Robots reason about the environment through dedicated representations. Popular choices for dense representations exploit Truncated Signed Distance Functions (TSDF) and Octree data structures. However, TSDF provides a projective or non-projective signed distance obtained directly from depth measurements that overestimate the Euclidean distance. Octrees, despite being memory efficient, require tree traversal and can lead to increased runtime in large scenarios. Other representations based on the Gaussian Process (GP) distance fields are appealing due to their probabilistic and continuous nature, but the computational complexity is a concern. In this paper, we present an online efficient mapping framework that seamlessly couples GP distance fields and the fast-access OpenVDB data structure. The key aspect is a latent Local GP Signed Distance Field (L-GPDF) contained in a local VDB structure that allows fast queries of the Euclidean distance, surface properties and their uncertainties for arbitrary points in the field of view. Probabilistic fusion is then performed by merging the inferred values of these points into a global VDB structure that is efficiently maintained over time. After fusion, the surface mesh is recovered, and a global GP Signed Distance Field (G-GPDF) is generated and made available for downstream applications to query accurate distance and gradients. A comparison with the state-of-the-art frameworks shows superior efficiency and accuracy of the inferred distance field and comparable reconstruction performance. https://github.com/UTS-RI/VDB_GPDF

翻译：机器人通过专用表示对环境进行推理。稠密表示的主流选择利用截断符号距离函数（TSDF）和八叉树数据结构。然而，TSDF提供的投影或非投影符号距离直接源自深度测量值，会高估欧氏距离。八叉树尽管具有内存效率，但需要树遍历，在大型场景中可能导致运行时间增加。基于高斯过程（GP）距离场的其他表示因其概率性和连续性而具有吸引力，但计算复杂度是值得关注的问题。本文提出一种在线高效建图框架，将GP距离场与快速访问的OpenVDB数据结构无缝耦合。其核心在于嵌入局部VDB结构中的潜在局部GP符号距离场（L-GPDF），该结构支持对视场中任意点进行欧氏距离、表面属性及其不确定性的快速查询。随后通过将这些点的推断值融合到全局VDB结构中实现概率融合，该结构可随时间高效维护。融合后恢复表面网格，并生成全局GP符号距离场（G-GPDF）供下游应用查询精确距离与梯度。与前沿框架的对比表明，本方法在推断距离场的效率与精度方面具有优越性，且重建性能相当。https://github.com/UTS-RI/VDB_GPDF