VF-Plan: Bridging the Art Gallery Problem and Static LiDAR Scanning with Visibility Field Optimization

2025-03-03

AI Summary

This work addresses the Viewpoint Planning Problem (VPP) for static LiDAR scanning, jointly optimizing coverage completeness, registration robustness, and viewpoint connectivity—objectives traditionally treated in isolation. We propose a novel Visibility Field (VF) modeling framework that integrates medial-axis-driven geometric abstraction with LiDAR line-of-sight modeling, reducing 2D visibility optimization to an efficient 1D structural search. A greedy VF optimization algorithm is designed to generate a minimal viewpoint set under full connectivity and redundancy-free constraints. Experiments demonstrate that the resulting viewpoint count matches expert-designed configurations, while the weighted average path length decreases by 95%, significantly enhancing network compactness, registrability, and navigability.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Viewpoint planning is crucial for 3D data collection and autonomous navigation, yet existing methods often miss key optimization objectives for static LiDAR, resulting in suboptimal network designs. The Viewpoint Planning Problem (VPP), which builds upon the Art Gallery Problem (AGP), requires not only full coverage but also robust registrability and connectivity under limited sensor views. We introduce a greedy optimization algorithm that tackles these VPP and AGP challenges through a novel Visibility Field (VF) approach. The VF captures visibility characteristics unique to static LiDAR, enabling a reduction from 2D to 1D by focusing on medial axis and joints. This leads to a minimal, fully connected viewpoint network with comprehensive coverage and minimal redundancy. Experiments across diverse environments show that our method achieves high efficiency and scalability, matching or surpassing expert designs. Compared to state-of-the-art methods, our approach achieves comparable viewpoint counts (VC) while reducing Weighted Average Path Length (WAPL) by approximately 95%, indicating a much more compact and connected network. Dataset and source code will be released upon acceptance.

Problem

• Optimizes viewpoint planning for static LiDAR scanning.
• Ensures full coverage, registrability, and connectivity in limited views.
• Reduces redundancy and improves network compactness and efficiency.

Innovation

• Greedy algorithm optimizes visibility field for LiDAR.
• Reduces 2D to 1D using medial axis and joints.
• Achieves compact, connected networks with minimal redundancy.