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 is a projective signed distance obtained directly from depth measurements that overestimates the Euclidean distance. Octrees, despite being memory efficient, require tree traversal and can lead to increased runtime in large scenarios. Other representations based on 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 VDB data structure. This framework incrementally builds the Euclidean distance field and fuses other surface properties, like intensity or colour, into a global scene representation that can cater for large-scale scenarios. 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. The accompanying code will be publicly available. 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。稠密表示的常用方法采用截断符号距离函数（TSDF）和八叉树数据结构。然而，TSDF是从深度测量直接获得的投影符号距离，会高估欧氏距离。八叉树尽管内存效率高，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，但计算复杂度是一个问题。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VDB数据结构无缝耦合。该框架增量式构建欧氏距离场，并将强度或颜色等其他表面属性融合到可适应大规模场景的全局场景表示中。其核心是包含在局部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随时间高效维护的全局VDB结构中实现概率融合。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，所提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。相关代码将公开提供。https://github.com/UTS-RI/VDB_GPDF