Parametric Point Cloud Completion for Polygonal Surface Reconstruction

TL;DR

This work introduces parametric point cloud completion (PaCo) to bridge point-level completion and polygonal surface reconstruction by learning plane proxies with parameters and inlier points. PaCo hierarchically encodes incomplete input into plane proxies, generates proposals via a Transformer, and recovers plane parameters, point distributions, and primitive confidences, all trained through a bipartite matching framework with multiple losses. The approach demonstrates state-of-the-art performance on the ABC dataset across completion, reconstruction, and simplification tasks, and shows robustness to noise and varying incompleteness, with fast inference. By shifting from point-based recovery to parametric primitives, PaCo enables high-quality, editable polygonal surfaces from incomplete data and suggests a path toward broader parametric primitives in 3D reconstruction.

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.

Figures (13)

• Figure 1: Unlike conventional point cloud completion that aims to recover individual points (middle, non-planar points shown in red), parametric completion recovers primitive parameters along with corresponding inlier points. PaCo recovers planar structures (right, each color denoting a planar primitive), directly enabling high-quality polygonal surface reconstruction.
• Figure 2: Architecture of PaCo. Starting from an incomplete point cloud, we hierarchically encode the points into plane proxies with a lookup table from segmentation. These proxies inform the proxy generator in producing a set of proxy proposals. The generated proxies are then passed to the parameter estimator and the point distributor for primitive estimation. Finally, the primitive selector identifies a subset of primitives to form the parametric completion, with selection optimized via bipartite matching. The resulting primitives enable direct assembly for polygonal surface reconstruction. Points are colored according to their planar primitives.
• Figure 3: Optimization objectives. Our bipartite matching incorporates four objectives: primitive classification loss ($\mathcal{L}_\mathrm{cls}$) for primitive selection, plane normal loss ($\mathcal{L}_\mathrm{norm}$) for plane parameter estimation, plane chamfer loss ($\mathcal{L}_\mathrm{cp}$) for inlier alignment, and repulsion loss ($\mathcal{L}_\mathrm{rep}$) for uniform point distribution. Some pairs are omitted for brevity.
• Figure 4: Qualitative comparison with conventional point cloud completion methods. Simple, moderate, and hard denote missing ratios of 25%, 50%, and 75%, respectively. For cases where reconstruction fails, the completed points are shown instead. Our method excels in recovering geometric structures with planar primitives directly usable by the reconstruction solver.
• Figure 5: Qualitative comparison with neural reconstruction methods directly from incomplete inputs. Our method demonstrates stronger capability in terms of structure recovery.