RIA: Formalization, Inference, and Query Processing of Spatial
Relations in Geographic Space
Interim Report, Year 2
For the second year of this 3-year grant, we planned two tasks in
Integrated Spatial Reasoning. We have accomplished both tasks and
advanced further than expected. Since we addressed already during
the first year some of the tasks planned initially for the second
year, we reformulated with last yearÕs progress report the
goals for this year. The following tasks refer to this revised
project plan.
- Task 1: Based on the results obtained during the first year, we
intended to use the results from the formalization of cardinal
directions between point-like objects and the solutions to
topological relations, and generalize them to deal with extended
objects.
We reached this goal by finding a canonical representation for
directions and topological relations, in which combined inferences
about directions and topological relations are possible. This
allows us to make such inferences as: given a direction between A
and B, and a topological relation between B and C, and another
direction between C and D, what is the direction between A and D?
(for example, A East of B, and B overlaps with C, and C East of D
implies A East of D). Likewise, non-trivial topological knowledge
may be derived from knowledge about two topological relations and
one cardinal direction. Results will appear in a paper at the
Fourth International Symposium on Large Spatial Databases.
- Task 2: Develop efficient algorithms to implement reasoning
mechanisms about individual qualitative spatial relations,
particularly considering the dependency among qualitative and
quantitative representations.
We focused on two aspects of the implementation of topological
relations: (1) we developed a fast filter that exploits
minimum-bounding rectangles to determine a subset of objects; and
(2) we designed an efficient method to process the 9-intersection
such that only those intersections absolutely necessary are
calculated. We demonstrated this for queries of the type, "Find all
objects that have a particular topological relation with respect to
a given object" and "What is the topological relation between two
given object?" Both algorithms have been prototyped.
All completed tasks have been documented in papers, theses, and
technical papers, some of which have been published already in
refereed conferences or have been accepted in refereed journals. A
complete list of publications is enclosed, as well as reprints of
published journal papers acknowledging support from IRI-9309230. To
date, a total of six refereed journal articles, seven refereed
conference proceedings, five non-refereed conference papers, and
one Ph.D. thesis have been published on Spatial Reasoning since the
start of the grant in September 1993. We found that our results
were extremely useful to address the assessment of consistency in
geographic databases with multiple representations for the same
spatial objects. Multiple-representation or multi-scale geographic
databases keep "copies" of the same scene at different levels of
detail. Representations of less detail are derived through
(cartographic) generalization operations from the more-detailed
operations. Consistency assessment is critical as, for instance,
the National Spatial Data Infrastructure (NSDI) assumes that such
generalizations can be obtained automatically; however, to date no
comprehensive methods exist for automated quality control of such
generalizations.
We also found that the 9-intersection, our model for topological
relations, provides an excellent basis for the definition of the
semantics of natural-language spatial predicates, such as "enters,"
"goes through," or "goes into." This may lead to much improved
spatial query languages, incorporating concepts and terms close to
the way humans think about spatial problems. During year 3, we plan
to focus on extending our investigations in Integrated Spatial
Reasoning with the following two tasks:
- The algebras for distance and directions will be integrated
with the algebra for topological relations to provide a single set
of inference rules.
- We will design and prototype an intelligent spatial query
processor that integrates qualitative and quantitative descriptions
of spatial relations.
List of Publications
- Modeling Topological Spatial
Relations: Strategies for Query Processing
E. Clementini, J. Sharma, and M. Egenhofer
Computers and Graphics 18 (6): 815-822, 1994.
- Deriving the Composition of Binary
Topological Relations
M. Egenhofer
Journal of Visual Languages and Computing, 5 (2): 133-149,
1994.
- Visual Map Algebra: A
Direct-Manipulation User Interface for GIS
M. Egenhofer and T. Bruns
IFIP Workshop on Visual Database Systems, Lausanne,
Switzerland
S. Spaccapietra and R. Jain (eds.) (in press).
- Evaluating Inconsistencies Among
Multiple Representations
M. Egenhofer, E. Clementini, and P. di Felice
Sixth International Symposium on Spatial Data Handling,
Edinburgh, Scotland, pp. 901-920, September 1994.
- On the Equivalence of Topological
Relations
M. Egenhofer and R. Franzosa
International Journal of Geographical Information Systems 9
(2): 133-152, 1995.
- On the Robustness of Qualitative Distance- and
Direction-Reasoning
J.-H. Hong, M. Egenhofer, and A. Frank
Autocarto 12, Charlotte, NC, D. Peuquet (ed.) February 1995.
- Calibrating the Meanings of Spatial
Predicates from Natural Language: Line-Region Relations
D. Mark and M. Egenhofer
Sixth International Symposium on Spatial Data Handling,
Edinburgh, Scotland, pp. 538-553, September 1994.
- Topology of Prototypical Spatial Relations Between Lines and
Regions in English and Spanish
D. Mark and M. Egenhofer
Autocarto 12, Charlotte, NC, D. Peuquet (ed.) February 1995.
- Topological Relations in the World of Minimum Bounding
Rectangles: A Study with R-Trees
D. Papadias, Y. Theodoridis, T. Sellis, and M. Egenhofer
SIGMOD `95, San Jose, CA
M. Carey and D. Schneider (eds.), SIGMOD RECORD 24 (2):
92-103, May 1995.
- A Qualitative Spatial
Reasoner
J. Sharma, D. Flewelling, and M. Egenhofer
Sixth International Symposium on Spatial Data Handling,
Edinburgh, Scotland, pp. 665-681, September 1994.
- Inferences from Combined Knowledge about Directions and
Topological Relations
J. Sharma and D. Flewelling
Advances in Spatial
Databases--Proceedings of the Fourth International Symposium on
Large Spatial Databases, SSD `95, Portland, ME
M. Egenhofer and J. Herring (eds.), Lecture Notes in Computer
Science, Springer-Verlag, August 1995.
[ Project Summary | Spatial Database Research Group | NCGIA Maine
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