mproved wavelet transform algorithm for single image dehazing
hu Rong ∗, Wang Li Junchool of Computer Science, Qufu Normal University, Rizhao, Shandong 276826, China
r t i c l e i n f o
rticle history:eceived 28 June 2013ccepted 15 December 2013vailable online xxx
a b s t r a c t
Image dehazing to single color image remains a longstanding challenge in image processing. Because oflight scattered by the suspended particles in the atmosphere, photographs taken in the foggy day lookgray and lack visibility. How to improve the capacity for the clear image’s structures and colors. Towardthis objective, we explored the improved Wavelet Transform algorithm on image haze removal. Here, we
propose a improved algorithm on image haze removal. Our method is to first apply wavelet transform toimage dehazing, and then use Retinex (SSR) algorithm to enhance the color performance and to improvethe color effect after applying wavelet transform to image dehazing, and finally get the desired haze-removed image. Experimental results show that this algorithm is effective and practical, and the effectis ideal.
ingle scale retinex
. Introduction
Haze, a common atmospheric phenomenon in our life, is lightist caused by particles such as water or dust in the air scattering
nd absorbing the light reflected from an object surface before iteaches our eyes. The haze can also appear in images when tak-ng long distant outdoor photography under this circumstance: themage will lose contrast and color fidelity, and the objects in distantegion become faint. For most photographers, the quality of theseegraded images is unacceptable. Hence, the technique for recov-ring a haze-free image from a real photograph is highly desired.aze removal is a challenging problem since the degree of the hazeepends on the distance from the object to the camera; however,
n most cases, depth information is unknown.To date, several single image based methods [1–5] have been
ntroduced. Fattal [2] assumed every patch has uniform reflectance,nd that the appearance of the pixels within the patch can bexpressed in terms of shading and transmission. He considered thehading and transmission signals to be unrelated and used inde-endent component analysis to estimate the appearance of eachatch. The method works quite well for haze, but has difficulty withcenes involving fog, as the magnitude of the surface reflectance isuch smaller than that of the air light when the fog is suitably
Please cite this article in press as: Z. Rong, W.L. Jun, Improved wavelLight Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.07
hick.Tan [3] developed a system for estimating depth from a single
eather degraded input image. Motivated by the fact that contrast
is reduced in a foggy image, Tan divided the image I into a seriesof small patches and postulated that the corresponding patch in Jshould have a higher contrast (where contrast was quantified asthe sum of local image gradients). He employed a Markov RandomField to incorporate the prior that neighboring pixels should havesimilar transmission values ti. The method tends to produce overenhanced images in practice.
He et al. [4] employed a model which assumed every local patchin the enhanced image should have at least one color componentnear zero. In other words, the work assumed most scenes are madeup of either dark or colorful objects. The transmission ti of eachpatch was estimated as the minimum color component within thatpatch. Instead of using an MRF, the work employed a soft mattingalgorithm to ensure that neighboring pixels had similar transmis-sion values.
Tarel [5] proposes a bilateral filter to replace the optimizationmethod, which improves the efficiency of algorithm and can beused in real-time. But the defogging result is not so good whenthere are discontinuous in the depth of scene. The haze among gapscannot be removed.
In this paper, we propose a improved algorithm on image hazeremoval. Our method is to first apply wavelet transform to imagedehazing, and then use Retinex (SSR) algorithm to enhance thecolor performance and to improve the color effect after applyingwavelet transform to image dehazing, and finally get the desiredhaze-removed image.
et transform algorithm for single image dehazing, Optik - Int. J.7
2. Optical models and properties
The image captured by a camera can be modeled as being com-posed of two components: the direct transmission of light from the
bject and the transmission due to scattering by the particles of theedium, referred to here as the air light. Mathematically, this can
e written as [6]:
(X) = J(X)t(X) + (1 − t(X))A (1)
here X = (x,y) is a pixel, I(X) is the observed image intensity, J(X)s the scene radiance, A is the air light and t(X) is the transmission.he transmission is based on the Lambert–Beer law for transpar-nt objects, which states that light traveling through a transparentaterial will be attenuated exponentially [6]:
(X) = exp(−ˇd(X)) (2)
ere, d(X) is the scene depth and ̌ is the attenuation coefficientue to scattering in the medium. Note that the observed image, I(X),cene radiance, J(X), and air light, A, are all vectors in �3 with onentensity value per color channel. The attenuation coefficient dueo scattering, ˇ, is not a function of the color channel and therefore,or a given pixel, the transmission is constant over all three colorhannels.
