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.

翻译：本文提出了一种新颖方法，用于从含噪点云中通过高斯过程回归估计距离场。距离场（或称距离函数）在点云配准、里程计、SLAM、路径规划、形状重建等应用中广受欢迎。距离场提供场景的连续表示，定义为任意查询点到最近表面的最短距离。该方法的关键概念是采用一种反转函数，将高斯过程推断的占据场转化为精确距离场。该反转函数取决于所选高斯过程核函数。本文给出了该方法的理论推导及其与现有技术的关系。通过大量模拟实验证明了该方法相比现有距离场具有更高的精度。所提方法的精度水平支持依赖精确距离估计的新颖应用。因此，除了3D点云配准，本文还提出了利用超声导波探测金属结构的回声定位与建图框架。这些方法将所提距离场融入基于物理的模型中，用于模拟信号传播，并与实际接收信号进行比较。通过模拟实验和真实世界实验验证了这些框架的合理性。