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

2026-03-30

AI Summary

Existing methods for real-time, large-scale signed distance function (SDF) estimation with uncertainty quantification are often hindered by fixed resolution, high training overhead, or poor scalability. This work proposes Kernel-SDF, an open-source library that uniquely integrates kernel regression with Gaussian processes. The front-end constructs a continuous occupancy field via kernel regression, while the back-end leverages surface-boundary samples to perform Gaussian process regression, enabling accurate estimation of the SDF, its gradient, and well-calibrated uncertainties—all while supporting real-time mesh reconstruction. By unifying these components, Kernel-SDF significantly enhances SDF accuracy and geometric continuity without compromising real-time performance, thereby overcoming the traditional trade-off among efficiency, precision, and uncertainty quantification. The approach is particularly suited for robotics applications demanding high geometric reliability, such as navigation, planning, and manipulation.

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.

Problem

• Signed Distance Function
• Uncertainty Quantification
• Real-Time Estimation
• Streaming Sensor Data
• Scalability

Innovation

• Signed Distance Function
• Kernel Regression
• Uncertainty Quantification
• Real-Time Estimation
• Gaussian Process