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：本文采用了一种新颖的方法,用高山进程(GP)回归法来估计热点云的距离面积; 距离字段或距离函数,对于点云登记、 odomaric、 SLAM、 路径规划、 形状重建等应用越来越受欢迎。 一个距离字段提供连续的场景。 它被定义为与任何查询点和最接近的表面的距离最短的距离。 拟议方法的关键概念是将GP- 推断的占用场变成准确的距离字段。 返回功能是选定GP内核的特异功能。 本文提供了拟议方法及其与现有技术关系的理论衍生。 与现有距离字段相比,与现有远程字段相比的准确性得到了广泛的模拟实验的证明。 拟议方法的精确度允许以精确的距离估计为基础进行新的应用。 因此, 与 3D 点云登记一样, 这项工作提出了一个回声定位和绘图框架, 使用超声波导波感测金属结构。 这些方法利用基于物理的模型中拟议的距离字段模拟信号传播并与实际收到的信号进行比较。 模拟和现实世界实验都展示了这些框架。</s>