# Spatial Relations Using High Level Concepts

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## Abstract

**:**

## 1. Introduction

**Figure 1.**A set of polygons corresponding to houses in a housing estate and a number of lines corresponding to roads are represented. The grey line represents the access road for the housing estate in question. Data taken from OpenStreetMap.

## 2. Related Work

#### 2.1. Implicit Spatial Information

#### 2.2. Spatial Relations

**Figure 2.**In (

**a**) the object is nearly completely contained inside the object ; In (

**b**) the object is between the objects and .

#### 2.3. Map Generalisation

## 3. Proposed Model

#### 3.1. Generalisation Step

**Figure 5.**The merging of the polygons in (

**a**) introduces a geometrical intersection with the line as illustrated in (

**b**).

#### 3.2. Inference Step

**Figure 6.**In each figure the set of 8 rays corresponding to a point are represented by arrows. represents the centroid of each polygon.

## 4. Evaluation

**Figure 7.**A set of polygons corresponding to houses in a housing estate and a number of lines corresponding to roads are represented. The grey lines represent the access roads for the housing estate in question. Data taken from OpenStreetMap.

#### 4.1. Spatial Data

**Figure 8.**The results of merging the polygons in (

**a**) and (

**b**) are displayed in (

**c**) and (

**d**) respectively.

#### 4.2. Qualitative Evaluation

#### 4.3. Access Road Classification

## 5. Conclusions

## Acknowledgments

## References

- Murphy, G. The Big Book of Concepts; MIT Press: Boston, MA, USA, 2002. [Google Scholar]
- Walter, V.; Luo, F. Automatic interpretation of digital maps. ISPRS J. Photogramm.
**2011**, 66, 519–528. [Google Scholar] [CrossRef] - Tryfona, N.; Egenhofer, M.J. Consistency among parts and aggregates: A computational model. Trans. GIS
**1997**, 1, 1–3. [Google Scholar] - Price, R.; Tryfona, N.; Jensen, C.S. Modeling Topological Constraints in Spatial Part-Whole Relationships. In Proceedings of the 20th International Conference on Conceptual Modeling: Conceptual Modeling, Yokohama, Japan, 27–30 November 2001; pp. 27–40.
- Egenhofer, M.; Wilmsen, D. Changes in Topological Relations when Splitting and Merging Regions. In Proceedings of the 12th International Symposium on Spatial Data Handling, Vienna, Austria, 12–14 July 2006.
- Mackaness, W.; Edwards, G. The Importance of Modelling Pattern and Structure in Automated Map Generalization. In Proceedings of Joint Workshop on Multi-Scale Representations of Spatial Data, Ottawa, ON, Canada, 7–8 July 2002.
- Touya, G. A road network selection process based on data enrichment and structure detection. Trans. GIS
**2010**, 14, 595–614. [Google Scholar] [CrossRef] - Werder, S.; Kieler, B.; Sester, M. Semi-Automatic Interpretation of Buildings and Settlement Areas in User-Generated Spatial Data. In Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, San Jose, CA, USA, 2–5 November 2010; pp. 330–339.
- Butenuth, M.; Gösseln, G.; Tiedge, M.; Heipke, C.; Lipeck, U.; Sester, M. Integration of heterogeneous geospatial data in a federated database. ISPRS J. Photogramm.
**2007**, 62, 328–346. [Google Scholar] [CrossRef] - Anders, K.; Fritsch, D. Automatics interpretation of digital maps for data revision. Int. Arch. Photogramm. Remote Sens.
**1996**, 31, 90–94. [Google Scholar] - Lüscher, P.; Weibel, R.; Mackaness, W. Where is the Terraced House? On the Use of Ontologies for Recognition of Urban Concepts in Cartographic Databases. In Headway in Spatial Data Handling; Ruas, A., Gold, C., Eds.; Springer: Berlin, Germany, 2008; pp. 449–466. [Google Scholar]
- Regnault, N. Recognition of Building Clusters for Generalization. In Proceedings of the 7th International Symposium on Spatial Data Handling, Delft, The Netherlands, 12–16 August 1996; pp. 185–198.
