisent des scalaires ou des objets. L'optimisateur reçoit la requête en expression algébrique et produit un QEP (Query Evaluation Plan) efficace dans deux étapes: génération de QEG (Query Evaluation Graph) et génération de QEP. Dans première étape un graphe (QEG) équivalent de l'expression algébrique est produit. Les règles de transformation sont utilisées pour transformer le graphe a un équivalent plus efficace. Dans deuxième étape un QEP est produit de QEG passé de l'étape précédente. Le QEP est un ensemble des opérations primitives consécutives qui produit les résultats finals (la réponse finale de la requête soumise au base de donnée). Nous avons implémenté l'optimisateur, un générateur de requête spatiale aléatoire, et une base de donnée simulée. La base de donnée spatiale simulée est un ensemble de fonctions pour simuler des opérations spatiales primitives. Les requêtes aléatoires sont soumis à l'optimisateur. Les QEPs générées sont soumis au simulateur de base de données spatiale. Les résultats expérimentaux sont utilisés pour discuter les performances et les caractéristiques de l'optimisateur.Abstract: In this thesis we introduce a query processing approach for spatial databases and explain the main concepts we defined and developed: a spatial algebra and a graph based approach used in the optimizer. The spatial algebra was defined to express queries and transformation rules during different steps of the query optimization. To cover a vast variety of potential applications, we tried to define the algebra as complete as possible. The algebra looks at the spatial data as maps of spatial objects. The algebraic operators act on the maps and result in new maps. Aggregate functions can act on maps and objects and produce objects or basic values (characters, numbers, etc.). The optimizer receives the query in algebraic expression and produces one efficient QEP (Query Evaluation Plan) through two main consecutive blocks: QEG (Query Evaluation Graph) generation and QEP generation. In QEG generation we construct a graph equivalent of the algebraic expression and then apply graph transformation rules to produce one efficient QEG. In QEP generation we receive the efficient QEG and do predicate ordering and approximation and then generate the efficient QEP. The QEP is a set of consecutive phases that must be executed in the specified order. Each phase consist of one or more primitive operations. All primitive operations that are in the same phase can be executed in parallel. We implemented the optimizer, a randomly spatial query generator and a simulated spatial database. The query generator produces random queries for the purpose of testing the optimizer. The simulated spatial database is a set of functions to simulate primitive spatial operations. They return the cost of the corresponding primitive operation according to input parameters. We put randomly generated queries to the optimizer, got the generated QEPs and put them to the spatial database simulator. We used the experimental results to discuss on the optimizer characteristics and performance. The optimizer was designed for databases with a very large number of spatial objects nevertheless most of the concepts we used can be applied to all spatial information systems."--Résumé abrégé par UMI