  The opacity of rigid 3D scenes with opaque surfaces is considered to be of a
binary type. However, we observed that this property is not followed by the
existing RGB-only NeRF-SLAM. Therefore, we are motivated to introduce this
prior into the RGB-only NeRF-SLAM pipeline. Unfortunately, the optimization
through the volumetric rendering function does not facilitate easy integration
of the desired prior. Instead, we observed that the opacity of ternary-type
(TT) is well supported. In this work, we study why ternary-type opacity is
well-suited and desired for the task at hand. In particular, we provide
theoretical insights into the process of jointly optimizing radiance and
opacity through the volumetric rendering process. Through exhaustive
experiments on benchmark datasets, we validate our claim and provide insights
into the optimization process, which we believe will unleash the potential of
RGB-only NeRF-SLAM. To foster this line of research, we also propose a simple
yet novel visual odometry scheme that uses a hybrid combination of volumetric
and warping-based image renderings. More specifically, the proposed hybrid
odometry (HO) additionally uses image warping-based coarse odometry, leading up
to an order of magnitude final speed-up. Furthermore, we show that the proposed
TT and HO well complement each other, offering state-of-the-art results on
benchmark datasets in terms of both speed and accuracy.
