Directed Distance Fields for Constant-Time Ray Queries on Gaussian Splatting
Authors: Subhankar MIshra
Organizations: School of Computer Sciences, National Institute of Science Education and Research (NISER), 752050, India
Abstract
3D Gaussian Splatting (3DGS) renders new views of a scene in real time. Like every rasterizer, it answers only primary rays, the rays from the camera through the image. It cannot trace the secondary rays that shadows, ambient occlusion, and global illumination need. We turn a trained 3DGS scene into a ray oracle by distilling a Directed Distance Function (DDF). The DDF is a small neural field. It takes a ray, given by an origin and a direction, and returns the distance to the first surface and whether the ray hits anything. Each query is one forward pass. The field is 52MB, and its size does not depend on the number of Gaussians, so its cost and memory stay flat as the scene grows. We make three points. First, we study what supervision a DDF needs. Depth rendered from the Gaussians is too blurry to teach thin parts, while clean distance supervision recovers them. Second, we measure speed. The DDF is 26 to 72 times faster than sphere tracing an equivalent signed distance field, and unlike a bounding volume hierarchy built over the Gaussians, even on dedicated RT-core hardware, its query time and memory do not grow with the scene. Third, we show a pipeline that needs no mesh: images give a 3DGS scene, a neural surface gives clean distances, and the DDF learns from them. We use the DDF as a secondary-ray oracle for global illumination. It reproduces reference ray-traced shadows at 30.3dB and ambient occlusion at 21.3~dB across 142 objects, and on real captured scenes. Our codes are available at https://github.com/smlab-niser/ddf-gs.
Recent Gaussian splatting (GS) methods have shown that scenes can be represented efficiently with optimisable Gaussians for high-quality reconstruction and rendering. In this paper, building on this principle, we introduce SplatlessDF, a continuous distance field (DF) mapping framework that uses anisotropic Gaussian elements from a spatial rather than photometric perspective. SplatlessDF directly parameterises the Gaussians and optimises to recover a differentiable DF, enabling distances and gradients to be queried in the spatial domain for downstream robotic tasks such as navigation. Furthermore, SplatlessDF can be coupled with 2D Gaussian splatting (2DGS), providing a unified framework based solely on Gaussian primitives that can learn continuous DF and surface models and supports photometric rendering. We consider two settings: a standalone DF-only formulation and a joint DF-rendering formulation coupled with 2DGS. Experiments show that the standalone formulation provides efficient and accurate distance and gradient queries, while the joint formulation improves rendering geometry and simultaneously models a continuous DF. These results highlight the potential of GS-style representations not only for surface modelling and rendering but also for mapping representations suited to robotic navigation.
Monisha Mushtary Uttsha, Lan Wu, Teresa Vidal-Calleja
We introduce a probabilistic splat-based radiance field framework that retains the fast rasterization and test-time efficiency of 3D Gaussian Splatting (3DGS) while replacing heuristic primitive manipulation with gradient-based optimization of a volumetric probability density. Rather than relocating, splitting, or culling Gaussians via hand-tuned densification (e.g., ADC), we treat primitive locations as samples drawn from a persistent, learnable density. We instantiate this density using a novel, memory-efficient multi-scale hierarchical grid that enables end-to-end gradient-based optimization. To stabilize the optimization, we derive an unbiased gradient estimator with control variates that markedly reduces variance. By allowing probability mass to flow to where the loss demands, our framework eliminates brittle priors and naturally explores the volume, achieving state-of-the-art reconstruction quality on mip-NeRF 360 while preserving 3DGS-level rendering speed.
Mia Gaia Polansky, George Kopanas, Stephan Garbin +2
We present BlitzGS, a distributed 3DGS framework that reduces active Gaussian workload for fast city-scale reconstruction. BlitzGS manages this workload at three coupled levels. At the system level, the framework shards Gaussians across GPUs by index parity rather than spatial blocks. This approach mitigates the cross-block visibility redundancy inherent in spatial partitioning. Furthermore, it distributes each rendering step through a single cross-GPU exchange that routes projected Gaussians to their tile owners. At the model level, scheduled importance-scoring passes shrink the global Gaussian population. During these passes, the framework generates a per-Gaussian visibility weight to bias density-control updates toward contributing primitives and a per-view importance mask for the view-level renderer. At the view level, BlitzGS trims each camera's active set with a distance-based LOD gate to exclude excessively fine primitives for the current frustum and the importance-based culling mask to skip Gaussians with negligible cross-view contribution. On large-scale benchmarks, BlitzGS matches the rendering quality of recent large-scale baselines while delivering an order-of-magnitude speedup, training city-scale scenes in tens of minutes. Our code is available at https: //github.com/AkierRaee/BlitzGS.