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On the Duality Between Retinex and Image Dehazing
Adrian Galdran, Aitor Alvarez-Gila, Alessandro Bria, Javier Vazquez-Corral, Marcelo Bertalmio
TL;DR
Haze reduces outdoor visibility, and the paper asks whether this dehazing problem can be directly related to Retinex. It proves that applying Retinex to inverted intensities and inverting the result gives a dehazed image, with experiments showing competitive results against current dehazing algorithms.
Problem
Haze attenuates captured radiance and reduces visibility in outdoor images, motivating methods to mitigate its effects.
Source: §1 · p. 1Method
Results
Qualitative and quantitative experiments show competitive results against current dehazing algorithms.
Source: §6 · pp. 6–7Takeaways & Limitations
Existing Retinex algorithms can be used for dehazing without modification by incorporating two intensity-inversion operations.
Source: §1 · p. 1The demonstrated relationship is complex when atmospheric light is considered, and the authors leave this for future research.
Source: §5.1 · p. 6
Abstract
from arXiv · showhide
Image dehazing deals with the removal of undesired loss of visibility in outdoor images due to the presence of fog. Retinex is a color vision model mimicking the ability of the Human Visual System to robustly discount varying illuminations when observing a scene under different spectral lighting conditions. Retinex has been widely explored in the computer vision literature for image enhancement and other related tasks. While these two problems are apparently unrelated, the goal of this work is to show that they can be connected by a simple linear relationship. Specifically, most Retinex-based algorithms have the characteristic feature of always increasing image brightness, which turns them into ideal candidates for effective image dehazing by directly applying Retinex to a hazy image whose intensities have been inverted. In this paper, we give theoretical proof that Retinex on inverted intensities is a solution to the image dehazing problem. Comprehensive qualitative and quantitative results indicate that several classical and modern implementations of Retinex can be transformed into competing image dehazing algorithms performing on pair with more complex fog removal methods, and can overcome some of the main challenges associated with this problem.
1. Introduction
The paper links haze removal and Retinex through a direct relationship, proposing that existing Retinex algorithms can be used for dehazing without modification by applying intensity inversions. It distinguishes this approach from earlier work that adapted Retinex-like methods to dehazing.
1. Introduction
- Haze attenuates captured radiance and reduces outdoor visibility; dehazing seeks to mitigate this effect for improved visualization or downstream vision performance.The particles lie in the atmosphere between the scene and observer.Source: §1 · p. 1
- Retinex began as a color-vision model for stable color perception under changing global illumination and was later used for image enhancement.In the model, color sensation is related to integrated reflectance rather than the radiance reaching the eye.Source: §1 · p. 1
- Earlier work connected Retinex to dehazing through contrast enhancement, wavelet-based chromatic enhancement, or heuristic parameter adjustments.The cited examples include multi-scale Retinex for contrast and depth estimation, single-scale Retinex after a wavelet transform, and the Stress framework.Source: §1 · p. 1
- The paper formally proves a direct relationship between Retinex and image dehazing rather than adapting Retinex-like ideas to dehazing.The authors report that the equivalence holds at both the algorithmic and modelization levels, and that transformed Retinex methods compete with current fog-removal techniques.Source: §1 · p. 1
2. Previous Approaches to Image Dehazing
Prior dehazing approaches include learned mappings from hazy to clear images and image-processing methods that estimate haze parameters using priors. The approaches differ in their data needs and assumptions about haze-free images.
2. Previous Approaches to Image Dehazing
- Learning a mapping from hazy to haze-free images requires annotated training examples, often synthesized from natural haze-free images using a haze-formation model.Learned visual features may be manually specified or automatically learned with deep convolutional neural networks.Source: §2 · p. 2
- Image-processing approaches impose priors on haze-free images to estimate transmission and atmospheric light, then invert the haze model.The Dark Channel Prior assumes most local patches in a haze-free image contain very low intensity in at least one color channel.Source: §2 · p. 2
- Dark Channel Prior methods estimate transmission by taking local minima after normalizing the haze model by atmospheric light and canceling the haze-free image term.The minima are taken over a local neighborhood.Source: §2 · p. 2
- Other haze-free-image priors include maximal local contrast or saturation and specified distributions of RGB color pixels.The paper points to comprehensive reviews of alternative methods.Source: §2 · p. 2
- Methods that recover physical scene radiance may require external information or multiple images, while one joint-estimation approach requires calibrated input and known atmospheric light.The latter assumption can result in chromatic distortions.Source: §2 · p. 2
3. The Retinex Theory of Color Vision
Retinex estimates lightness through image-intensity comparisons, with implementations varying in how they sample and aggregate local information. A key property of threshold-free Retinex is that it does not decrease brightness.