- Yan, H.; Weibel, R.; Yang, B. A multi-parameter approach to automated building grouping and generalization. Geoinformatica
**2008**, 12, 73–89. [Google Scholar] - Steinhauer, J.H.; Wiese, T.; Freksa, C.; Barkowsky, T. Recognition of Abstract Regions in Cartographic Maps. In Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science, Morro Bay, CA, USA, 19–23 September 2001; pp. 306–321.
- Qi, H.B.; Li, Z.L. An approach to building grouping based on hierarchical constraints. Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.
**2008**, XXXVII, 449–454. [Google Scholar] - Zhang, X.; Ai, T.; Stoter, J. Characterization and Detection of Building Patterns in Cartographic Data: Two Algorithms. In Advances in Spatial Data Handling and GIS; Shi, W., Yeh, A., Leung, Y., Zhou, C., Eds.; Springer: Berlin, Germany, 2012; pp. 93–107. [Google Scholar]
- Christophe, S.; Ruas, A. Detecting Building Alignments for Generalisation Purposes. In Advances in Spatial Data Handling; Richardson, D., van Oosterom, P., Eds.; Springer: Berlin, Germany, 2002; pp. 419–432. [Google Scholar]
- Mao, B.; Harrie, L.; Ban, Y. Detection and typification of linear structures for dynamic visualization of 3D city models. Comput. Environ. Urban Syst.
**2012**, 36, 233–244. [Google Scholar] [CrossRef] - Luscher, P.; Weibel, R.; Burghardt, D. Integrating ontological modelling and Bayesian inference for pattern classification in topographic vector data. Comput. Environ. Urban Syst.
**2009**, 33, 363–374. [Google Scholar] [CrossRef] [Green Version] - Haunert, J. Detecting Symmetries in Building Footprints by String Matching. In Advancing Geoinformation Science for a Changing World; Geertman, S., Reinhardt, W., Toppen, F., Eds.; Springer: Berlin, Germany, 2011; pp. 319–336. [Google Scholar]
- Egenhoger, M.J.; Franzosa, R.D. Point-set topological spatial relations. Int. J. Geogr. Inf. Syst.
**1991**, 5, 161–174. [Google Scholar] [CrossRef] - Shariff, A.; Egenhofer, M.; Mark, D. Natural-language spatial relations between linear and areal objects: The topology and metric of english-language terms. Int. J. Geogr. Inf. Sci.
**1998**, 12, 215–246. [Google Scholar] - Hernandez, D. Qualitative Representation of Spatial Knowledge; Springer: Berlin, Germany, 1994. [Google Scholar]
- Cohn, A.G.; Hazarika, S.M. Qualitative spatial representation and reasoning: An overview. Fundam. Inform.
**2001**, 46, 1–29. [Google Scholar] - Riedemann, C. Matching Names and Definitions of Topological Operators. In Spatial Information Theory; Cohn, A., Mark, D., Eds.; Springer: Berlin, Germany, 2005; Volume 3693, pp. 165–181. [Google Scholar]
- Cai, G.; Wang, H.; MacEachren, A.; Fuhrmann, S. Natural conversational interfaces to geospatial databases. Trans. GIS
**2005**, 9, 199–221. [Google Scholar] [CrossRef] - Sjoo, K.; Jensfelt, P. Functional Topological Relations for Qualitative Spatial Representation. In Proceedings of the International Conference on Advanced Robotics, Montevideo, Uruguay, 20–23 June 2011.
- Egenhofer, M. Reasoning about Binary Topological Relations. In Proceedings of the Second International Symposium on Advances in Spatial Databases, Zurich, Switzerland, 28–30 August 1991; pp. 143–160.
- Egenhofer, M. A Reference System for Topological Relations between Compound Spatial Objects. In Advances in Conceptual Modeling—Challenging Perspectives; Heuser, C., Pernul, G., Eds.; Springer: Berlin, Germany, 2009; Volume 5833, pp. 307–316. [Google Scholar]
