English

Learning to solve geometric construction problems from images

Computer Vision and Pattern Recognition 2021-06-29 v1 Artificial Intelligence Computational Geometry Machine Learning Logic in Computer Science

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 image processing 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 a purely image-based learning has been trained to solve geometric construction problems of this difficulty.

Keywords

Cite

@article{arxiv.2106.14195,
  title  = {Learning to solve geometric construction problems from images},
  author = {J. Macke and J. Sedlar and M. Olsak and J. Urban and J. Sivic},
  journal= {arXiv preprint arXiv:2106.14195},
  year   = {2021}
}

Comments

16 pages, 7 figures, 3 tables

R2 v1 2026-06-24T03:38:16.719Z