  Learning methods for relative camera pose estimation have been developed
largely in isolation from classical geometric approaches. The question of how
to integrate predictions from deep neural networks (DNNs) and solutions from
geometric solvers, such as the 5-point algorithm, has as yet remained
under-explored. In this paper, we present a novel framework that involves
probabilistic fusion between the two families of predictions during network
training, with a view to leveraging their complementary benefits in a learnable
way. The fusion is achieved by learning the DNN uncertainty under explicit
guidance by the geometric uncertainty, thereby learning to take into account
the geometric solution in relation to the DNN prediction. Our network features
a self-attention graph neural network, which drives the learning by enforcing
strong interactions between different correspondences and potentially modeling
complex relationships between points. We propose motion parmeterizations
suitable for learning and show that our method achieves state-of-the-art
performance on the challenging DeMoN and ScanNet datasets. While we focus on
relative pose, we envision that our pipeline is broadly applicable for fusing
classical geometry and deep learning.
