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Unsupervised Single Image Dehazing Using Dark Channel Prior Loss
Alona Golts, Daniel Freedman, Michael Elad
TL;DR
Single-image dehazing lacks reliable matched outdoor hazy-clear training data, while synthetic supervision depends on imperfect depth assumptions. The paper trains a DNN unsupervisedly on real hazy images by minimizing DCP energy, achieving state-of-the-art outdoor performance and improving classical DCP.
Problem
Matched clear and hazy images are difficult to obtain, so supervised methods use synthetic datasets whose depth assumptions may be inaccurate for outdoor scenes.
Method
A CAN-based DNN is trained from scratch on real-world hazy images only by minimizing the Dark Channel Prior energy function.
Results
Deep-DCP achieves state-of-the-art outdoor dehazing and approximately 6.5dB higher outdoor PSNR than classical DCP.
Takeaways & Limitations
The network improves DCP through additional regularization from its architecture and learning process while eliminating synthetic training sets and per-image optimization.
Abstract
from arXiv · showhide
Single image dehazing is a critical stage in many modern-day autonomous vision applications. Early prior-based methods often involved a time-consuming minimization of a hand-crafted energy function. Recent learning-based approaches utilize the representational power of deep neural networks (DNNs) to learn the underlying transformation between hazy and clear images. Due to inherent limitations in collecting matching clear and hazy images, these methods resort to training on synthetic data; constructed from indoor images and corresponding depth information. This may result in a possible domain shift when treating outdoor scenes. We propose a completely unsupervised method of training via minimization of the well-known, Dark Channel Prior (DCP) energy function. Instead of feeding the network with synthetic data, we solely use real-world outdoor images and tune the network's parameters by directly minimizing the DCP. Although our "Deep DCP" technique can be regarded as a fast approximator of DCP, it actually improves its results significantly. This suggests an additional regularization obtained via the network and learning process. Experiments show that our method performs on par with large-scale supervised methods.
I. INTRODUCTION
Single-image dehazing is important for outdoor vision, but existing approaches rely on costly optimization or synthetic training pairs whose depth inaccuracies can limit outdoor applicability. Deep-DCP instead trains on real hazy images with DCP loss, improving classical DCP while avoiding per-image optimization and synthetic data.
- Motivation: Haze reduces outdoor-image contrast and detail by attenuating scene radiance and adding airlight through a transmission-controlled formation model.Recovering the clear radiance requires solving an under-constrained system.
- Motivation: Prior-based dehazing formulates inference as energy minimization, while learning-based methods require thousands of input-output examples.Dehazing is also used as preprocessing for tasks such as object detection and autonomous navigation.
- Motivation: Outdoor depth maps used to synthesize supervised training pairs are substantially less accurate than indoor depth data.Make3D and KITTI exceed 4 meters average rMSE, compared with 0.5 for NYU2.
- Proposed approach: Deep-DCP trains a CAN-based network end-to-end on real-world hazy images by minimizing the DCP energy function, producing transmission maps for reconstruction.The network is trained from scratch without external data and acts as a feed-forward DCP approximator.
- Reported contributions: Deep-DCP reports state-of-the-art outdoor results, approximately 6.5 dB higher outdoor PSNR than classical DCP, and successful sky treatment.It learns the transformation during training, replacing DCP’s separate per-image optimization with a fast test-time forward pass.
- Paper organization: The paper surveys prior-based and data-driven methods, then presents DCP loss, architecture, experiments, discussion, and conclusions.
II. RELATED WORK
Prior-based methods exploit hand-crafted image statistics but require per-image optimization and can fail in skies or produce artifacts. Learning-based methods offer fast inference yet commonly depend on synthetic supervision and imperfect depth assumptions, especially outdoors.
- Prior-based approaches: Early dehazing methods used multiple weather or polarization images, while later outdoor approaches incorporated geo-referenced terrain, urban models, depth, texture, and GIS data.
- Prior-based approaches: Other priors estimate haze using local contrast, transmission-shading independence, edge-preserving filters, color lines, or clustered haze-free colors.These methods encode different statistical assumptions about image patches or RGB distributions.
