Fast and robust wavelet-based dynamic range compression with local contrast enhancement

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1 Fast an robust waveet-base ynamic range compression with oca contrast enhancement Numan UNLDI a,b, Vijayan K. sari a,zia-ur Rahman a a Department of Eectrica an Computer Engineering, ODU, Norfo V, US b eronautics an Space Technoogies Institute, HHO, Yesiyurt, Istanbu, Turkey {nuna001, vasari, zrahman}@ou.eu BSTRCT In this paper, a new waveet-base ynamic range compression agorithm is propose to improve the visua quaity of igita images capture in the high ynamic range scenes with non-uniform ighting conitions. Waveet transform is use especiay for imension reuction such that a ynamic range compression with oca contrast enhancement agorithm is appie ony to the approximation coefficients which are obtaine by ow-pass fitering an own-samping the origina intensity image. The normaize approximation coefficients are transforme using a hyperboic sine curve an the contrast enhancement is reaize by tuning the magnitue of the each coefficient with respect to surrouning coefficients. The transforme coefficients are then e-normaize to their origina range. The etai coefficients are aso moifie to prevent the ege eformation. The inverse waveet transform is carrie out resuting in a ow ynamic range an contrast enhance intensity image. coor restoration process base on reationship between spectra bans an the uminance of the origina image is appie to convert the enhance intensity image back to a coor image. Keywors: Waveet base image enhancement, ynamic range compression, oca contrast enhancement. 1. INTRODUCTION It is we known that human eyes perform much better than cameras when imaging rea wor scenes, which generay presents high ynamic range that can span more than six orers of magnitue. Human eyes have about 10 8 :1 absoute range from fuy aapte ark vision to fuy aapte ighting conitions at noon on the equator. They can see about :1 range of uminance when aapte to a norma working range. This is achieve through a series of aaptive mechanisms for brightness perception. First, the size of pupi is variabe to accommoate ifferent eves of raiance from ifferent regions in a scene whie the camera aperture is fixe when capturing the scene. When staring at a highybright region in the scene, the pupi wi shrink to compress the ynamic range so that the eyes can ea with it. Secony, an more importanty, the major ynamic range compression process is taking pace via the atera processing at the retina eve [1]. Finay, the eary visua cortex is aso foun participating in some of the ynamic range processing. Currenty avaiabe imaging evices can measure ony about three orers of magnitue. In aition, image ispay evices, ike monitors an printers, aso emonstrate imite ynamic range. s a resut, images capture in high ynamic ranges scenes commony suffer from poor visibiity ue to either overexposure causing saturation or unerexposure resuting in ow contrast ark images in which some important features are ost or become har to etect by human eyes. Computer vision agorithms aso have ifficuty processing those images. To cope with the high ynamic range scenes given the imite ynamic ranges of cameras, monitors an printers, various image processing techniques which compress the ynamic range have been eveope. Some of those are goba histogram moification techniques, such as gamma ajustment, ogarithmic compression, an eves/curves methos. However, those conventiona methos generay have very imite performance such that some features may be ost uring the image processing, or some cannot be sufficienty enhance. The resuting images suffer from egrae goba an oca contrast which is reate with the visua quaity an the fine features. Visua Information Processing XVII, eite by Zia-ur Rahman, Stephen E. Reichenbach, Mark en Neife, Proc. of SPIE Vo. 6978, , (2008) X/08/$18 oi: / SPIE Digita Library -- Subscriber rchive Copy Proc. of SPIE Vo