- Randell, D.; Cui, Z.; Cohn, A. A Spatial Logic based on Regions and Connection. In Proceedings of the International Conference on Knowledge Representation and Reasoning, Cambridge, MA, USA, 16–29 October 1992; 92, pp. 165–176.
- Knauff, M.; Rauh, R.; Renz, J. A Cognitive Assessment of Topological Spatial Relations: Results from an Empirical Investigation. In Spatial Information Theory A Theoretical Basis for GIS; Hirtle, S., Frank, A., Eds.; Springer: Berlin, Germany, 1997; Volume 1329, pp. 193–206. [Google Scholar]
- Renz, J.; Rauh, R.; Knauff, M. Towards Cognitive Adequacy of Topological Spatial Relations. In Spatial Cognition II, Integrating Abstract Theories, Empirical Studies, Formal Methods, and Practical Applications; Springer-Verlag: London, UK, 2000; pp. 184–197. [Google Scholar]
- Klippel, A. Spatial information theory meets spatial thinking—Is topology the Rosetta Stone of spatial cognition? Ann. Assoc. Am. Geogr.
**2012**. [Google Scholar] [CrossRef] - Mark, D.; Egenhofer, M. Modeling spatial relations between lines and regions: Combining formal mathematical models and human subjects testing. Cartogr. Geogr. Inf. Syst.
**1994**, 21, 195–212. [Google Scholar] - Egenhofer, M.; Mark, D. Naive Geography. In Spatial Information Theory A Theoretical Basis for GIS; Frank, A., Kuhn, W., Eds.; Springer: Berlin, Germany, 1995; Volume 988, pp. 1–15. [Google Scholar]
- Clementini, E.; di Felice, P.; van Oosterom, P. A Small Set of Formal Topological Relationships Suitable for End-User Interaction. In Advances in Spatial Databases; Abel, D., Chin Ooi, B., Eds.; Springer: Berlin, Germany, 1993; Volume 692, pp. 277–295. [Google Scholar]
- Cai, G.; Wang, H.; MacEachren, A. Communicating Vague Spatial Concepts in Human-GIS Interactions: A Collaborative Dialogue Approach. In Spatial Information Theory. Foundations of Geographic Information Science; Kuhn, W., Worboys, M., Timpf, S., Eds.; Springer: Berlin, Germany, 2003. [Google Scholar]
- Zhan, F.B. A Fuzzy Set Model of Approximate Linguistic Terms in Descriptions of Binary Topological Relations between Simple Regions. In Applying Soft Computing in Defining Spatial Relations; Matsakis, P., Sztandera, L.M., Eds.; Physica-Verlag GmbH: Heidelberg, Germany, 2002; pp. 179–202. [Google Scholar]
- Bloch, I.; Colliot, O.; Cesar, R.M., Jr. On the ternary spatial relation “between”. IEEE Trans. Syst. Man Cybern. B Cybern.
**2006**, 36, 312–327. [Google Scholar] [CrossRef] - Raubal, M. Cognitive engineering for geographic information science. Geogr. Compass
**2009**, 3, 1087–1104. [Google Scholar] [CrossRef] - Sarjakoski, L. Chapter 2 Conceptual Models of Generalisation and Multiple Representation. In Generalisation of Geographic Information; Mackaness, W., Ruas, A., Sarjakoski, L., Eds.; Elsevier Science B.V.: Amsterdam, The Netherlands, 2007; pp. 11–35. [Google Scholar]
- Weibel, R. Generalization of Spatial Data: Principles and Selected Algorithms. In Algorithmic Foundations of Geographic Information Systems; van Kreveld, M., Nievergelt, J., Roos, T., Widmayer, P., Eds.; Springer: Berlin, Germany, 1997; Volume 1340, pp. 99–152. [Google Scholar]
- Mackaness, W.A. Generalisation of Geographic Information: Cartographic Modelling and Applications; Mackaness, W.A., Ruas, A., Sarjakoski, L.T., Eds.; Elsevier Science B.V.: Amsterdam, The Netherlands, 2007. [Google Scholar]
- Jones, C.B.; Ware, J.M. Map generalization in the Web age. Int. J. Geogr. Inf. Sci.
**2005**, 19, 859–870. [Google Scholar] [CrossRef] - Weibel, R. A Typology of Constraints to Line Simplification. In Proceedings of 7th International Symposium on Spatial Data Handling, Delft, The Netherlands, 12–16 August 1996; pp. 533–546.
- Regnauld, N.; Revell, P. Automatic amalgamation of buildings for producing ordnance survey 1:50,000 scale maps. Cartogr. J.