- Prior-based approaches: DCP assumes that the darkest pixel across color channels in a clear-image patch is near zero, then estimates transmission under locally constant transmission.The assumption does not hold reliably in sky regions, and refinement is needed for the coarse transmission map.
- Prior-based approaches: Prior-based methods can create excessive saturation, contrast, unrealistic colors, and sky-region errors, while requiring separate non-trivial optimization for every image.This per-image computation can be prohibitive for real-time applications.
- Data-driven approaches: CAP combines hand-crafted observations with supervised regression from synthesized hazy patches and depth maps to enable fast test-time inference.
- Data-driven approaches: CNN methods such as MSCNN, DehazeNet, AOD-Net, and GFN learn dehazing from paired or transformed inputs, with some using multi-stage or multi-scale designs.
- Data-driven approaches: Learning-based methods rely on synthetic datasets, often favoring accurate indoor depth or making outdoor depth assumptions that can yield block and halo artifacts requiring postprocessing.
III. OUR METHOD
The haze model represents each observed pixel as a transmission-weighted mixture of clear scene radiance and airlight. Because the model is under-constrained from a single hazy image, additional image priors are required.
- Method overview: The paper introduces its method through an unsupervised loss, the DCP, its CNN implementation, and a task-specific architecture.
- Haze model: The haze formation model expresses observed image I(x) as a convex linear combination of clear radiance J(x) and atmospheric light A.
- Haze model: Transmission t(x) controls the relative contribution of radiance and airlight at each pixel and depends on scene depth d(x).
- Haze model: Recovering J(x) from a single hazy image requires solving 3N equations with 4N + 3 unknowns, so prior knowledge is necessary.
B. Dark Channel Prior
The Dark Channel Prior states that small patches of haze-free outdoor images usually contain a very dark pixel in at least one color channel. This property supports transmission estimation, with sky regions requiring a special assumption and refinement.
- Prior definition: The DCP defines a statistical property in which the darkest pixel across color channels within a small haze-free outdoor patch is close to zero.
- Prior definition: Shadows, colorful objects, and naturally dark objects explain why outdoor patches commonly contain near-zero dark-channel values.Examples include vegetation, blue sea, tree trunks, and rocks.
- Transmission estimation: Assuming known airlight and locally constant transmission, minimum operations on the haze model yield a predicted coarse transmittance.
- Transmission estimation: The method uses ω = 0.95 to retain a small amount of haze, assumes I/A →1 and t̃(x) →0 in sky regions, and then refines the coarse map.
C. Soft Matting
The soft-matting formulation refines the coarse transmission map by combining an image-matting term with fidelity to the dark-channel solution.
- The haze model is treated like image matting, replacing the alpha matte with the coarse transmission map to estimate a refined transmission.
- The energy balances successful image matting against fidelity to the dark-channel solution.The trade-off is controlled by λ = 10^-4.
- The Laplacian-like matrix is constructed from local image-patch statistics for the matting-based refinement.For each patch, the formulation uses its mean, covariance, identity matrix, and smoothing parameter ε = 10^-6.
D. Implementation as a Loss Function
The DCP energy is rewritten in a tensor-friendly form and minimized directly over real hazy training images, without using clear-image labels.
- The energy is rewritten using Laplacian weights so the matting and data-fidelity terms can be represented in tensor form.
- The implementation sums over overlapping patches and pixel-pair combinations, with up to 81 combinations per 3 × 3 patch.
- The vectorized loss uses elementwise weighting over 81 pixel-pair indices for each 3 × 3 patch.W stores the vectorized weights, while T^I and T^J repeat transmission values in the required pairwise arrangements.
- Network parameters are optimized by minimizing the loss computed from predicted transmission maps over the hazy training images.The clear images are not used as labels during training.
- The loss module receives the network prediction and hazy image, then outputs the DCP energy loss.
E. Computing the Scene Radiance
The network predicts a transmission map for each new hazy image, which is then used with the haze model to recover scene radiance.
- After training, a new hazy image is processed with a forward pass to obtain its transmission map.
- The transmission map and haze formation model are used to recover the scene radiance.
- Airlight is estimated by selecting the brightest hazy-image pixel among the 0.1% brightest dark-channel pixels.The transmission lower bound is t0 = 0.1 to discourage division by values near zero.
