Larger Hausdorff Dimension in Scanning Pattern Facilitates Mamba-Based Methods in Low-Light Image Enhancement
Xinhua Wang, Caibo Feng, Xiangjun Fu, Chunxiao Liu
TL;DR
This work tackles the challenge of efficient, high-fidelity low-light image enhancement by rethinking how two-dimensional image data are traversed by Vision Mamba architectures. It introduces a Hausdorff-dimension‑aware scanning paradigm and two concrete space-filling scans, HilbertMamba and PeanoMamba, which map 2D image grids to 1D sequences while preserving local structure and improving coverage. The authors formalize the concept with a Hausdorff-dimension measurement and dispersion-based error bounds, and validate the approach on LOLv1 and LOLv2 datasets, reporting substantial gains in PSNR/SSIM/LPIPS and reduced inference time compared to state-of-the-art methods. Overall, the Hilbert/Peano scanning strategy offers a principled, efficient pathway to enhance Mamba-based LLIE and holds promise for broader applications in vision where 2D data must be effectively sampled by sequential models.
Abstract
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.