Large-scale 3D scene reconstruction with Hilbert Maps

3D scene reconstruction involves the volumetric modeling of space, and it is a fundamental step in a wide variety of robotic applications, including grasping, obstacle avoidance, path planning, mapping and many others. Nowadays, sensors are able to quickly collect vast amounts of data, and the challenge has become one of storing and processing all this information in a timely manner, especially if real-time performance is required. Recently, a novel technique for the stochastic learning of discriminative models through continuous occupancy maps was proposed: Hilbert Maps [18], that is able to represent the input space at an arbitrary resolution while capturing statistical relationships between measurements. The original framework was proposed for 2D environments, and here we extend it to higher-dimensional spaces, addressing some of the challenges brought by the curse of dimensionality. Namely, we propose a method for the automatic selection of feature coordinate locations, and introduce the concept of localized automatic relevance determination (LARD) to the Hilbert Maps framework, in which different dimensions in the projected Hilbert space operate within independent length-scale values. The proposed technique was tested against other state-of-the-art 3D scene reconstruction tools in three different datasets: a simulated indoors environment, RIEGL laser scans and dense LSD-SLAM pointclouds. The results testify to the proposed framework's ability to model complex structures and correctly interpolate over unobserved areas of the input space while achieving real-time training and querying performances.