2 mong the contrast enhancement techniques, histogram equaization (HE) an its moifie versions are commony use for enhancement. though HE works we for scenes that have uni-moa or weaky bi-moa histograms; its performance is poor for scenes with strongy bi-moa histograms. To make it work for muti-moa histograms, aaptive histogram equaization (HE) was introuce [2]. In HE which is aso cae ocaize or winowe HE, histogram equaization is performe ocay within an ajustabe size winow. HE provies oca contrast enhancement an performs better than norma HE. However, HE suffers from intensive noise enhancement in fat regions an ring artifacts at strong eges ue to its strong contrast enhancement [3]. In contrast imiting HE (CLHE [4]), unesire noise ampification is reuce by seecting the cipping eve of the histogram an controing oca contrast enhancement. Boun artifacts in CLHE can be eiminate by performing backgroun subtraction [5]. Muti-scae HE (MHE)[6] is the most avance variation of HE. Unike traitiona singe scae techniques, waveet-base MHE is capabe of moifying/enhancing the image components aaptivey base on their spatia-frequency properties. Those avance HE variations generay have very strong contrast enhancement, which is especiay usefu in feature extraction appications ike meica imaging for iagnosis. They are not commony use in processing coor images probaby because their strong contrast enhancement may ea to excessive noise or artifacts an cause the image to ook unnatura. In orer to obtain better performance, more avance image enhancement techniques to compress the ynamic range maintaining or even boosting oca contrast have been eveope. Retinex base agorithms are exampes of such techniques base on E. Lan s theory [7] of human visua perception of ightness an coor. Since the introuction of Retinex, severa variants [8]-[11] on the origina metho have been eveope mainy to improve the computationa efficiency whie preserving the basic principes. MSRCR (Mutiscae Retinex with Coor Restoration) [12]-[14], propose by Jobson, et a, a wiey cite image processing technique which is a Retinex base agorithm. MSRCR uses ogarithmic compression an spatia convoution to impement the iea of Retinex. It aims to synthesize oca contrast enhancement, coor constancy, an ightness/coor renition for igita coor image enhancement. MSRCR works we with a arge variety of images. INDNE (aptive an Integrate Neighborhoo Depenent pproach for Noninear Enhancement) [15] an IRME (Iuminance-Refectance Moe for Noninear Enhancement) [16] are two other nove techniques propose by Li et a. They are both constitute by two separate processes viz. aaptive uminance enhancement an aaptive contrast enhancement to provie more fexibiity an better contro over image enhancement. INDNE prouces better resuts for most natura images when compare to IRME, whie IRME is the fastest of the a retinex-base agorithms incuing INDNE an it was primariy esigne for rea-time vieo enhancement on PC patforms. In this paper, we introuce a nove fast an robust Waveet-base Dynamic Range Compression with Loca Contrast Enhancement (WDRC) agorithm base on the principes introuce by MSRCR an INDNE to improve the visibiity of igita images capture uner non-uniform ighting conitions. The scheme of the propose agorithm is shown in Fig.1. We give the etais of the propose agorithm in section 2. The experimenta resuts an iscussion are presente in sections 3, an the concusions in section LGORITHM The propose enhancement agorithm consists of four main stages, three of which are appie in iscrete waveet omain: 1. Luminance enhancement via ynamic range compression of approximation coefficients. 2. Loca contrast enhancement using average uminance information of neighboring pixes which is inherite to approximation coefficients 3. Detai coefficients moification. 4. Coor restoration. For input coor images, the intensity image I(x, is obtaine by empoying the foowing transformation: I (x, = max[r(x,, g(x,, b(x, ] (1) where r, g an b are the RGB components of coor image in the RGB coor space. This is the efinition of the vaue (V) component in HSV coor space. The enhancement agorithm is appie on this intensity image. Proc. of SPIE Vo

