A Modified Retinex Algorithm based on Wavelet Transformation

A modi?ed Retinex Algorithm based on Wavelet Transformation

Ming Hao

Sichuan University of Science&Engineering Dept.of Electronic Engineering

IN-F Zigong,Sichuan643000,P.R.China haomingeleven@https://www.360docs.net/doc/197745651.html,

Xingbo Sun

Sichuan University of Science&Engineering Dept.of Electronic Engineering

Zigong,Sichuan643000,P.R.China

sxb741021@https://www.360docs.net/doc/197745651.html,

Abstract

Retinex method mainly consists of two steps:estimation and normalization of illumination.The illumination is es-timated as a smooth version of input image using low-pass ?lters.Some high-frequency components of image will in-evitably be lost in the?ltering processing,and images will lose details and information,correspondingly.In this pa-per,we propose a novel Retinex method applying concepts of wavelet transform,which decrease the damage in the de-tail information and preserve the edges and location details of images ef?ciently.As the illumination is low-frequency component compared with the re?ectance,the illumination is estimated just using the coarse component in the wavelet expansion of the image.The experimental results shows that,compared with traditional Retinex Algorithm,the re-sult images using modi?ed Retinex Algorithm have greater entropy and average gradient,as well as smaller standard variance,which indicating that the images contain more de-tails and information,and have more uniform illumination.

1.Introduction

The Retinex theory motivated by Land[1]is based on the physical imaging model,in which an image I(x,y)is regarded as the product I(x,y)=R(x,y)·L(x,y)where R(x,y)is the re?ectance and L(x,y)is the illumination at each pixel(x,y).Here,the nature of L(x,y)is determined by the illumination source,whereas R(x,y)is determined by the characteristics of the imaged objects.Therefore,the illumination normalization can be achieved by estimating the illumination L and then dividing the image I by it.How-ever,it is impossible to estimate L from I,unless something else is known about either L or R.Hence,various assump-tions and simpli?cations about L,or R,or both are pro-posed to solve this problem[2].A common assumption is that edges in the scene are edges in the re?ectance,while illumination spatially changes slowly in the scene.Thus, in most Retinex methods,the re?ectance R is estimated as the ratio of the image I and its smooth version which serves as the estimate of the illumination L,and many smoothing ?lters to estimate the illumination have been proposed.Sin-gle scale Retinex(SSR),the latest version of Lands Retinex that was implemented and tested by Jobson et al.[3],em-ployed a simple linear?lter with Gaussian kernel.How-ever,strong shadows cast from a direct light source violate the assumption that the illumination slowly varies,and halo effects are often visible at large illumination discontinuities in I.To solve this problem,Jobson extended SSR to multi scale Retinex(MSR)[4]by combining several low-pass?l-tered copies of the logarithm of I using different cut-off frequencies for each low-pass?lter.Recently,Gross and Brajovie[2]introduced an anisotropic?lter to reduce these halo effects to some extent.More recently,self-quotient image(SQI)[5][6]has been proposed with impressive im-provement of performance for illumination problem.SQI employs the weighed Gaussian?lter in which the convolu-tion region is divided into two sub-regions with respect to a threshold,and separate values of weights are applied in each sub-region.These Retinex methods have common ad-vantages that they do not require training images and has relatively low computational complexity.

Retinex method mainly consists of two steps:estimation and normalization of illumination.As mentioned above,il-lumination L is estimated as a smooth version of input im-age I.Once the estimation is completed,illumination is normalized by taking the difference between the logarithms of the input image and the estimated illumination.Smooth-ing should especially be carried out among pixels which have homogeneous illumination because illumination dis-continuities such as cast shadow violate the assumption that the illumination slowly varies.This robustness requirement implies that the estimated illumination must be discontin-uous at locations where the input image I has strong dis-continuities of intensity.However,these methods lack in adaptability which can preserve discontinuities ef?ciently.

2010 Second International Conference on MultiMedia and Information Technology

As a result,they still cannot completely remove cast shad-ows,and they ultimately cannot avoid the damage in the detail information of images.

In this paper,we propose a novel Retinex method ap-plying concepts of wavelet transform,which decrease the damage in the detail information and preserve the edges and location details of images.Our method is mainly based on the point that illumination L is of lower frequency visa the re?ectance R.Only the coarse component in the wavelet expansion of the image be processed using Retinex method, and the enhanced image is obtained through reverse trans-form using the new coarse component and other three com-ponents in the wavelet expansion of the images.

2.Retinx Theory

Retinx theory mainly compensate for the impact of im-ages affected by illumination.Based on Retinx image for-mation model:

S(x,y)=R(x,y)·L(x,y)(1)

An image is piexl-by-piexl product of the ambient illumina-tion and the scene re?ectance.As the ambient illumination is independent of object itself,only the scene re?ectance re-?ect the inhesion characteristic of object itself.illumination is a kind of low-frequency image information which is slow-changing,and re?ectance contains the most high-frequency detailed image information.The Retinx theory deal with the problem of separating the two quantities:?rst estimat-ing the illumination and then obtaining the re?ectance by division.

From the mathematical point of viewbased on logarith-mic domaim,complex multiplication can be converted to a simple addition operation.So the?rst step taken by most Retinx Algorithms is the conversion of the given image into Logarithmic domaim.As shown in formula2:

log S=log R+log L(2)

Therefore,as shown in formula3,the logarithm of the re-?ectance can be obtained by the logarithm of the image sub-tract the logarithm of the illumination.

log R=log S?log L(3)

Then the re?ectance can be obtained by taken its index form,as shown in formula4The re?ectance is inherent properties of object itself.

