# Larger Hausdorff Dimension in Scanning Pattern Facilitates Mamba-Based Methods in Low-Light Image Enhancement

arXiv: https://arxiv.org/abs/2510.26001 · HTML: https://mlsanity.com/paper/2510.26001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mamba for image restoration, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 18 of its 47 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Mamba for image restoration](https://mlsanity.com/ssm/mamba-for-image-restoration/)

## Builds on (most cited first, 18 of 18)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Zero-Reference Deep Curve Estimation for Low-Light Image Enhancement](https://mlsanity.com/paper/2001.06826/) (2020)
- [EnlightenGAN: Deep Light Enhancement without Paired Supervision](https://mlsanity.com/paper/1906.06972/) (2019)
- [Kindling the Darkness: A Practical Low-light Image Enhancer](https://mlsanity.com/paper/1905.04161/) (2019)
- [Learning Enriched Features for Real Image Restoration and Enhancement](https://mlsanity.com/paper/2003.06792/) (2020)
- [Retinex-inspired Unrolling with Cooperative Prior Architecture Search for Low-light Image Enhancement](https://mlsanity.com/paper/2012.05609/) (2020)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)
- [LLNet: A Deep Autoencoder Approach to Natural Low-light Image Enhancement](https://mlsanity.com/paper/1511.03995/) (2015)
- [Low-Light Image Enhancement with Normalizing Flow](https://mlsanity.com/paper/2109.05923/) (2021)
- [Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining](https://mlsanity.com/paper/2402.03302/) (2024)
- [Learning Enriched Features for Fast Image Restoration and Enhancement](https://mlsanity.com/paper/2205.01649/) (2022)
- [Low-Light Image and Video Enhancement Using Deep Learning: A Survey](https://mlsanity.com/paper/2104.10729/) (2021)
- [Diff-Retinex: Rethinking Low-light Image Enhancement with A Generative Diffusion Model](https://mlsanity.com/paper/2308.13164/) (2023)
- [Low-light Image Enhancement via Breaking Down the Darkness](https://mlsanity.com/paper/2111.15557/) (2021)
- [MambaLLIE: Implicit Retinex-Aware Low Light Enhancement with Global-then-Local State Space](https://mlsanity.com/paper/2405.16105/) (2024)

## Abstract (arXiv)

We propose an innovative enhancement to the Mamba framework by increasing the Hausdorff dimension of its scanning pattern through a novel Hilbert Selective Scan mechanism. This mechanism explores the feature space more effectively, capturing intricate fine-scale details and improving overall coverage. As a result, it mitigates information inconsistencies while refining spatial locality to better capture subtle local interactions without sacrificing the model's ability to handle long-range dependencies. Extensive experiments on publicly available benchmarks demonstrate that our approach significantly improves both the quantitative metrics and qualitative visual fidelity of existing Mamba-based low-light image enhancement methods, all while reducing computational resource consumption and shortening inference time. We believe that this refined strategy not only advances the state-of-the-art in low-light image enhancement but also holds promise for broader applications in fields that leverage Mamba-based techniques.