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

TL;DR

This paper introduces a manifold-aware framework for point cloud completion that leverages geodesic distances and attention mechanisms to improve geometric consistency and semantic coherence in reconstructed 3D shapes.

Contribution

It proposes a novel geodesic distance approximation and a manifold-aware feature extractor with geodesic-relational attention for better point cloud reconstruction.

Findings

Outperforms state-of-the-art methods in benchmark tests

Enhances geometric and semantic fidelity of completed point clouds

Effectively captures nonlinear manifold structures

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.