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DeepMIF: Deep Monotonic Implicit Fields for Large-Scale LiDAR 3D Mapping

Kutay Yılmaz, Matthias Nießner, Anastasiia Kornilova, Alexey Artemov

TL;DR

The paper introduces monotonic implicit fields (MIF) for large-scale LiDAR 3D mapping, addressing the challenge of sparse, view-dependent LiDAR data by enforcing monotone behavior along laser rays and avoiding the need for exact oblique distance measurements. It presents a neural implicit representation f_θ(x; z) conditioned on hierarchical latent features, trained with a set of losses including surface, sign, monotonicity, and an eikonal regularizer, and learns this field through a ray-aware sampling pipeline and an octree-based feature framework. The method achieves competitive quantitative results and strong perceptual quality on Mai City and Newer College benchmarks, with qualitative gains on KITTI, while ablations confirm the importance of the monotonicity and surface losses. Overall, MIF enables robust, large-scale outdoor 3D reconstruction from LiDAR without dense ground-truth SDF supervision, offering practical benefits for autonomous mapping and robotics, with code to be released publicly.

Abstract

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.

DeepMIF: Deep Monotonic Implicit Fields for Large-Scale LiDAR 3D Mapping

TL;DR

The paper introduces monotonic implicit fields (MIF) for large-scale LiDAR 3D mapping, addressing the challenge of sparse, view-dependent LiDAR data by enforcing monotone behavior along laser rays and avoiding the need for exact oblique distance measurements. It presents a neural implicit representation f_θ(x; z) conditioned on hierarchical latent features, trained with a set of losses including surface, sign, monotonicity, and an eikonal regularizer, and learns this field through a ray-aware sampling pipeline and an octree-based feature framework. The method achieves competitive quantitative results and strong perceptual quality on Mai City and Newer College benchmarks, with qualitative gains on KITTI, while ablations confirm the importance of the monotonicity and surface losses. Overall, MIF enables robust, large-scale outdoor 3D reconstruction from LiDAR without dense ground-truth SDF supervision, offering practical benefits for autonomous mapping and robotics, with code to be released publicly.

Abstract

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.
Paper Structure (23 sections, 6 equations, 6 figures, 4 tables)

This paper contains 23 sections, 6 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Method Overview
  5. Monotonic Implicit Scene Representation
  6. Neural Implicits and Level Sets
  7. Our Implicit Representation
  8. Neural Architecture for 3D Mapping
  9. Query Point Sampling
  10. Hierarchical Feature Octree
  11. Network Architecture
  12. Losses
  13. Experiments
  14. Experimental Setup
  15. Baselines
  16. ...and 8 more sections

Figures (6)

  • Figure 1: LiDAR 3D scans (a) generate view-inconsistent range data (pointed to by arrow) rather than projective SDF (b). Direct optimization supervised by oblique rather than projective distances park2019deepsdf does not account for this effect, resulting in loss of surface features (c); in contrast, learning our implicit function (d) is able to preserve higher detail. Red line corresponds to zero level set.
  • Figure 2: LiDAR scanners generate oblique distances (distance along the ray, color of foreground lines) deviating from projective distances ((b)--(c), background color). Depending on scanner position (red dots) and scanning angles, these quantities can be either slightly (areas pointed by green arrows) or significantly (areas pointed by red arrows) different.
  • Figure 3: Our algorithm comprises three main components: a sampling strategy, a feature octree, and an MLP decoder. For visualization purposes, each point is colored based on its input order and sized by its signed distance to the surface. Monotonicity loss is enforced according to this coloring order.
  • Figure 4: Qualitative large-scale 3D mapping results on Newer College ramezani2020newer (upper part) and Mai City vizzo2021poisson (lower part). For Newer College, our algorithm delivers significantly cleaner reconstruction compared to NeRF-LOAM deng2023nerf, more complete results compared to PUMA vizzo2021poisson and Make-It-Dense vizzo2022make, and performs qualitatively comparably to VDBFusion vizzo2022vdbfusion and SHINE zhong2023shine. Similarly for Mai City, our algorithm obtains more complete, robust reconstructions, particularly at object edges.
  • Figure 5: Qualitative large-scale 3D mapping results on KITTI geiger2012we. Compared to baselines, our method produces more complete, smooth, and sharp reconstruction.
  • ...and 1 more figures