Learning Scene-Level Signed Directional Distance Function with Ellipsoidal Priors and Neural Residuals

Dense reconstruction and differentiable rendering are fundamental tightly connected operations in 3D vision and computer graphics. Recent neural implicit representations demonstrate compelling advantages in reconstruction fidelity and differentiability over conventional discrete representations such as meshes, point clouds, and voxels. However, many neural implicit models, such as neural radiance fields (NeRF) and signed distance function (SDF) networks, are inefficient in rendering due to the need to perform multiple queries along each camera ray. Moreover, NeRF and Gaussian Splatting methods offer impressive photometric reconstruction but often require careful supervision to achieve accurate geometric reconstruction. To address these challenges, we propose a novel representation called signed directional distance function (SDDF). Unlike SDF and similar to NeRF, SDDF has a position and viewing direction as input. Like SDF and unlike NeRF, SDDF directly provides distance to the observed surface rather than integrating along the view ray. As a result, SDDF achieves accurate geometric reconstruction and efficient differentiable directional distance prediction. To learn and predict scene-level SDDF efficiently, we develop a differentiable hybrid representation that combines explicit ellipsoid priors and implicit neural residuals. This allows the model to handle distance discontinuities around obstacle boundaries effectively while preserving the ability for dense high-fidelity distance prediction. Through extensive evaluation against state-of-the-art representations, we show that SDDF achieves (i) competitive SDDF prediction accuracy, (ii) faster prediction speed than SDF and NeRF, and (iii) superior geometric consistency compared to NeRF and Gaussian Splatting.