• Corpus ID: 767629

Oriented Straight Line Segment Algebra: Qualitative Spatial Reasoning about Oriented Objects

@article{Moratz2009OrientedSL,
  title={Oriented Straight Line Segment Algebra: Qualitative Spatial Reasoning about Oriented Objects},
  author={Reinhard Moratz and Dominik L{\"u}cke and Till Mossakowski},
  journal={ArXiv},
  year={2009},
  volume={abs/0912.5533}
}
Nearly 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. This work received substantial interest amongst the qualitative spatial reasoning community. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new investigation into dipole constraint calculi which uses algebraic methods to derive sound results on the… 

Qualitative Spatial Reasoning about Relative Orientation - A Question of Consistency

A new approach is introduced for calculating the composition table for DRAf using condensed semantics, that performs far better than algebraic closure, and investigates morphisms between qualitative spatial calculi.

Relations Between Spatial Calculi About Directions and Orientations ( Extended Abstract 1 )

This work applies universal algebraic tools to binary qualitative calculi and their relations to find a better match with human concepts related to natural language and better efficiency for reasoning.

Relations Between Spatial Calculi About Directions and Orientations (Extended Abstract)

This work considers notions of qualitative constraint calculus, of homomorphism between calculi, and of quotient of calculi and derives important properties for spatial calculi from corresponding properties of related calculi.

Qualitative reasoning about relative direction of oriented points

Left-Right Relations for Qualitative Representation and Alignment of Planar Spatial Networks

It is shown in an empirical evaluation that performing sketch-to-metric map alignment with the new representation of the “left/right” relations is more effective than using the original \(\mathcal {DRA}\) calculi.

Qualitative Reasoning about Relative Direction on Adjustable Levels of Granularity

This paper presents simple geometric rules that enable reasoning about relative direction between oriented points that have a scalable granularity m, and develops a simple algorithm for computing the OPRA_m composition tables and proves its correctness.

Extending Binary Qualitative Direction Calculi with a Granular Distance Concept: Hidden Feature Attachment

In this paper we introduce a method for extending binary qualitative direction calculi with adjustable granularity like OPRAmor the star calculus with a granular distance concept. This method is

Combining DRA and CYC into a Network Friendly Calculus

This paper combines the DRA and CYC algebras into a new calculus for reasoning within network structures, and proves some interesting results about some properties of the standard operations, converse and composition, for versions of CYC and DRA.

Route Matching in Sketch and Metric Maps

The results show that by considering the specific conditions (not availability of descriptive data of routes and geometric/descriptive information of landmarks), this paper has been able to take an important step toward finding an acceptable solution for the matching problem.

References

SHOWING 1-10 OF 67 REFERENCES

Qualitative Spatial Reasoning about Line Segments

A novel approach for dealing with intrinsic orientation information by specifying qualitative relations between oriented line segments, the simplest possible spatial entities being extended and having an intrinsic direction is presented.

The Finest of its Class: The Natural Point-Based Ternary Calculus for Qualitative Spatial Reasoning

The main result of the paper is the identification of a maximally refined calculus amongst the practical natural RST calculi, which turns out to be very similar to Ligozat's flip-flop calculus.

Qualitative Triangulation for Spatial Reasoning

This paper presents a systematic way of defining qualitative calculi for spatial reasoning, which allows for in a general setting the notions of coarse and fine inference, as well as the conceptual neighborhood properties of sets of spatial relations.

Qualitative spatial reasoning about relative point position

Qualitative spatial reasoning using orientation, distance, and path knowledge

The paper presents the basic iconic notation for spatial orientation relations that exploits the structure of the spatial domain and explores a variety of ways in which these relations can be manipulated and combined for spatial reasoning.

Representing Relative Direction as a Binary Relation of Oriented Points

A new calculus about oriented points is introduced which has a scalable granularity and can generate the minimal composition table, and the algebraic closure for a set of $\mathcal{OPRA}$ statements is sufficient to solve knowledge integration tasks in robotics.

Qualitative Spatial Reasoning with Cardinal Directions

An algebraic method is used to formalize the meaning of cardinal directions and two examples of systems to determine and reason with cardinal directions are discussed in some detail and results from a prototype are given.

Reasoning About Ordering

A system of line segment relations which generalizes Allen's system of interval relations to two dimensions is introduced and it is shown that this generalization differs in interesting properties from the generalizations based on topological relations which have been proposed so far.

What Is a Qualitative Calculus? A General Framework

It is shown that the natural algebraic object governing this kind of calculus is a non-associative algebra (in the sense of Maddux), and that the notion of weak representation is the right notion for describing most basic properties.
...