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Learning to Solve Geometric Construction Problems from Images

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Intelligent Computer Mathematics (CICM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12833))

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Abstract

We describe a purely image-based method for finding geometric constructions with a ruler and compass in the Euclidea geometric game. The method is based on adapting the Mask R-CNN state-of-the-art visual recognition neural architecture and adding a tree-based search procedure to it. In a supervised setting, the method learns to solve all 68 kinds of geometric construction problems from the first six level packs of Euclidea with an average 92% accuracy. When evaluated on new kinds of problems, the method can solve 31 of the 68 kinds of Euclidea problems. We believe that this is the first time that purely image-based learning has been trained to solve geometric construction problems of this difficulty.

This work was partly supported by the European Regional Development Fund under the projects IMPACT and AI&Reasoning (reg. no. CZ.02.1.01/0.0/0.0/15_003/0000468 and CZ.02.1.01/0.0/0.0/15_003/0000466) and the ERC Consolidator grant SMART no. 714034.

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Notes

  1. 1.

    https://imo-grand-challenge.github.io/.

  2. 2.

    https://github.com/mackej/Learning-to-solve-geometric-construction-problems-from-images, https://github.com/mirefek/py_euclidea/.

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Author information

Authors and Affiliations

  1. Charles University, Prague, Czech Republic

    Jaroslav Macke

  2. Czech Technical University, Prague, Czech Republic

    Jaroslav Macke, Jiri Sedlar, Josef Urban & Josef Sivic

  3. University of Innsbruck, Innsbruck, Austria

    Miroslav Olsak

Authors
  1. Jaroslav Macke
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  2. Jiri Sedlar
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  3. Miroslav Olsak
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  4. Josef Urban
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  5. Josef Sivic
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Corresponding author

Correspondence to Jiri Sedlar .

Editor information

Editors and Affiliations

  1. Heriot-Watt University, Edinburgh, UK

    Fairouz Kamareddine

  2. University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

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Macke, J., Sedlar, J., Olsak, M., Urban, J., Sivic, J. (2021). Learning to Solve Geometric Construction Problems from Images. In: Kamareddine, F., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2021. Lecture Notes in Computer Science(), vol 12833. Springer, Cham. https://doi.org/10.1007/978-3-030-81097-9_14

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  • DOI: https://doi.org/10.1007/978-3-030-81097-9_14

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  • Online ISBN: 978-3-030-81097-9

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