MambaH-Fit: Rethinking Hyper-surface Fitting-based Point Cloud Normal Estimation via State Space Modelling

2025-10-10

AI Summary

Existing point cloud normal estimation methods exhibit insufficient capability in fine-grained local geometric modeling, while mainstream Mamba-based architectures emphasize global structure at the expense of local detail. To address this, we propose a hypersurface-fitting framework grounded in state space models (SSMs). Our key contributions are: (1) a patch-wise SSM that treats local point neighborhoods as implicit hypersurfaces, explicitly capturing micro-scale geometry; and (2) an attention-driven multi-scale hierarchical feature fusion mechanism that strengthens local–global collaborative representation. Extensive experiments on multiple benchmark datasets demonstrate significant improvements in normal estimation accuracy, robustness to noise, and cross-scene generalization. Ablation studies confirm both the effectiveness and necessity of each component.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: State Estimation
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We present MambaH-Fit, a state space modelling framework tailored for hyper-surface fitting-based point cloud normal estimation. Existing normal estimation methods often fall short in modelling fine-grained geometric structures, thereby limiting the accuracy of the predicted normals. Recently, state space models (SSMs), particularly Mamba, have demonstrated strong modelling capability by capturing long-range dependencies with linear complexity and inspired adaptations to point cloud processing. However, existing Mamba-based approaches primarily focus on understanding global shape structures, leaving the modelling of local, fine-grained geometric details largely under-explored. To address the issues above, we first introduce an Attention-driven Hierarchical Feature Fusion (AHFF) scheme to adaptively fuse multi-scale point cloud patch features, significantly enhancing geometric context learning in local point cloud neighbourhoods. Building upon this, we further propose Patch-wise State Space Model (PSSM) that models point cloud patches as implicit hyper-surfaces via state dynamics, enabling effective fine-grained geometric understanding for normal prediction. Extensive experiments on benchmark datasets show that our method outperforms existing ones in terms of accuracy, robustness, and flexibility. Ablation studies further validate the contribution of the proposed components.

Problem

• Improving fine-grained geometric structure modeling in point clouds
• Enhancing local geometric detail understanding via state space models
• Advancing hyper-surface fitting accuracy for point cloud normal estimation

Innovation

• State space modeling for hyper-surface fitting
• Attention-driven hierarchical feature fusion scheme
• Patch-wise state space model for geometric understanding