  Monocular depth estimation is a highly challenging problem that is often
addressed with deep neural networks. While these are able to use recognition of
image features to predict reasonably looking depth maps the result often has
low metric accuracy. In contrast traditional stereo methods using multiple
cameras provide highly accurate estimation when pixel matching is possible. In
this work we propose to combine the two approaches leveraging their respective
strengths. For this purpose we propose a network structure that given an image
provides a parameterization of a set of depth maps with feasible shapes.
Optimizing over the parameterization then allows us to search the shapes for a
photo consistent solution with respect to other images. This allows us to
enforce geometric properties that are difficult to observe in single image as
well as relaxes the learning problem allowing us to use relatively small
networks. Our experimental evaluation shows that our method generates more
accurate depth maps and generalizes better than competing state-of-the-art
approaches.
