SplatlessDF: Continuous Distance Field Mapping with Non-Splatting Gaussians

2026-06-11

AI Summary

This work proposes a continuous signed distance field modeling approach based on anisotropic Gaussian primitives, pioneering the use of Gaussian representations for joint geometric and distance field learning in robot navigation. By parameterizing Gaussians from a spatial geometry perspective, the method directly optimizes a differentiable distance field and enables end-to-end joint training with 2D Gaussian Splatting (2DGS). The resulting distance field supports efficient and accurate distance and gradient queries without requiring explicit splatting, while joint training simultaneously enhances rendering fidelity and geometric consistency. This study extends the applicability of Gaussian representations to robotic perception and navigation, demonstrating their potential in concurrently addressing geometric modeling and visual rendering tasks.

Abstract

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.

Problem

• distance field
• Gaussian splatting
• continuous mapping
• robotic navigation
• surface modeling

Innovation

• Gaussian primitives
• continuous distance field
• differentiable mapping
• robotic navigation
• 2D Gaussian splatting