3 Input Image Intensity Image pproximation Coeff.- Detai Coef.-D LPF Normaize Coeff.- new Moifie Detai Coeff. Dnew Mappe Coef.-Ã Loca verage f f Loca Contrast Enhancement Enhance Intensity Image De-normaize Coeff.-new Output Coor Image Fig. 1. The propose agorithm 2.1 Dynamic Range Compression ccoring to orthonorma waveet transform, the uminance vaues are ecompose by Eq. (2): I( x, = + a z J, j J z Φ J, v j, ( x, + Ψ v j, j J z ( x, + h j, Ψ j J z h j, j, ( x, Ψ j, ( x, (2) where a J, are the approximation coefficients at scae J with corresponing scaing functions Φ J, ( x,, an j, are the etai coefficients at each scae with corresponing waveet functions Ψ j, ( x,. Whie the first term on the right-han sie of (2) represents the coarse-scae approximation to I ( x,, the secon, the thir, an the fourth terms represent the etai components in horizonta, vertica an iagona irections, respectivey. Base on some assumptions about image formation an human vision behavior, the image intensity I(x, can be simpifie as a prouct of the refectance R(x, an the iuminance L(x, at each point (x,. The iuminance L is assume to be containing the ow frequency component of the image whie the refectance R mainy incues the high frequency component, since R generay varies much faster than L oes in most parts of an image with a few exceptions, ike shaow bounaries. In most cases the iuminance has severa orers arger ynamic range when compare to Proc. of SPIE Vo

4 refectance. By compressing ony the ynamic range of the iuminance an preserving the refectance, ynamic range compression of the image can be achieve. ccurate estimation of iuminance, which is ifficut to be etermine, can be approximate by ow pass fitering the image. The waveet transform with which any image can be expane as a sum of its approximate image at some scae J aong with corresponing etai components at scae J an at finer scaes is use especiay for imension reuction in our agorithm. Besies, we use the approximate image represente by normaize approximation coefficients, which can be obtaine by ow pass fitering an own-samping the origina image in the waveet transform, to estimate the ownsampe version of the iuminance. raise hyperboic sine function given in (4) which maps the normaize range [0,1] of a J, to the same range is use for compressing the ynamic range represente by the coefficients. We have chosen hyperboic sine function for ynamic range compression since the function is two-sie that aows us to pu-up sma coefficients an pu-own arge coefficients to some extent at the same time. This is consistent with the human visua system that has mechanisms through which it can aapt itsef aowing goo visua iscrimination in a ighting conitions. The normaize an compresse coefficients at eve J can be obtaine by a r sinh( a J, ) + 5 J, = (3) 10 where a J, are normaize coefficients given by (4) an r is the curvature parameter which ajusts the shape of the hyperboic sine function. aj, a J, = (4) J In Fig 2. the hyperboic sine function with ifferent curvature parameters is shown. To ease the comparison, ientity transformation (r=0, a J, = a J, ) is aso given. For vaues of r ess than 1, sma pixe vaues are pue up much more than arge pixe vaues are pue own, an for vaues greater than 1 vice versa. We etermine r=0.5 as a efaut vaue, which provies goo range compression especiay in shaowe scenes. We foun the greater vaues of r usefu for bright scenes with no ark regions an for scientific appications such as meica image enhancement especiay when the region of interest is too bright. moifie sinh(x) Fig. 2. Raise hyperboic sine function fter appying the mapping operator to the coefficients, if we e-normaize the new coefficients an take the inverse waveet transform, the resut wi show a compresse ynamic range with a significant oss of contrast. The new image wi ook washe-out. Such an exampe is shown in Fig 3.(b) Thus, we nee to increase the oca contrast to get a high visua quaity. Proc. of SPIE Vo

