VDB-GPDF: Online Gaussian Process Distance Field with VDB Structure

TL;DR

VDB-GPDF presents an online mapping framework that integrates Gaussian Process Distance Fields with the OpenVDB data structure to produce scalable ESDF representations. By maintaining a latent Local GP Signed Distance Field (L-GPDF) in a local VDB and probabilistically fusing results into a global GP Signed Distance Field (G-GPDF) within a global VDB, the method achieves accurate distance estimates, gradients, and surface properties with online efficiency. The approach demonstrates competitive reconstruction quality while delivering superior distance-field accuracy and robust handling of dynamic scenes, outperforming several state-of-the-art baselines in efficiency and distance inference. The framework supports multiple outputs, including distance, gradients, surface properties, and textured meshes, making it suitable for downstream tasks such as navigation and manipulation; code is publicly available.

Abstract

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

Figures (9)

• Figure 1: 3D dense reconstruction and distance field from VDB-GPDF framework. a) Shows the incrementally built mesh coloured with the fused LiDAR intensity. Zooming in to visualise b) the ceiling inside the corridor and c) the stairs and windows around the corner of the quad. d) Shows a horizontal slice of the inferred distance field 0.9m above the ground.
• Figure 2: Block Diagram of the proposed VDB-GPDF framework. We first model the temporary Local Gaussian Process Signed Distance Field (L-GPDF) and surface properties using $\mathcal{P}_{v\{i\}}$. A set of testing points along the ray from the sensor origin to $\mathcal{P}_{v\{i\}}$ are generated to query the distance and surface properties inferences of L-GPDF. Each point in $\mathcal{P}_{t\{i\}}$ with its inferred $\hat{d}_{t}$ and $\hat{c}_{t}$ are fused with the full map represented by a global VDB. Then we have all fused voxels $\mathcal{P}_{\{0,...,i\}}$. The marching cube is applied on the active voxels in $\mathcal{P}_{\{0,...,i\}}$ to update the zero crossing points $\mathcal{P}_{\mathcal{S}\{0,...,i\}}$ and dense reconstruction. The global Gaussian Process Signed Distance Field (G-GPDF) is modelled by $\mathcal{P}_{\mathcal{S}\{0,...,i\}}$ in each leaf node in the global VDB separately.
• Figure 3: Qualitative and quantitative comparison of a) the TSDF fusion from VDBFusion and b) our proposed ESDF fusion with full testing points in the frustum. b) shows that our approach reasons directly in the Euclidean space. After the fusion, our reconstruction in d) shows less noise in the wall and is more complete on the mattress and cow legs than c).
• Figure 4: Efficiency statistical evaluation of the time per frame for the Cow and Lady (top), the Newer College (middle) and Mai City (bottom) datasets respectively.
• Figure 5: Qualitative reconstruction comparison of a) VDBFusion and b) our proposed method shows that VDB-GPDF produces a more complete and natural reconstruction, especially when the sensor is in parallel with the observed surface. Our mesh covers on the top of the mattress, and the colour is properly fused for visualisation.