Single Image Defogging Using a Fourth-Order Telegraph PDE Guided by Physical Haze Modeling
A hybrid fourth-order telegraph PDE beats traditional defogging by up to 20% on structural metrics
Single-image defogging remains a challenging inverse problem due to unknown depth, scattering, and lack of ground truth. Kumar and Ray (IIT Mandi) tackle this with a fourth-order telegraph PDE guided by the Koschmieder haze model. The approach first estimates atmospheric light and transmission map using Dark Channel Prior, then evolves a fourth-order telegraph equation with edge-adaptive diffusion and a fidelity term weighted by the transmission map. The hyperbolic formulation improves numerical stability and convergence, while fourth-order diffusion suppresses haze without over-smoothing edges.
Extensive experiments benchmark the method against Dark Channel Prior, modified DCP, and variational-based defogging. On synthetic foggy images (with ground truth), MSE and SSIM show the hybrid PDE method retains fine details better than competitors. For real-world images, no-reference metrics (FADE, Contrast Restoration Index, Average Gradient, Entropy) confirm superior haze removal and edge preservation. The method converges via relative error norm criteria, making it practical for deployment in autonomous driving, surveillance, and computational photography.
- Combines fourth-order telegraph PDE with physical haze model for edge-aware defogging
- Uses Dark Channel Prior for atmospheric light estimation; fidelity term weighted by transmission map
- Outperforms traditional DCP and variational methods on SSIM and no-reference contrast metrics
Why It Matters
Enables clearer images from fog without training data, critical for autonomous vehicles and outdoor surveillance.