- The network is a fully convolutional dilated residual architecture that preserves resolution while expanding receptive fields through dilated convolutions.It uses six dilated residual blocks with dilation factors increasing by powers of two.
IV. EXPERIMENTAL RESULTS
The experiments use RESIDE indoor and outdoor synthetic benchmarks plus HSTS, including both synthetic and real-world outdoor images, with PSNR/SSIM reported for selected training epochs.
- Dataset: RESIDE’s training set contains 13,990 synthetic indoor images, while SOTS-indoor and SOTS-outdoor each contain 500 synthetic test images.
- Evaluation: Table I reports quantitative PSNR and SSIM results, with higher values indicating better performance.Results use epoch 27 for SOTS-outdoor and HSTS, and epoch 30 for SOTS-indoor.
- Dataset: HSTS contains 20 outdoor images, split between 10 synthetic images with known ground truth and 10 real-world images.
- Dataset: The real-world RTTS collection is augmented to produce 17,288 training images.The total is obtained as 4,322 × 4.
C. Quantitative Evaluation
On SOTS-outdoor and HSTS, Deep-DCP achieves the strongest reported quantitative results among the compared methods, while indoor performance is lower than several alternatives. Qualitative comparisons show preserved colors and contrast, though sky coloration can vary because training is unsupervised.
- Deep-DCP obtains the highest PSNR and SSIM on SOTS-outdoor and the highest SSIM on HSTS among the compared methods.The comparisons include prior-based and data-driven approaches.
- Training on real-world outdoor images helps Deep-DCP outperform methods concentrated on synthetic indoor images when addressing outdoor data.The paper attributes competing methods’ weaker outdoor results partly to domain shift and coarse synthetic depth maps.
- On SOTS-indoor, Deep-DCP performs favorably but scores lower than other data-driven methods and DCP.The authors describe this as a tradeoff from training on outdoor images.
- Deep-DCP maintains true colors and contrast more often than competing methods, while prior-based methods tend to exaggerate sky regions.Compared with deep-learning methods, MSCNN and GFN produce more contrast-enhanced images; Deep-DCP can sometimes alter sky color.
- Deep-DCP’s unsupervised training means it does not observe clear images, and its outputs can therefore retain haze or change sky colors.The real-world examples compare outputs after different training durations.
E. Runtime Comparison
Deep-DCP replaces per-image explicit DCP optimization with feed-forward inference and reaches substantially faster runtime than slow-DCP. It performs comparably to fast-DCP while providing better visual quality and higher PSNR.
- Deep-DCP inference combines a network forward-pass for the transmission map with image reconstruction using Equation 9.The forward-pass runs in TensorFlow and reconstruction in Numpy.
- Deep-DCP feed-forward inference is 30× faster on GPU and 12× faster on CPU than slow-DCP’s explicit optimization.The comparison averages runtimes over 500 SOTS-outdoor images.
- Deep-DCP performs on par with fast-DCP while producing much better visual quality and a ∼9.5 dB increase in PSNR.It is faster than fast-DCP on GPU but slower on CPU.
V. DISCUSSION
Deep-DCP does not simply reproduce DCP: its training trajectory requires early stopping because minimizing the loss further can reduce visual and quantitative quality. The resulting method improves DCP and achieves strong outdoor performance while avoiding synthetic training sets.
- V. DISCUSSION: Deep-DCP learns a corpus-level universal solution that increasingly resembles per-image DCP as training progresses.Unlike DCP, which operates on one image at a time, the network optimizes across the image corpus.
- V. DISCUSSION: Early stopping is necessary because reaching the loss minimum is not always beneficial for visual or quantitative results.The authors select a model using PSNR and SSIM on a supervised validation subset, which rise and then decline as loss decreases.
- V. DISCUSSION: ∼6.5dB outdoor PSNR improvement over classical DCP demonstrates that Deep-DCP substantially improves its underlying prior.The authors attribute this improvement to effective regularization from the network and learning process.
- V. DISCUSSION: The method delivers state-of-the-art outdoor dehazing performance while eliminating the need for synthetic training sets.The conclusion identifies DCP-based unsupervised training as the basis for both outcomes.