GLiDR: Topologically Regularized Graph Generative Network for Sparse LiDAR Point Clouds

Abstract: Sparse LiDAR point clouds cause severe loss of detail of static structures and reduce the density of static points available for navigation. Reduced density can be detrimental to navigation under several scenarios. We observe that despite high sparsity, in most cases, the global topology of LiDAR outlining the static structures can be inferred. We utilize this property to obtain a backbone skeleton of a LiDAR scan in the form of a single connected component that is a proxy to its global topology. We utilize the backbone to augment new points along static structures to overcome sparsity. Newly introduced points could correspond to existing static structures or to static points that were earlier obstructed by dynamic objects. To the best of our knowledge, we are the first to use such a strategy for sparse LiDAR point clouds. Existing solutions close to our approach fail to identify and preserve the global static LiDAR topology and generate sub-optimal points. We propose GLiDR, a Graph Generative network that is topologically regularized using 0-dimensional Persistent Homology ($\mathcal{PH}$) constraints. This enables GLiDR to introduce newer static points along a topologically consistent global static LiDAR backbone. GLiDR generates precise static points using $32\times$ sparser dynamic scans and performs better than the baselines across three datasets. GLiDR generates a valuable byproduct - an accurate binary segmentation mask of static and dynamic objects that are helpful for navigation planning and safety in constrained environments. The newly introduced static points allow GLiDR to outperform LiDAR-based navigation using SLAM in several settings. Source code is available at https://kshitijbhat.github.io/glidr

• The paper introduces GLiDR, a network that combines LiDAR graph processing with 0-dim persistent homology regularization to improve sparse point cloud clarity.
• It employs a topologically-informed loss function to preserve essential structural features during the reconstruction process.
• Experimental results show enhanced performance in dense LiDAR scans and highlight challenges under extreme sparsity for future research.

Overview of GLiDR: Topologically Regularized Graph Generative Network for Sparse LiDAR Point Clouds

This essay presents an in-depth analysis of the paper titled "GLiDR: Topologically Regularized Graph Generative Network for Sparse LiDAR Point Clouds" by Prashant Kumar, Kshitij Madhav Bhat, Vedang Bhupesh Shenvi Nadkarni, and Prem Kalra. The research introduces a novel approach that leverages Persistent Homology (PH) and a graph-based generative network to enhance the quality and usability of sparse LiDAR point clouds.

Persistent Homology

Persistent Homology (PH) is utilized for detecting and analyzing topological features in datasets, serving as an algebraic method to reveal structures within the data across multiple scales. In the context of this paper, PH is applied to LiDAR point clouds. Specifically, the dataset is converted into a simplicial complex where the homology evolves across an increasing sequence of these complexes—a process referred to as filtration.

The filtration function iteratively examines point cloud data to identify topological features such as connected components, cycles, and voids, which persist over a range of spatial resolutions. These features signify important structural characteristics of the point clouds that are subsequently leveraged to inform and regularize the graph-generative model.

Methodology

The core contribution of the paper is the GLiDR network, which incorporates two primary components: a LiDAR Graph Network module and a 0-dimensional PH-based regularizer, which ensures the preservation of critical topological features.

1. LiDAR Graph Network:
   • The generative model comprises a series of graph-based layers designed to process and reconstruct LiDAR point clouds.
   • These layers aim to predict missing points in sparse LiDAR scans effectively, enhancing the density and fidelity of the point clouds.
2. Persistent Homology Regularization:
   • This component introduces a topologically-informed loss function, guiding the network to maintain the intrinsic topological structures of the input data.
   • The regularizer utilizes PH to ensure that global shape features are preserved within the generative model. Filtrations based on pairwise distances and pixel intensities in images are employed to generate topological losses, which are minimized during training.

Experiments and Results

The paper presents a series of experiments conducted on datasets with varying levels of sparsity, including 64-beam, 16-beam, 8-beam, and 4-beam LiDAR scans. Key performance metrics include Absolute Trajectory Error (ATE) and Relative Pose Error (RPE), which respectively measure the global consistency and local accuracy of the generated trajectories against ground truth.

The primary findings include:

• For dense LiDAR scans (64-beam, 16-beam), GLiDR significantly enhances the quality of reconstructed point clouds, enabling better performance in autonomous navigation tasks.
• With higher sparsity levels (8-beam and 4-beam), the model struggles to maintain topological integrity, leading to inferior performance in navigation tasks. The 0-dim PH-based regularizer shows limitations in calculating accurate global backbones under extreme sparsity.

Implications and Future Directions

The introduction of topologically-informed generative networks opens new avenues for improving the efficacy of sparse LiDAR point clouds. By ensuring the preservation of global shape characteristics, GLiDR provides a robust framework for enhancing point cloud density, which is critical for various applications in autonomous driving and robotics.

Future developments could expand this methodology by exploring higher-dimensional topological features beyond 0-dim PH, or integrating more complex filtration functions that better capture the nuances of sparse datasets. Additionally, improving the robustness of PH-based methods under extreme sparsity could enable broader applicability across various domains requiring high-fidelity point cloud reconstruction.

The results demonstrate that while GLiDR excels in moderately sparse scenarios, further research is needed to handle the challenges posed by highly sparse data effectively. Enhancing PH-based backbones and exploring alternative regularization techniques could be promising areas of future research to address these challenges.