  Crater counting on the Moon and other bodies is crucial to constrain the
dynamical history of the Solar System. This has traditionally been done by
visual inspection of images, thus limiting the scope, efficiency, and/or
accuracy of retrieval. In this paper we demonstrate the viability of using
convolutional neural networks (CNNs) to determine the positions and sizes of
craters from Lunar digital elevation maps (DEMs). We recover 92% of craters
from the human-generated test set and almost double the total number of crater
detections. Of these new craters, 15% are smaller in diameter than the minimum
crater size in the ground-truth dataset. Our median fractional longitude,
latitude and radius errors are 11% or less, representing good agreement with
the human-generated datasets. From a manual inspection of 361 new craters we
estimate the false positive rate of new craters to be 11%. Moreover, our
Moon-trained CNN performs well when tested on DEM images of Mercury, detecting
a large fraction of craters in each map. Our results suggest that deep learning
will be a useful tool for rapidly and automatically extracting craters on
various Solar System bodies. We make our code and data publicly available at
https://github.com/silburt/DeepMoon.git and
https://doi.org/10.5281/zenodo.1133969 .
