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Shape Similarity Based on the Qualitative Spatial Reasoning Calculus eOPRAm

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9368)

Abstract

In our paper we investigate the use of qualitative spatial representations (QSR) about relative direction and distance for shape representation. Our new approach has the advantage that we can generate prototypical shapes from our abstract representation in first-order predicate calculus. Using the conceptual neighborhood which is an established concept in QSR we can directly establish a conceptual neighborhood between shapes that translates into a similarity metric for shapes. We apply this similarity measure to a challenging computer vision problem and achieve promising first results.

Keywords

  • Qualitative spatial reasoning
  • Qualitative shape representation
  • Computer vision

R. Moratz—The Principal Investigator and responsible lab author.

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Notes

  1. 1.

    Material in this section is presented as an abridged summary of previous work by Moratz and Wallgrün [22].

  2. 2.

    Note that while this analogy makes use of three-dimensional space, our model refers to the 2D plane.

  3. 3.

    The first three letters of the symbol \(e\mathcal {OPRA}_m\) stand for elevated oriented point.

  4. 4.

    Note, that our parameters are elements of a cyclic group so that no modulo operation is required.

  5. 5.

    The stop parameter can also be defined with respect to the number of desired vertices, i.e., some pre-specified resolution. This is the approach taken in this paper to enable comparison between polylines with the same number of vertices.

  6. 6.

    For the first edge, the last edge is used as the control.

  7. 7.

    In 6.2, we present a more detailed look at the \(e\mathcal {OPRA}_m\) direction matrix comparison metric.

  8. 8.

    Currently, this is defined as \(gap\le 10\,\%\) of the shortest hull edge length.

  9. 9.

    Given the cyclic property of direction intervals in \(e\mathcal {OPRA}_m\), we are interested in the shortest-path distance from one interval to another instead of the raw absolute difference. I.e., any error greater than 2m can be expressed as \(4m-error\).

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Acknowledgment

The authors would like to thank Jan Oliver Wallgrün for helpful discussions related to the topic of this paper. Our work was supported in part by the National Science Foundation under Grant Nos. CDI-1028895, OIA-1027897 and IIS-1302164. The information, data, or work presented herein was funded in part by the Office of Energy Efficiency and Renewable Energy (EERE), U.S. Department of Energy, under Award Number DE-EE0006803. (Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.)

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Correspondence to Christopher H. Dorr , Longin Jan Latecki or Reinhard Moratz .

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Dorr, C.H., Latecki, L.J., Moratz, R. (2015). Shape Similarity Based on the Qualitative Spatial Reasoning Calculus eOPRAm. In: Fabrikant, S., Raubal, M., Bertolotto, M., Davies, C., Freundschuh, S., Bell, S. (eds) Spatial Information Theory. COSIT 2015. Lecture Notes in Computer Science(), vol 9368. Springer, Cham. https://doi.org/10.1007/978-3-319-23374-1_7

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