R=exp(log S?log L)(4)

As the illumination compared with the re?ectance is low-frequency component,so the Retinx Algorithm uses the low-pass?lter to estimate the illumination.However,as Gaussian?lter used in the?ltering process will inevitably lose some high-frequency components,image will lose some of the details and edges,resulting in image distortion.3.Modi?ed Retinx Algorithm

In this paper we propose a modi?ed Retinx Algorithm based on wavelet transform.As based on wavelet transform Gaussian?lter is used to estimate the illumination,and then re-synthesis image to obtain the enhanced image.There-fore,this algorithm can solve the shortcoming of traditional Retinx Algorithm.

3.1.Wavelet Transform

Wavelet transformation demonstrates some features shared with Fourier transformation.The Fourier transfor-mation converts the signal from spatial domain into fre-quency domain.The wavelet transform is a frequency-spatial representation,i.e.it is possible to localize each co-ef?cient spatially,what is impossible in the case of Fourier

transform.

Figure1.The structure of multi-level decom-

position

The procedure for determining the image wavelet expan-sions(two-dimensional signals)with the help of multi-level decomposition utilizing one-dimensional?lters,separately applied to the rows and columns of the image,was given by (Mallat,1998).There are four components in the wavelet expansion of the image:so-called coarse component(LL) and three details,named as vertical-(LH),horizontal-(HL) and diagonal(HH)detail.The characteristic feature of wavelet transformation is the possibility to continue apply-ing it to the chosen component.This is the coarse detail that is expanded most often.

Figure2.The image wavelet expansions

3.2.Modi?ed Algorithm

Based on wavelet transform,we propose a modi?ed al-gorithm.First,the image is processed by wavelet trans-form.Second,the horizontal and vertical low-frequency component LL obtained by wavelet transform is processed by Retinex algorithm.And then an enhanced image is ob-tained by inverse wavelet transform.Speci?c steps are as follows:

1)The gray-scale image is processed by wavelet trans-

form.And then four component is obtained,including horizontal and vertical low-frequency component LL, horizontal high-frequency and vertical low-frequency component HL,horizontal low-frequency and vertical high-frequency LH and horizontal and vertical com-ponent HH.

2)The horizontal and vertical low-frequency component

LL is processed by Gaussian low-pass?lter.Only the horizontal and vertical low-frequency component LL is processed by Gaussian low-pass?lter can overcome the shortcoming of traditional Retinx Algorithm that some high-frequency components are losed by?lter-ing.

3)The logarithm of the re?ectance of LL can be obtained

log R LL=log S LL?log L LL(5) 4)Then the re?ectance of LL can be obtained

R LL=exp(log S LL?log L LL)(6) 5)R LL which has been processed by Retinx Algorithm

and HL,LH,HH are processed by inverse wavelet transform.And then an enhanced image is obtained.4.Results And Discussions

To illustrate the effectiveness and superiority of the mod-i?ed Retinx Algorithm on image enhancement,the modi?ed Retinx Algorithm is compared with traditional Retinx Al-gorithm by enhancing a image with poor visibility and little visual

contrast.

Figure3.Original

image

Figure4.Image processed by traditional Ret-

inx Algorithm

Fig.3is a original image with poor visibility and lit-tle visual contrast,?gure4is the result image which has been processed by traditional Retinx Algorithm,?gure5is output image which has been processed by modi?ed Ret-inx Algorithm.It can be found,compared with the image processed by traditional Retinx Algorithm,the image pro-cessed by modi?ed Retinx Algorithm has clearer details and more uniform illumination.

To further illustrate the effectiveness and superiority of

Figure5.Image processed by modi?ed Ret-

inx Algorithm

the modi?ed Retinx Algorithm,we have compared some of the parameters of these images.

Table1.’Compare between result of traditional and mod-

i?ed Retinx Algorithm’.

entropy average gradient variance Original image 6.93240.035367.7370 Traditional Retinx7.51530.075363.9312 Modi?ed Retinx7.63580.099660.7311 It can be found from table1,compared with the im-age processed by traditional Retinx Algorithm,the entropy and average gradient of the image processed by modi?ed Retinx Algorithm is greater,and the variance of the image processed by modi?ed Retinx Algorithm is smaller.The greater entropy and average gradient indicating that the im-age contains more details and information,and the smaller variance indicating that the image has more uniform illumi-nation.

5.Conclusion

In this paper,we proposes a modi?ed Retinx Algo-rithm based on Wavelet Transformation in image enhance-ment.Because the illumination is estimated as a smooth version of input image using low-pass?lters,some high-frequency components of image will inevitably be lost and images will lose details and edges.In this paper,we propose a novel Retinex method applying concepts of wavelet trans-form,which decrease the damage in the detail information and preserve the edges and location details of images ef?-ciently.As the illumination compared with the re?ectance is low-frequency component,the illumination is estimated just using the coarse component in the wavelet expansion of the image.Therefore,the modi?ed Retinx Algorithm can overcome the shortcoming of traditional Retinx Algorithm, and get a better enhanced image.The results show that the modi?ed Retinx Algorithm is satisfying and superior over the other traditional Retinx Algorithm. Acknowledgments

This work was supported by the Scienti?c Re-search Fund of Sichuan Provincial Education Department (07ZZ017).

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