Single Image Defogging Using a Fourth-Order Telegraph PDE Guided by Physical Haze Modeling

2026-05-05 · Source: cs.CV updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This paper introduces a novel hybrid defogging model that integrates a fourth-order nonlinear Telegraph Partial Differential Equation (PDE) with a physical haze formation model for single image defogging. The method utilizes the Dark Channel Prior (DCP) to estimate atmospheric parameters and generate a guidance image, with the final restoration achieved through a fourth-order PDE-based evolution incorporating an edge-adaptive diffusion coefficient and a transmission map-weighted fidelity term. This approach effectively suppresses haze while preserving structural details, and its hyperbolic formulation enhances numerical stability and convergence behavior. The proposed model is quantitatively evaluated against DCP, modified DCP, and variational-based techniques using metrics like MSE, SSIM, FADE, CRI, Average Gradient, and Entropy. Experimental results demonstrate that the hybrid PDE-based method provides comparable or superior visual quality, maintains structural details, and reduces common artifacts, particularly under moderate and heavy fog conditions.

Key takeaway

A novel single-image defogging method leverages a fourth-order telegraph Partial Differential Equation (PDE), guided by the Dark Channel Prior, to effectively remove haze. This hybrid approach outperforms existing DCP, MDCP, and variational models, demonstrating superior MSE and SSIM scores and enhanced structural detail preservation, especially in moderate to dense fog. Its ability to restore balanced color contrast and sharper edges makes it highly relevant for robust outdoor vision systems, including autonomous driving.

Topics

• Single Image Defogging
• Fourth-Order Telegraph PDE
• Physical Haze Modeling
• Dark Channel Prior
• Atmospheric Scattering Model

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CV updates on arXiv.org.