Learning to solve geometric construction problems from images

TL;DR

This paper presents an image-based neural network approach combined with search algorithms to solve geometric construction problems in Euclidea, achieving high accuracy on known problems and generalizing to new ones.

Contribution

It introduces a novel purely image-based learning method for solving complex geometric constructions, integrating Mask R-CNN with a tree search.

Findings

Achieved 92% accuracy on known Euclidea problems

Solved 31 out of 68 new problem types

First image-based learning approach for such geometric problems

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.