  This work presents a novel approach for monocular dense Simultaneous
Localization and Mapping. The surface to be estimated is represented as a
piecewise planar surface, defined as a group of surfels each having as
parameters its position and normal. These parameters are then directly
estimated from the raw camera pixels measurements, by a Gauss-Newton iterative
process. As far as the authors know, this is the first time this approach is
used for monocular depth estimation. The representation of the surface as a
group of surfels has several advantages. It allows the recovery of robust and
accurate pixel depths, without the need to use a computationally demanding
depth regularization schema. This has the further advantage of avoiding the use
of a physically unlikely surface smoothness prior. New surfels can be correctly
initialized from the information present in nearby surfels, avoiding also the
need to use an expensive initialization routine commonly needed in Gauss-Newton
methods. The method was written in the GLSL shading language, allowing the
usage of GPGPU thus achieving real-time. The method was tested against several
datasets, showing both its depth and normal estimation correctness, and its
scene reconstruction quality. The results presented here showcase the
usefulness of the more physically grounded piecewise planar scene depth prior,
instead of the more commonly pixel depth independence and smoothness prior.
