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

arXiv: https://arxiv.org/abs/2510.09088 · HTML: https://mlsanity.com/paper/2510.09088/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Point clouds, detection and remote sensing, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Point clouds, detection and remote sensing](https://mlsanity.com/ssm/point-clouds-detection-and-remote-sensing/)

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [Semantic3D.net: A new Large-scale Point Cloud Classification Benchmark](https://mlsanity.com/paper/1704.03847/) (2017)
- [The Mamba in the Llama: Distilling and Accelerating Hybrid Models](https://mlsanity.com/paper/2408.15237/) (2024)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Cobra: Extending Mamba to Multi-Modal Large Language Model for Efficient Inference](https://mlsanity.com/paper/2403.14520/) (2024)
- [Point Cloud Mamba: Point Cloud Learning via State Space Model](https://mlsanity.com/paper/2403.00762/) (2024)
- [Voxel Mamba: Group-Free State Space Models for Point Cloud based 3D Object Detection](https://mlsanity.com/paper/2406.10700/) (2024)
- [Mamba3D: Enhancing Local Features for 3D Point Cloud Analysis via State Space Model](https://mlsanity.com/paper/2404.14966/) (2024)
- [Nesti-Net: Normal Estimation for Unstructured 3D Point Clouds using Convolutional Neural Networks](https://mlsanity.com/paper/1812.00709/) (2018)
- [DeepFit: 3D Surface Fitting via Neural Network Weighted Least Squares](https://mlsanity.com/paper/2003.10826/) (2020)
- [Learning Graph-Convolutional Representations for Point Cloud Denoising](https://mlsanity.com/paper/2007.02578/) (2020)
- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [AdaFit: Rethinking Learning-based Normal Estimation on Point Clouds](https://mlsanity.com/paper/2108.05836/) (2021)
- [PoinTramba: A Hybrid Transformer-Mamba Framework for Point Cloud Analysis](https://mlsanity.com/paper/2405.15463/) (2024)
- [HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces](https://mlsanity.com/paper/2210.07158/) (2022)
- [3DMambaIPF: A State Space Model for Iterative Point Cloud Filtering via Differentiable Rendering](https://mlsanity.com/paper/2404.05522/) (2024)
- [GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation](https://mlsanity.com/paper/2207.11484/) (2022)
- [Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2303.17167/) (2023)
- [Contrastive Learning for Joint Normal Estimation and Point Cloud Filtering](https://mlsanity.com/paper/2208.06811/) (2022)
- [PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering](https://mlsanity.com/paper/2209.00798/) (2022)
- [Neural Gradient Learning and Optimization for Oriented Point Normal Estimation](https://mlsanity.com/paper/2309.09211/) (2023)
- [CMG-Net: Robust Normal Estimation for Point Clouds via Chamfer Normal Distance and Multi-scale Geometry](https://mlsanity.com/paper/2312.09154/) (2023)

## Abstract (arXiv)

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.