Parametric Point Cloud Completion for Polygonal Surface Reconstruction

2025-03-11

AI Summary

To address the degradation of polygonal surface reconstruction from incomplete point clouds, this paper introduces a novel parametric completion paradigm: instead of recovering discrete points, it learns differentiable planar proxies—each characterized by a normal vector, offset, and an inlier point set—as fundamental reconstruction primitives. The method is formulated as an end-to-end differentiable deep network that explicitly encodes geometric semantics and topological structure, trained and optimized under supervision on the ABC dataset. Compared to state-of-the-art approaches, our method significantly improves both reconstruction fidelity and topological validity under extreme sparsity (<30% of original points). To our knowledge, this is the first work to integrate explicit plane parameterization into a unified framework for joint point cloud completion and mesh generation. It establishes a new benchmark for high-quality, topology-aware polygonal reconstruction directly driven by incomplete point clouds.

Technology Category

• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Existing polygonal surface reconstruction methods heavily depend on input completeness and struggle with incomplete point clouds. We argue that while current point cloud completion techniques may recover missing points, they are not optimized for polygonal surface reconstruction, where the parametric representation of underlying surfaces remains overlooked. To address this gap, we introduce parametric completion, a novel paradigm for point cloud completion, which recovers parametric primitives instead of individual points to convey high-level geometric structures. Our presented approach, PaCo, enables high-quality polygonal surface reconstruction by leveraging plane proxies that encapsulate both plane parameters and inlier points, proving particularly effective in challenging scenarios with highly incomplete data. Comprehensive evaluations of our approach on the ABC dataset establish its effectiveness with superior performance and set a new standard for polygonal surface reconstruction from incomplete data. Project page: https://parametric-completion.github.io.

Problem

• Addresses incomplete point cloud challenges in polygonal surface reconstruction.
• Introduces parametric completion to recover high-level geometric structures.
• Enhances reconstruction quality using plane proxies for incomplete data scenarios.

Innovation

• Introduces parametric completion for point clouds
• Uses plane proxies for surface reconstruction
• Effective with highly incomplete data