**2007**, 44, 239–250. [Google Scholar] [CrossRef] - Haunert, J.; Wolff, A. Optimal and Topologically Safe Simplification of Building Footprints. In Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, San Jose, CA, USA, 2–5 November 2010; pp. 192–201.
- Kieler, B.; Haunert, J.; Sester, M. Deriving scale-transition matrices from map samples for simulated annealing-based aggregation. Ann. GIS
**2009**, 15, 107–116. [Google Scholar] [CrossRef] - Haunert, J.; Wolff, A. Area aggregation in map generalisation by mixed-integer programming. Int. J. Geogr. Inf. Sci.
**2010**, 24, 1871–1897. [Google Scholar] [CrossRef] - Corcoran, P.; Mooney, P.; Winstanley, A.C. Planar and non-planar topologically consistent vector map simplification. Int. J. Geogr. Inf. Sci.
**2011**, 25, 1659–1680. [Google Scholar] [CrossRef] - Jones, C.B. Geographical Information Systems and Computer Cartography; Prentice Hall: Upper Saddle River, NJ, USA, 1997. [Google Scholar]
- Regnauld, N.; McMaster, R. A Synoptic View of Generalisation Operators. In Generalisation of Geographic Information; Mackaness, W., Ruas, A., Sarjakoski, L., Eds.; Elsevier Science B.V.: Amsterdam, The Netherlands, 2007; pp. 37–66. [Google Scholar]
- Regnauld, N. Algorithms for the Amalgamation of Topographic Data. In Proceedings of the 21st International Cartographic Conference, Durban, South Africa, 10–16 August 2003.
- Ware, J.; Jones, C.; Bundy, G. A Triangulated Spatial Model for Cartographic Generalisation of Areal Objects. In Spatial Information Theory A Theoretical Basis for GIS; Frank, A., Kuhn, W., Eds.; Springer-Verlag: Berlin, Germany, 1995; Volume 988, pp. 173–192. [Google Scholar]
- Yang, L.; Zhang, L.; Ma, J.; Xie, J.; Liu, L. Interactive visualization of multi-resolution urban building models considering spatial cognition. Int. J. Geogr. Inf. Sci.
**2011**, 25, 5–24. [Google Scholar] [CrossRef] - Li, Z.; Yan, H.; Ai, T.; Chen, J. Automated building generalization based on urban morphology and Gestalt theory. Int. J. Geogr. Inf. Sci.
**2004**, 18, 513–534. [Google Scholar] [CrossRef] - Damen, J.; van Kreveld, M.; Spaan, B. High Quality Building Generalization by Extending the Morphological Operators. In Proceedings of the ICA Workshop on Generalization, Montpellier, France, 20–21 June 2008.
- Dupenois, M.; Galton, A. Assigning Footprints to Dot Sets: An Analytical Survey. In Spatial Information Theory; Hornsby, K., Claramunt, C., Denis, M., Ligozat, G., Eds.; Springer: Berlin, Germany, 2009; Volume 5756, pp. 227–244. [Google Scholar]
- Goodchild, M. Citizens as sensors: The world of volunteered geography. GeoJournal
**2007**, 69, 211–221. [Google Scholar] [CrossRef] - DeGroot, M.; Schervish, M. Probability and Statistics, 4th ed; Pearson: London, UK, 2011. [Google Scholar]
- Zhang, X.; Ai, T.; Stoter, J.; Kraak, M.; Molenaar, M. Building pattern recognition in topographic data: Examples on collinear and curvilinear alignments. GeoInformatica
**2013**, in press. [Google Scholar]

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**MDPI and ACS Style**

Corcoran, P.; Mooney, P.; Bertolotto, M.
Spatial Relations Using High Level Concepts. *ISPRS Int. J. Geo-Inf.* **2012**, *1*, 333-350.
https://doi.org/10.3390/ijgi1030333

**AMA Style**

Corcoran P, Mooney P, Bertolotto M.
Spatial Relations Using High Level Concepts. *ISPRS International Journal of Geo-Information*. 2012; 1(3):333-350.
https://doi.org/10.3390/ijgi1030333

**Chicago/Turabian Style**

Corcoran, Padraig, Peter Mooney, and Michela Bertolotto.
2012. "Spatial Relations Using High Level Concepts" *ISPRS International Journal of Geo-Information* 1, no. 3: 333-350.
https://doi.org/10.3390/ijgi1030333