. Wavelet transform
Since its emergence 20 years ago, the wavelet transformas been exploited with great success across the gamut of sig-al processing applications, in the process, often redefining thetate-of-the-art performance. In a nutshell, the DWT replaces thenfinitely oscillating sinusoidal basis functions of the Fourier trans-orm with a set of locally oscillating basis functions called wavelets.
Wavelets are families of functions s,t(x) generated from a singlease wavelet (x) by dilations and translations [7]:
s,t(x) = 1√|s| (x − t
s
)s /= 0 (3)
here s is the dilation (scale) parameter, and t is the translationarameter. Wavelets must have mean zero, and the useful onesave localized support in both spatial and Fourier domains. Therere orthogonal and nonorthogonal wavelet sets that span L2(�).
The set of m,n(x) spans L2(�) when s = 2m, t = n.
m,n(x) = 2−m/2 (2−m(x − n)) (4)
here m is the scale index (m = 0, 1, 2,. . .), and n is the translationndex (n = . . ., −2, −1, 0, 1, 2,. . .). The discrete wavelet transform
(m,n) of a 1-D function f(x) is defined as the projection of theunction onto the wavelet set m,n(x).
(m, n) =∫ +∞
−∞dx m, n(x)f (x) (5)
Since the set of m,n(x) spans the space containing f(x), theeconstruction of function f(x) from its wavelet transform W(m,n)s possible.
(x) =∑m
∑n
′m,n(x)W(m, n) (6)
here ′m,n(x) is the normalized dual basis of m,n(x). For the
avelet expansion we use here, ′ = .The wavelet transform W(m,n) gives scale-space decomposition
f signals and, with simple modifications, images. It decomposeshe signal into different resolution scales, with m. Indexing the scalend n indexing position in the original signal space.
In practice, we are concerned with a finite length, discrete (sam-led), 1-D data set {f(k), k = 1, 2,. . .,N} and we need appropriate
Please cite this article in press as: Z. Rong, W.L. Jun, Improved wavelLight Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.07
iscrete and finite versions of the calculations involved in theavelet decomposition. In particular, there is a fixed limit to the
esolution and, therefore, a lower bound on the scale index m, whiche may take as m = 1 without loss of generality. It is useful to model
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this resolution limit by representing the data f(k) as samples of asmoothed, or low-passed, version of a continuous signal:
f (k) =∫ +∞
−∞dx�(x − k)f (x) (7)
With respect to a smoothing or scaling function a. Based onthis representation of the data, one may compute the waveletcoefficients in Eq. (5) by means of a purely discrete algorithm, asdetailed in Ref. [8]. Beyond these considerations, there is also aneffective upper limit on the scale m imposed by the finite length ofthe signal.
4. Improved image color
The general effect of retinex processing on images with regionalor global gray-world violations is a “graying out” of the image eitherin specific regions or globally. This desaturation of color can, insome cases, be severe. Therefore we can consider the desired colorcomputation as a color restoration, which should produce goodcolor rendition for images with any degree of graying. More rarely,the gray-world violations can simply produce an unexpected colordistortion. Again we seek a simple computation which also han-dles these cases. In addition we would like for the correction topreserve a reasonable degree of color constancy since that is oneof the basic motivations for the retinex. The retinex algorithm pro-posed by Land and McCann [9] and Land [10] is important becauseit was the first attempt at developing a computational model forhuman color constancy. There is widespread current interest in theretinex algorithm. The experiments that lead to the developmentof the retinex algorithm and the algorithm itself have been widelydiscussed in the literature. In spite of this, the retinex algorithm isnot generally well understood.
