Superposition of Qualitative Rectangles using a Quantitative Model

Takeaki Kato, Sosuke Moriguchi, Kazuko Takahashi

Abstract

This paper describes an approach to qualitative problem-solving using the quantitative method in spatial reasoning. We consider the superposition of two objects, such that pre-specified parts of the objects are visible. First, we qualify an object to create a model. It is expressed as a matrix of tiles, which are either black or white depending on the visibility requirement. We use this to determine the location of two objects. This process involved quantitative treatment. We describe a sound and complete algorithm that provides quantitative solutions and implemented it as a system with a graphical user interface. Then, we extend this algorithm so that we may search for a better solution considering a qualitatively equivalent model of the objects; that is, the topological relationships between the black and white regions are identical. This approach is useful for analyzing or designing a projection of three-dimensional objects onto a two-dimensional plane, because it not only reduces the computational expense but also provides a better fit with common sense and human reasoning.

References

  1. Birgin, G., Lobato, R. D., and Morabito, R. (2010). An effective recursive partitioning approach for the packing of identical rectangles in a rectangle. Journal of the Operational Research Society, 61:306-320.
  2. Chen, J., Cohn, A., Liu, D., Wang, S., Ouyang, J., and Yu, Q. (2013). A survey of qualitative spatial representations. The Knowledge Engineering Review, 30(1):106-136.
  3. Cohn, A. G. and Hazarika, S. M. (2001). Qualitative spatial representation and reasoning: An overview. Fundamental Informaticae, 46(1-1):1-29.
  4. Cohn, A. G. and Renz, J. (2007). Handbook of Knowledge Representation, chapter 13. Qualitative Spatial Reasoning, pages 551-596. Elsevier.
  5. Freeman, H. (1991). Geographical Information Systems, chapter Computer name placement, pages 449-460. John Wiley.
  6. Ghourabi, F. and Takahashi, K. (2015a). Formalizing the qualitative superposition of rectangles in proof assistant Isabelle/HOL. In Seventh International Conference on Agents and Artificial Intelligence, pages 530- 539.
  7. Ghourabi, F. and Takahashi, K. (2015b). Generalization of superposition of rectangles based on direction relations. In The 28th International Workshop on Qualitative Reasoning.
  8. Goyal, R. K. and Egenhofer, M. J. (2001). Similarity of cardinal directions. In Proceedings of the Advances in Spatial and Temporal Databases, 7th International Symposium, SSTD 2001, pages 36-58.
  9. Konishi, T. and Takahashi, K. (2012). Superposition of rectangles with visibility requirement: A qualitative approach. International Journal on Advances in Software, 4(3&4):422-433.
  10. Lapaugh, A. S. (1996). Layout algorithm for VLSI design. ACM Computing Surveys, 28(1):59-61.
  11. Li, J., Plaisant, C., and Shneriderman, B. (1998). Data object and label placement for information abundant visualizations. In Proceedings of the Workshop of New Paradigms Information Visualization and Manipulation, pages 41-48.
  12. Li, S. and Liu, W. (2015). Cardinal directions: A comparison of direction relation matrix and objects interaction matrix. International Journal of Geographical Information Science, 29(2):194-216.
  13. Lodi, A., Martello, S., and Monaci, M. (2002). Twodimensional packing problems: a survey. European Journal of Operational Research, (141):242-252.
  14. Randell, D., Witkowski, M., and Shanahan, M. (2001). From images to bodies: Modelling and exploiting spatial occlusion and motion parallax. In Proceedings of Seventeenth International Joint Conference on Artificial Intelligence, pages 57-66.
  15. Renz, J. and Mitra, D. (2004). Qualitative direction calculi with arbitrary granularity. In PRICAI 2004: Trends in Artificial Intelligence, pages 65-74.
  16. Skiadopoulos, S. and Koubarakis, M. (2005). On the consistency of cardinal direction constraints. Artificial Intelligence, 163(1):91-135.
  17. Stock, O. (1997). Spatial and Temporal Reasoning. Kluwer Academic Press.
Download


Paper Citation


in Harvard Style

Kato T., Moriguchi S. and Takahashi K. (2017). Superposition of Qualitative Rectangles using a Quantitative Model . In Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-220-2, pages 423-430. DOI: 10.5220/0006123404230430


in Bibtex Style

@conference{icaart17,
author={Takeaki Kato and Sosuke Moriguchi and Kazuko Takahashi},
title={Superposition of Qualitative Rectangles using a Quantitative Model},
booktitle={Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2017},
pages={423-430},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006123404230430},
isbn={978-989-758-220-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Superposition of Qualitative Rectangles using a Quantitative Model
SN - 978-989-758-220-2
AU - Kato T.
AU - Moriguchi S.
AU - Takahashi K.
PY - 2017
SP - 423
EP - 430
DO - 10.5220/0006123404230430