A Divide-and-Conquer Approach for Global Orientation of Non-Watertight Scene-Level Point Clouds Using 0-1 Integer Optimization

2025-05-29

AI Summary

This paper addresses the global normal orientation consistency problem for large-scale, non-watertight scene-level point clouds. Methodologically, we propose DACPO—a divide-and-conquer orientation framework: (1) partitioning the point cloud into blocks and estimating initial normals independently; (2) modeling inter-block geometric consistency via visibility-connected regions, constructing an undirected graph to represent block adjacency; and (3) formulating and solving a 0–1 integer linear program to jointly optimize global flip states. Our key contributions include: the first integration of divide-and-conquer strategy with graph-structured modeling for scene-level orientation; a novel visibility-connectivity metric enabling robust inter-block constraints; and a scalable optimization model. Experiments demonstrate that DACPO significantly outperforms state-of-the-art methods on large non-watertight scenes, efficiently handling hundreds of blocks while achieving high accuracy and robustness. The code is publicly available.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Orienting point clouds is a fundamental problem in computer graphics and 3D vision, with applications in reconstruction, segmentation, and analysis. While significant progress has been made, existing approaches mainly focus on watertight, object-level 3D models. The orientation of large-scale, non-watertight 3D scenes remains an underexplored challenge. To address this gap, we propose DACPO (Divide-And-Conquer Point Orientation), a novel framework that leverages a divide-and-conquer strategy for scalable and robust point cloud orientation. Rather than attempting to orient an unbounded scene at once, DACPO segments the input point cloud into smaller, manageable blocks, processes each block independently, and integrates the results through a global optimization stage. For each block, we introduce a two-step process: estimating initial normal orientations by a randomized greedy method and refining them by an adapted iterative Poisson surface reconstruction. To achieve consistency across blocks, we model inter-block relationships using an an undirected graph, where nodes represent blocks and edges connect spatially adjacent blocks. To reliably evaluate orientation consistency between adjacent blocks, we introduce the concept of the visible connected region, which defines the region over which visibility-based assessments are performed. The global integration is then formulated as a 0-1 integer-constrained optimization problem, with block flip states as binary variables. Despite the combinatorial nature of the problem, DACPO remains scalable by limiting the number of blocks (typically a few hundred for 3D scenes) involved in the optimization. Experiments on benchmark datasets demonstrate DACPO's strong performance, particularly in challenging large-scale, non-watertight scenarios where existing methods often fail. The source code is available at https://github.com/zd-lee/DACPO.

Problem

• Orienting large-scale non-watertight 3D scenes remains underexplored
• Proposing divide-and-conquer strategy for scalable point cloud orientation
• Achieving global consistency via 0-1 integer optimization across blocks

Innovation

• Divide-and-conquer strategy for scalable orientation
• Two-step normal estimation and refinement process
• 0-1 integer optimization for global consistency