Curvature-Aware Captioning:Leveraging Geodesic Attention for 3D Scene Understanding

TL;DR

This paper introduces a curvature-aware captioning framework using non-Euclidean geodesic attention mechanisms to improve 3D scene understanding in robotics and AR.

Contribution

It proposes a novel non-Euclidean attention approach that resolves localization and semantic modeling conflicts in 3D scene captioning.

Findings

Achieves state-of-the-art results on ScanRefer and Nr3D benchmarks.

Significant improvements in localization accuracy.

Enhanced descriptive richness of scene captions.

Abstract

Accurate 3D scene description is fundamental to robotic navigation and augmented reality, yet current dense captioning methods face significant limitations in processing sparse point cloud data. % Existing approaches that apply Euclidean embedding spaces struggle to simultaneously preserve fine-grained local geometric details and model exponentially growing global semantic hierarchies, leading to either inaccurate localization or disjointed, shallow scene descriptions. % In this work, we propose a novel \textbf{\textsc{Curvature-Aware Captioning}} framework, integrating novel non-Euclidean geodesic attention mechanisms, to resolve the localization-contextualization conflict. % Specifically, self-attention within Oblique space enforces dimensional homogeneity while establishing long-range dependencies. Bidirectional geodesic cross-attention within Lorentz space models hierarchical semantic relationships across scene instances, enabling simultaneous precision in object localization and coherence in scene descriptions. % Theoretical analysis confirms that the curvature complementarity between the Oblique manifold and Lorentz hyperboloid resolves the Euclidean-hyperbolic conflict, ensuring feature stability via isotropic optimization while preserving inherent hierarchical relationships. Extensive experiments on ScanRefer and Nr3D benchmarks demonstrate state-of-the-art performance, with significant gains in both localization accuracy and descriptive richness.