  Recently, significant progress has been achieved in sensing real large-scale
outdoor 3D environments, particularly by using modern acquisition equipment
such as LiDAR sensors. Unfortunately, they are fundamentally limited in their
ability to produce dense, complete 3D scenes. To address this issue, recent
learning-based methods integrate neural implicit representations and
optimizable feature grids to approximate surfaces of 3D scenes. However,
naively fitting samples along raw LiDAR rays leads to noisy 3D mapping results
due to the nature of sparse, conflicting LiDAR measurements. Instead, in this
work we depart from fitting LiDAR data exactly, instead letting the network
optimize a non-metric monotonic implicit field defined in 3D space. To fit our
field, we design a learning system integrating a monotonicity loss that enables
optimizing neural monotonic fields and leverages recent progress in large-scale
3D mapping. Our algorithm achieves high-quality dense 3D mapping performance as
captured by multiple quantitative and perceptual measures and visual results
obtained for Mai City, Newer College, and KITTI benchmarks. The code of our
approach will be made publicly available.
