A Formal Definition of Binary Topological Relationships
| Type of publication: | Incollection |
| Citation: | egenhofer_89_a |
| Booktitle: | 3rd International Conference, {FODO} 1989 on Foundations of Data Organization and Algorithms |
| Series: | Lecture Notes in Computer Science |
| Volume: | 367 |
| Year: | 1989 |
| Pages: | 457-472 |
| Publisher: | Springer |
| ISBN: | 3-540-51295-0 |
| Abstract: | The exploration of spatial relationships is a multi-disciplinary effort involving researchers from linguistics, cognitive science, psychology, geography, cartography, semiology, computer science, surveying engineering, and mathematics. Hence, a formal definition of spatial relationships is necessary to clarify the users' diverse understanding of spatial relationships and to actually deduce relationships among spatial objects. Based upon such formalisms, spatial reasoning and inference will be possible. Topological relationships are a specific subset of the large variety of spatial relationships. They are characterized by the property to be preserved under topological transformations, such as translation, rotation, and scaling. A model of topological relations is presented which is based upon fundamental concepts of algebraic topology in combination with set theory. Binary topological relationships may be defined in terms of the boundaries and interiors of the two objects to be compared. A formalism is developed which identifies 16 potential relationships. Prototypes are shown for the eight relationships that may exist between two objects of the same dimension embedded in the corresponding space. |
| Userfields: | date-added={2012-09-03 15:47:30 +0200}, date-modified={2012-09-03 15:47:30 +0200}, project={fremdliteratur}, registry={A61}, state={copied}, |
| Keywords: | algebraic topology, cartography, cognitive science, COMPUTER GRAPHICS, computer science, DATABASE MANAGEMENT SYSTEMS, DATABASE THEORY, diverse understanding, formal definition, FORMAL LOGIC, formalism, geography, inference, INFERENCE MECHANISMS, Linguistics, mathematics, multi-disciplinary effort, psychology, semiology, set theory, SET THEORY binary topological relationships, spatial objects, Spatial Reasoning, spatial relationships, surveying engineering, topological transformations |
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