  Estimating depth information from endoscopic images is a prerequisite for a
wide set of AI-assisted technologies, such as accurate localization and
measurement of tumors, or identification of non-inspected areas. As the domain
specificity of colonoscopies -- deformable low-texture environments with
fluids, poor lighting conditions and abrupt sensor motions -- pose challenges
to multi-view 3D reconstructions, single-view depth learning stands out as a
promising line of research. Depth learning can be extended in a Bayesian
setting, which enables continual learning, improves decision making and can be
used to compute confidence intervals or quantify uncertainty for in-body
measurements. In this paper, we explore for the first time Bayesian deep
networks for single-view depth estimation in colonoscopies. Our specific
contribution is two-fold: 1) an exhaustive analysis of scalable Bayesian
networks for depth learning in different datasets, highlighting challenges and
conclusions regarding synthetic-to-real domain changes and supervised vs.
self-supervised methods; and 2) a novel teacher-student approach to deep depth
learning that takes into account the teacher uncertainty.
