Kernel-SDF: An Open-Source Library for Real-Time Signed Distance Function Estimation using Kernel Regression

Abstract

Accurate and efficient environment representation is crucial for robotic applications such as motion planning, manipulation, and navigation. Signed distance functions (SDFs) have emerged as a powerful representation for encoding distance to obstacle boundaries, enabling efficient collision-checking and trajectory optimization techniques. However, existing SDF reconstruction methods have limitations when it comes to large-scale uncertainty-aware SDF estimation from streaming sensor data. Voxel-based approaches are limited by fixed resolution and lack uncertainty quantification, neural network methods require significant training time, while Gaussian process (GP) methods struggle with scalability, sign estimation, and uncertainty calibration. In this letter, we develop an open-source library, Kernel-SDF, which uses kernel regression to learn SDF with calibrated uncertainty quantification in real-time. Our approach consists of a front-end that learns a continuous occupancy field via kernel regression, and a back-end that estimates accurate SDF via GP regression using samples from the front-end surface boundaries. Kernel-SDF provides accurate SDF, SDF gradient, SDF uncertainty, and mesh construction in real-time. Evaluation results show that Kernel-SDF achieves superior accuracy compared to existing methods, while maintaining real-time performance, making it suitable for various robotics applications requiring reliable uncertainty-aware geometric information.

Figures (10)

• Figure 1: Example of SDF estimation, visualized as a heatmap in (a), and mesh reconstruction in (b) of a large-scale environment, obtained using Kernel-SDF.
• Figure 2: Overview of Kernel-SDF. The front-end estimates surface points and normals from point cloud observations using BHM and the marching cubes algorithm. The surface points are used as training data for the back-end, which learns SDF and its gradient using multiple GPs organized in an octree data structure.
• Figure 4: Surface points colored by their log-odds values from BHM. The ground has lower log-odds than the walls.
• Figure 5: Qualitative comparison of mesh reconstruction on the Replica dataset replica19arxiv. Our method achieves the best visual quality, accuracy and completeness compared to the baselines. For example, the textures of the bed sheets are better preserved in our reconstruction.
• Figure 6: Qualitative comparison of mesh reconstruction of the cow in the Cow and Lady dataset oleynikova_voxblox_2017. Our method successfully recovers the detailed geometry, such as the horns, ears, and legs, which are missing in the baseline reconstructions.

Theorems & Definitions (1)

• proof