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.
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