5 '4 Fig. 3. Resuts of the propose agorithm at each step Top, eft: Origina image; right: Range compresse image; bottom eft: Loca contrast enhance image; right: Image with moifie etai coefficients. 2.2 Loca Contrast Enhancement The goba contrast enhancement techniques which moify the histogram of the image by stretching it or boosting the bright pixes an ecreasing the vaue of ark pixes gobay can not generay prouce satisfying resuts. Those methos have imite performance in enhancing fine etais especiay when there are sma uminance ifferences between ajacent pixes. Therefore, the surrouning pixes shou be taken into account when one pixe is being processe. We use the centre/surroun ratio introuce by Lan [8], an efficienty moifie by Rahman et. a.[13] to achieve the compresse ynamic range preserving or even enhancing the oca contrast. The center/surroun ratio is use as a variabe gain matrix, by simpy mutipying with the moifie coefficients when the ratio is ess than 1 an by appying inverse of this matrix as a power transform to the coefficients when the ratio is greater than 1. In such a way, the resut images wi not suffer either hao artifacts, or saturation cause by over-enhancement. In this metho, epening on their surrouning pixe intensity, pixes with the same uminance can have ifferent outputs. When surroune by arker or brighter pixes, the uminance of the pixe being processe (the center pixe) wi be booste or owere respectivey. In such a way, image contrast an fine etais can be sufficienty enhance whie ynamic range expansion can be controe without egraing image quaity. The oca average image represente by moifie approximation coefficients is obtaine by fitering the normaize coefficients obtaine from the waveet ecomposition of the origina image with a Gaussian kerne. We have chosen Gaussian kerne ike in MSRCR which prove to give goo resuts over a wie range of space constants. The stanar eviation (aso cae scae or space constant) of the 2D Gaussian istribution etermines the size of the surroun. The 2D Gaussian function G(x, is given by, 2 2 ( ) x + y 2 (, ) = σ G x y κe (5) where κ is etermine by Proc. of SPIE Vo

6 x y G ( x, = 1 (6) an σ is the surroun space constant. Surrouning intensity information is obtaine by 2D convoution of (5) with image, whose eements are the normaize approximation coefficients a J, given by (4) such as M 1 N 1 f ( x, = ( x, G( x, = ( x', y') G( x x', y y') (7) x' = 0 y' = 0 The ratio between an f etermines whether the center coefficient is higher than the average surrouning intensity or not. If it is higher, the corresponing coefficient wi be increase, otherwise it wi be owere. s state above, the size of the surrouning which has a irect effect on the contrast enhancement resut is controe by the space constant σ of the surroun function G. The oca contrast enhancement is carrie out as foows: J. R * 255* 2 = 1 ( ) R * 255* 2 J for R < 1 new (8) for R > 1 where, R is the centre/surroun ratio, is the matrix whose eements are the output of the hyperboic sine function given by (3) an new is the new coefficient matrix which wi repace the approximation coefficients a J, obtaine by the ecomposition of the origina image at eve J. R is given by R = (9) f with the parameter which is an enhancement strength constant with a efaut vaue of 1. It can be tune for an optima resut. When it is greater than 1, the resut contrast wi be high with a cost of increase noise. When it is ess than 1, the resuting image wi have ess contrast with ess noise. In Fig.3(c) the resut of the contrast enhancement agorithm after taking the inverse waveet transform of the moifie coefficients an appying a inear coor restoration process is given. In Fig.4, 1D comparison of the range compression an the contrast enhancement resuts are shown. The curves show the pixe vaues in the mie row of the origina, ynamic range compresse an enhance intensity images, respectivey IOU IOU 60 Fig. 4. Resut of the propose agorithm. Intensity variations aong the ine passing through the center of an image. The contrast enhancement transformation given in (8) consists of two ifferent equations: The first one is an aaptive mutipicative gain an it is use when the centre/surroun ratio is ess than 1. Mutipication with such a number wi ower the coefficients. The secon equation is aaptive power transform with ifferent vaues for each coefficient an is vai when the center coefficient is greater than the oca average. Since the coefficients are normaize to [0,1] an the Proc. of SPIE Vo

