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.

中文翻译：

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学习从图像中解决几何构造问题

我们描述了一种纯粹基于图像的方法，用于在欧几里得几何游戏中使用尺子和指南针寻找几何结构。该方法基于调整 Mask R-CNN 最先进的图像处理神经架构并向其添加基于树的搜索程序。在有监督的设置中，该方法学习解决来自 Euclidea 的前六级包的所有 68 种几何构造问题，平均准确率为 92%。在对新问题进行评估时，该方法可以解决 68 种欧几里得问题中的 31 种。我们相信，这是第一次训练纯基于图像的学习来解决这种困难的几何构造问题。