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.
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