The success of neural fields for 3D vision tasks is now indisputable. Following this trend, several methods aiming for visual localization (e.g., SLAM) have been proposed to estimate distance or density fields using neural fields. However, it is difficult to achieve high localization performance by only density fields-based methods such as Neural Radiance Field (NeRF) since they do not provide density gradient in most empty regions. On the other hand, distance field-based methods such as Neural Implicit Surface (NeuS) have limitations in objects' surface shapes. This paper proposes Neural Density-Distance Field (NeDDF), a novel 3D representation that reciprocally constrains the distance and density fields. We extend distance field formulation to shapes with no explicit boundary surface, such as fur or smoke, which enable explicit conversion from distance field to density field. Consistent distance and density fields realized by explicit conversion enable both robustness to initial values and high-quality registration. Furthermore, the consistency between fields allows fast convergence from sparse point clouds. Experiments show that NeDDF can achieve high localization performance while providing comparable results to NeRF on novel view synthesis. The code is available at https://github.com/ueda0319/neddf.
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