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.

翻译：我们提出MambaH-Fit，一种专门为基于超曲面拟合的点云法向估计设计的状态空间建模框架。现有法向估计方法在建模细粒度几何结构方面往往存在不足，从而限制了预测法向的精度。近来，状态空间模型（SSMs），特别是Mamba，通过以线性复杂度捕获长距离依赖关系展现了强大的建模能力，并启发了其在点云处理中的适应性调整。然而，现有基于Mamba的方法主要聚焦于理解全局形状结构，而对于局部、细粒度几何细节的建模则尚未充分探索。为解决上述问题，我们首先引入一种注意力驱动的层次化特征融合（AHFF）方案，以自适应地融合多尺度点云块特征，显著增强局部点云邻域中的几何上下文学习。在此基础上，我们进一步提出一种基于块的状态空间模型（PSSM），该模型通过状态动力学将点云块建模为隐式超曲面，从而实现对法向预测有效的细粒度几何理解。在基准数据集上的大量实验表明，我们的方法在准确性、鲁棒性和灵活性方面均优于现有方法。消融研究进一步验证了所提出组件的贡献。