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.

翻译：摘要：近期高斯溅射（GS）方法表明，通过可优化的高斯函数能够高效表征场景，实现高质量重建与渲染。本文基于该原理，提出SplatlessDF——一种从空间视角（而非光度视角）利用各向异性高斯单元构建连续距离场（DF）的建图框架。SplatlessDF直接参数化高斯函数并优化以恢复可微距离场，使得能够在空间域中查询距离与梯度信息，从而支持导航等下游机器人任务。此外，SplatlessDF可与二维高斯溅射（2DGS）结合，形成基于高斯基元的统一框架，同时学习连续距离场与表面模型，并支持光度渲染。我们考虑两种设置：独立距离场公式，以及结合2DGS的联合距离场-渲染公式。实验表明，独立公式能够实现高效准确的距离与梯度查询，而联合公式在提升渲染几何质量的同时可同步建模连续距离场。这些结果揭示了高斯溅射式表征不仅适用于表面建模与渲染，在适配机器人导航的建图表征中同样具有潜力。