Accurate Gaussian Process Distance Fields with applications to Echolocation and Mapping

This paper introduces a novel method to estimate distance fields from noisy point clouds using Gaussian Process (GP) regression. Distance fields, or distance functions, gained popularity for applications like point cloud registration, odometry, SLAM, path planning, shape reconstruction, etc. A distance field provides a continuous representation of the scene. It is defined as the shortest distance from any query point and the closest surface. The key concept of the proposed method is a reverting function used to turn a GP-inferred occupancy field into an accurate distance field. The reverting function is specific to the chosen GP kernel. This paper provides the theoretical derivation of the proposed method and its relationship to existing techniques. The improved accuracy compared with existing distance fields is demonstrated with extensive simulated experiments. The level of accuracy of the proposed approach allows for novel applications that rely on precise distance estimation. Thus, alongside 3D point cloud registration, this work presents echolocation and mapping frameworks using ultrasonic guided waves sensing metallic structures. These methods leverage the proposed distance field in physics-based models to simulate the signal propagation and compare it with the actual signal received. Both simulated and real-world experiments are conducted to demonstrate the soundness of these frameworks.