3. The Retinex Theory of Color Vision
- Retinex was introduced as a model of human color vision and later applied to image enhancement, with variational and non-local variants also proposed.The name combines “Retina” and “Cortex.”Source: §3 · pp. 2–3
- Retinex computes lightness from chains of adjacent-pixel intensity ratios along paths between image locations.The model averages estimates from N paths ending at each pixel, with a non-decreasing scaling function often chosen as a logarithm.Source: §3 · pp. 2–3
- At a brighter point along a path, the reset mechanism restarts the product of ratios, making the result equivalent to comparing against the path's maximum-intensity pixel.That maximum-intensity point acts as a local white reference.Source: §3 · p. 3
- Threshold-free Retinex increases brightness at every pixel, with lightness l(x) ≥ I(x).The paper illustrates this property with Random Spray Retinex and Multi-Scale Retinex outputs.Source: §3 · p. 3, Figure 2 · p. 3
- Retinex implementations include path-based sampling, random sprays, and kernel-based sampling that models the spray density.Kernel-based Retinex represents the sampling density with a two-dimensional kernel, with its reset mechanism implemented in the function definition.Source: §3 · p. 3
- Center-surround Retinex computes a ratio between pixel intensity and its surroundings, integrating local information through a weighted average.A Gaussian kernel was an early practical implementation of the average operator.Source: §3 · p. 3
- Multi-scale Retinex combines center-surround computations made with different standard deviations.The scaling function in the center-surround model is a logarithm.Source: §3 · p. 3
4. The Duality between Retinex and Image Dehazing
For globally white-balanced images, the paper establishes a duality between dehazing and Retinex: applying Retinex to inverted intensities and inverting the output solves the dehazing problem. The relationship also runs in the other direction, with dehazing on inverted intensities removing illumination from under-exposed images.
4. The Duality between Retinex and Image Dehazing
- DehRet decreases image intensities, matching the decrease required of a solution to the haze-formation model.The paper derives this property from the usual intensity increase of Retinex applied to the inverted image.Source: §4 · pp. 3–4
- Under the white-balance assumption A = (1, 1, 1), Theorem 4.2 establishes DehRet as a solution to the image dehazing problem.The resulting dehazed image has intensities no greater than the hazy input.Source: §4 · pp. 3–4
- Applying Retinex to inverted hazy-image intensities and inverting the result provides a dehazing operator without modifying Retinex algorithms.The proof uses the piecewise-smooth transmission field to remove transmission through Retinex.Source: §4 · p. 4
- Conversely, dehazing inverted intensities can remove non-uniform illumination, but the operator works only for under-exposed images.Figure 3 illustrates illumination computed by dehazing method and the resulting enhanced image.Source: §4 · p. 4, Figure 3 · p. 4
4.1. Dark Channel as Retinex
- The Dark Channel solution for Retinex links the denominators of the haze-inversion and Retinex equations, using identity scaling and unweighted square neighborhoods.The paper notes the need to refine transmission in this method and related techniques.Source: §4.1 · p. 5
5. Experiments and Results
The experiments apply several established Retinex methods to inverted intensities, then invert their outputs, and compare them with dehazing techniques. Qualitative and quantitative assessments report competitive performance, while noting unnatural colors in some Retinex results and a complex relationship when atmospheric light is considered.
5. Experiments and Results
- The evaluation applies SSR, MSR, RSR, LRSR, Homomorphic Filtering, and WVRI to inverted intensities and then inverts the outputs, using authors’ default parameters rather than extensive optimization.The comparison also includes established dehazing methods and histogram equalization; MSR and SSR outputs are mapped to [0, 1] with 1% saturation at each extreme.Source: §5 · p. 5
5.1. Qualitative Evaluation
- Retinex-based methods improved visibility similarly to specialized dehazing algorithms, including in distant scene areas; Homomorphic Filtering also retrieved visibility there.Figure 5 results also showed increased visibility near the bottom of the scene, though some Retinex implementations produced unnatural colors.Source: §5.1 · p. 5
- Per-channel Retinex processing is associated with disparate color recovery, and the relationship to dehazing when atmospheric light is considered remains complex and open for future research.Retinex performance under color shifts is described as reasonable.Source: §5.1 · p. 6
5.2.1 Full-Reference Quality Assessment
- Retinex-based methods were competitive with specialized dehazing methods on full-reference metrics, with DCP and WVRI on inverted intensities among the best performers.DCP and WVRI on inverted intensities achieved first and second place under two different metrics; the three top-performing methods were distributed between dehazing and Retinex-based approaches.Source: §5.2.1 · p. 6
5.2.2 No-Reference Quality Assessment
- On 500 hazy images, DEFADE had the best FADE score, while Retinex methods performed on par with dehazing techniques and RSR revealed new edges while avoiding saturation.DEFADE had been trained on the same image set; histogram equalization performed poorly compared with other methods.Source: §5.2.2 · p. 6
6. Conclusions
The paper presents a rigorous mathematical proof of a bidirectional relationship between dehazing and non-uniform illumination separation. Experiments report that Retinex-based dehazing methods achieve competitive results against current dehazing algorithms.
6. Conclusions
- Applying Retinex to an inverted image and inverting the result provides a dehazed result, and the relationship also works in the reverse direction.The paper reports the relationship holds for a wide range of Retinex methods.Source: §6 · p. 6
- Experiments showed competitive results against current dehazing algorithms; quantitative evaluation reports SSIM/CPSNR/∆E00 errors for synthetic foggy images and FADE, e, r, and σ metrics.Source: §6 · p. 7, Table 1 · p. 7, Table 2 · p. 7