用非点阵高斯实现连续距离场，让机器人能实时获取空间距离与梯度。
SplatlessDF: Continuous Distance Field Mapping with Non-Splatting Gaussians
- 从空间视角设计各向异性高斯，直接参数化构建可微分距离场
- 独立使用时精准查询距离与梯度，联合2DGS时兼顾渲染与地图建模
- 适合需要实时空间感知的机器人导航任务，统一高斯基表示框架
近期高斯点阵（GS）方法证明了用可优化高斯表示场景能在高质量重建与渲染中高效实现。本文基于此思想，提出SplatlessDF，一种基于空间而非光度视角的各向异性高斯元素构成的连续距离场（DF）映射框架。该方法直接参数化高斯并优化以恢复可微分的距离场，支持在空间域中查询距离与梯度，适用于导航等下游机器人任务。此外，SplatlessDF可与2D高斯点阵（2DGS）结合，形成仅基于高斯原语的统一框架，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：纯距离场形式与耦合2DGS的联合形式。实验表明，独立形式实现高效精准的距离与梯度查询；联合形式提升渲染几何精度，同步建模连续距离场。结果表明，类似高斯的表示不仅适用于表面建模与渲染，也适用于机器人导航所需的映射表示。
原文摘要 · Abstract (English)
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.
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