  The widespread adoption of Neural Radiance Fields (NeRFs) have ensured
significant advances in the domain of novel view synthesis in recent years.
These models capture a volumetric radiance field of a scene, creating highly
convincing, dense, photorealistic models through the use of simple,
differentiable rendering equations. Despite their popularity, these algorithms
suffer from severe ambiguities in visual data inherent to the RGB sensor, which
means that although images generated with view synthesis can visually appear
very believable, the underlying 3D model will often be wrong. This considerably
limits the usefulness of these models in practical applications like Robotics
and Extended Reality (XR), where an accurate dense 3D reconstruction otherwise
would be of significant value. In this paper, we present the vital differences
between view synthesis models and 3D reconstruction models. We also comment on
why a depth sensor is essential for modeling accurate geometry in general
outward-facing scenes using the current paradigm of novel view synthesis
methods. Focusing on the structure-from-motion task, we practically demonstrate
this need by extending the Plenoxel radiance field model: Presenting an
analytical differential approach for dense mapping and tracking with radiance
fields based on RGB-D data without a neural network. Our method achieves
state-of-the-art results in both mapping and tracking tasks, while also being
faster than competing neural network-based approaches. The code is available
at: https://github.com/ysus33/RGB-D_Plenoxel_Mapping_Tracking.git
