  The representation of geometry in real-time 3D perception systems continues
to be a critical research issue. Dense maps capture complete surface shape and
can be augmented with semantic labels, but their high dimensionality makes them
computationally costly to store and process, and unsuitable for rigorous
probabilistic inference. Sparse feature-based representations avoid these
problems, but capture only partial scene information and are mainly useful for
localisation only.
  We present a new compact but dense representation of scene geometry which is
conditioned on the intensity data from a single image and generated from a code
consisting of a small number of parameters. We are inspired by work both on
learned depth from images, and auto-encoders. Our approach is suitable for use
in a keyframe-based monocular dense SLAM system: While each keyframe with a
code can produce a depth map, the code can be optimised efficiently jointly
with pose variables and together with the codes of overlapping keyframes to
attain global consistency. Conditioning the depth map on the image allows the
code to only represent aspects of the local geometry which cannot directly be
predicted from the image. We explain how to learn our code representation, and
demonstrate its advantageous properties in monocular SLAM.
