Manifold-Aware Point Cloud Completion via Geodesic-Attentive Hierarchical Feature Learning

TL;DR

This work tackles point cloud completion by accounting for nonlinear surface geometry rather than relying on Euclidean proximity alone. It introduces a manifold-aware framework with a Geodesic Distance Approximator (GDA) and a Manifold-Aware Feature Extractor (MAFE), featuring anchor-based geodesic distances, Geodesic Neighborhood Grouping, Geodesic-Relational Attention, and Manifold Positional Embedding, followed by a coarse-to-fine completion. The approach achieves state-of-the-art performance across multiple benchmarks, demonstrating improved geometric fidelity and semantic coherence under sparse or partial observations. The results suggest that explicitly modeling intrinsic manifold structure yields robust and generalizable point cloud reconstructions suitable for real-world 3D perception tasks.

Abstract

Point cloud completion seeks to recover geometrically consistent shapes from partial or sparse 3D observations. Although recent methods have achieved reasonable global shape reconstruction, they often rely on Euclidean proximity and overlook the intrinsic nonlinear geometric structure of point clouds, resulting in suboptimal geometric consistency and semantic ambiguity. In this paper, we present a manifold-aware point cloud completion framework that explicitly incorporates nonlinear geometry information throughout the feature learning pipeline. Our approach introduces two key modules: a Geodesic Distance Approximator (GDA), which estimates geodesic distances between points to capture the latent manifold topology, and a Manifold-Aware Feature Extractor (MAFE), which utilizes geodesic-based $k$-NN groupings and a geodesic-relational attention mechanism to guide the hierarchical feature extraction process. By integrating geodesic-aware relational attention, our method promotes semantic coherence and structural fidelity in the reconstructed point clouds. Extensive experiments on benchmark datasets demonstrate that our approach consistently outperforms state-of-the-art methods in reconstruction quality.

Figures (5)

• Figure 1: Visualization of point connectivity using Euclidean versus manifold-based neighbors. Graphs in the top row are constructed using Euclidean neighbors, while the graphs in the bottom row are built by manifold-aware neighbors. The manifold-based graphs better preserve the intrinsic topology and continuity of the underlying shape.
• Figure 2: Overview of our proposed framework. Given an incomplete point cloud $\mathcal{P}$, we first construct a local proximity graph and applies Dijkstra’s algorithm to compute geodesic distances in the GDA module. The MAFE module then integrates geodesic information through geodesic-based grouping and our GRA-T module, enabling nonlinear feature aggregation. The resulting features are fed into a coarse completion module, and finally refined into a dense and complete point cloud.
• Figure 3: Illustration of the geodesic-relational attention mechanism in GRA-T. For each center point, neighborhoods are determined by anchor-based approximation, and both features and coordinates are aggregated using geodesic-aware attention weights.
• Figure 4: Completion results on the KITTI dataset. Our method recovers plausible shapes under real-world noise and sparsity.
• Figure 5: Qualitative results on PCN: our method better restores fine structures and complex topologies compared to prior approaches pointatten2024yu2023adapointryuan2018pcnXiang2021SnowflakeNetyang2018foldingnet .