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

2025-10-29

AI Summary

Existing Mamba-based low-light image enhancement methods struggle to simultaneously model long-range dependencies and capture local details, resulting in feature inconsistency and weak spatial locality. To address this, we propose the Hilbert Selective Scanning (HSS) mechanism—the first approach to optimize feature traversal by increasing the Hausdorff dimension of the scanning path. HSS preserves Mamba’s inherent long-range modeling capability while significantly enhancing spatially localized interaction awareness. It integrates the high-dimensional space-filling property of Hilbert curves with selective state-space modeling and efficient feature aggregation, jointly improving computational efficiency and reconstruction quality. On mainstream benchmarks, our method achieves substantial gains in PSNR and SSIM over existing Mamba-based approaches, accelerates inference by 1.3×, and reduces GPU memory consumption by 22%.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Learning with Manifolds
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Enhancing Mamba framework for low-light image enhancement
• Improving fine detail capture through Hausdorff dimension optimization
• Reducing computational costs while maintaining enhancement quality

Innovation

• Hilbert Selective Scan increases Hausdorff dimension
• Refines spatial locality while maintaining long-range dependencies
• Reduces computational consumption and shortens inference time