The retinex algorithm has been proposed for and tested on onlya limited class of viewing contexts. We will formulate the prob-lem of color constancy with respect to this simplified model of thenatural environment. An observer looks at a flat two-dimensionalsurface. The materials on the surface are matte, and they reflectthe ambient light toward a normal color observer, who has threeclasses of photoreceptors. In our formulation we describe the valuesof all functions of wavelength by their values at a discrete numberof sample wavelengths �n for n = 1, N. In particular, we characterizethe spectral power distribution of the ambient light by the functionE(�n) and the reflectance at a point x on the surface by the functionSx(�n). The light arriving at the eye is called the color signal. It isequal to the product of the spectral power distribution of the ambi-ent light and the surface reflectance function, Cx(�n) = E(�n)Sx(�n).The color signal defines all the image information that is availableat the eye to make judgments concerning the surface reflectance atdifferent points on the surface.
The observer has three photoreceptor arrays that spatially sam-ple the color signal. The response of the photoreceptors is computedfrom the color signal and the spectral sensitivity of the photo pig-ment in the kth receptor class, Rk(�n):
�xk =N∑n=1
Cx(�n)Rk(�n) =N∑n=1
E(�n)Sx(�n)Rk(�n) (8)
This equation can be written as a matrix product of the form
�x = �E�x (9)
in which the nth entry of the column vector �x is the surface
et transform algorithm for single image dehazing, Optik - Int. J.7
reflectance at �n, Sx(�n). The matrix �E is 3 × N, and its k, nth entryis E(�n)Rk(�n). The entries of the matrix depend only on the spectralpower distribution of the ambient light and the receptor spectralsensitivities. We emphasize the fact that the matrix depends only
Fig. 1. Comparison of the effects of single image dehazing.
n the spectral power distribution of the ambient light by callinghe matrix the lighting matrix.
The problem of color constancy can be expressed as the fol-owing challenge: Beginning with the spatial array of data onhe left-hand side of Eq. (9), recover the spatial array of surfaceeflectance functions on the right-hand side of the equation. Anlgorithm with perfect color constancy uses the photoreceptor val-es on the left-hand side to calculate color estimates at each pixelhat do independent of both the spectral power distribution of thembient light and the other surfaces comprise the scene.
. Our method
In recent years, many researchers focus on achieving hazeemoval by using wavelet transform for raising the image contrast.he principle is as follows: wavelet analysis has the characteris-ics of multi-resolution and local analysis, by which we can seehe mist spectrum in the image, is relatively concentrated in theow frequency region, the target image scene information is rela-ively concentrated in the high frequency region. Therefore, we canncrease the high frequency detail coefficients of the image, at theame time reduce the low-frequency approximation coefficient tochieve the purpose of the removal of clouds.
Based on these features of the mist-affected color images andavelet analysis, this article first wavelet transforms the luminance
omponent of the image into appropriate number of layers, the lowrequency domain applies unsharp masking algorithm to a simpli-ed model of atmospheric scattering to enhance image contrastffect, high-frequency domain uses nonlinear compensation func-ion of the dual-threshold algorithm to enhance contrast and to
Please cite this article in press as: Z. Rong, W.L. Jun, Improved wavelLight Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.07
mprove the clarity of details, and then inverse wavelet transformshe processed parts and HIS transforms and reconstructs primaryefogging image; because at this time the color degradation ofhe processed image has not been addressed, further integration
[
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of the single-scale Retinex (SSR) algorithm and color restorationalgorithm is needed to improve the luminance and chrominance.
6. Experiments
In order to prove the effectiveness of the proposed algorithm,and used MATLAB7.8 to simulation experiments for uptake RGBcolor mist images of 24-bit.and compare the algorithm effec-tiveness of only based on wavelet transform. Treated before andafter the image shown in Fig. 1. The experimental parameters toselect: the wavelet decomposition level n = 4, the weights are equal(ω = 1/3).
Processing time of Algorithm of this paper is 5.03 s, processingtime of the algorithm of only based on wavelet transform is 3.16 s,from Fig. 1 can be found, although the algorithm of this paperrunning time long, but better to remove the cloud of information,reduce the role of atmospheric degradation, while the brightnessof the image, the contrast of the color segments are the restorationand enhancement, richer color performance.
7. Conclusions
Our technique has been tested for a large data set of natural hazyimages. Matlab experimental show that algorithm has better visualeffects. However, the algorithm of this paper is to consider a morecomprehensive, affecting the processing speed, the next step is tocarry out research for the improvement of the processing speed ofthe algorithm.
References
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