7 term ( R 1 <1 ) is aways satisfie, the power transform given in (8) wi aways prouce a higher vaue but ess than or equa to 1. This prevents saturation an hao errors that wou occur if the first equation in (8) was use instea. The secon equation cou be use instea of the first one as in INDNE, but it wou not provie as much contrast enhancement as the mutipicative gain. Using a singe scae is incapabe of simutaneousy proviing sufficient ynamic range compression an tona renition[13]-[14], therefore ifferent scae constants (e.g. sma, meium, arge) of the Gaussian kerne can be use to gather surroun information an the contrast enhancement process given by (5)-(9) is repeate for each scae. The fina output is a inear combination of the new coefficients cacuate using these mutipe scaes. This nees three times more cacuations compare to using ony one scae. Instea of using three convoutions, the same resut can be approximate using a specificay esigne Gaussian kerne. Such kerne which we name Combine-scae Gaussian (CG) is a inear combination of three kernes with three ifferent scaes. with W k 2 2 ( x y ) σ G( x, = W k k κ k e (10) k= 1 1 =. The CG kerne obtaine using three scaes (2, 40, 120) is shown in Fig.5. 3 O OU Fig. 5. Spatia form of CG operator. Left: 3-D representation, right: Cross-section to iustrate the surroun (Both representation are istorte to visuaize the surroun) 2.3 Detai Coefficient Moification Contrast enhancement through etai coefficient moification is a we-estabishe technique an a arge variety of appication can be seen in iterature [17]-[18]. In such a contrast enhancement technique generay sma vaue coefficients, which aso represent the noise content are weakene or eft untouche whie arge vaue ones are strengthene by inear or non-inear curve mapping operators. Determining the thresho that separates the sma an arge coefficients is sti merit of interest. Moifying these coefficients is very susceptibe an may ea to unesire noise magnification or unpreictabe ege eterioration such as jaggy eges. Thus, the inverse waveet transform with the moifie approximation coefficients wi suffer from ege eterioration if the etai coefficient is not moifie in an appropriate way. To meet this requirement, the etai coefficients are moifie using the ratio between the enhance an origina approximation coefficients. This ratio is appie as an aaptive gain mask such as: D = h new h v new v new new = D D new = D D new D (11) where an new are the origina an enhance approximation coefficients at eve 1, respectivey. D, D, D are h v the etai coefficient matrices for horizonta, vertica an iagona etais at eve 1, an D, D, D are new h new v new Proc. of SPIE Vo

8 the corresponing moifie matrices, respectivey. If the waveet ecomposition is carrie out for more than one eve, equation (12) is use instea. D h new, j h v new, j v new, j new, j = D j D new, j = D j D new, j = D j (12) j j j with j=j,j-1,.2,1. Here j an new, j is etermine by 1 eve reconstruction using j+1 an D j+ 1 for j ; new, j+1 an Dnew, j+ 1 for new, j at each step. ppying the waveet agorithm more than 1 step wi be computationa inefficient. In our impementations 1 eve ecomposition for iumination estimation yiee fast resuts with high visua quaity. In Fig.3(c) () resut obtaine without an with etai coefficient moification is given. The nee for this step is more apparent in the exampes given in Fig. 6. Fig 6. Exampes showing the effect of etai moification. Origina images eft, enhancement without an with etai coefficient moification mie an right images, respectivey. 2.4 Coor Restoration Coor restoration process is straight forwar. For converting the enhance intensity image to RGB coor image, the ratio between origina an enhance intensity image aong with the chromatic information of the origina image are empoye. The RGB vaues ( r enh, genh, benh ) of the restore coor image are obtaine by, Ienh Ienh Ienh renh = r genh = g benh = b (13) I I I Here I is given by (1) an I enh is the resuting enhance intensity image erive from the inverse waveet transform of the moifie coefficients. Thus, the coor consistency between the origina coor image an the enhance coor image can be achieve. 3. RESULTS ND DISCUSSION The propose agorithm has been appie to process numerous coor images capture uner varying ighting conitions. From our observations we can concue that the agorithm is capabe of removing shaes in the high ynamic range images whie preserving or even enhancing the oca contrast we. Besies, the prouce coors are consistent with the coors of the origina images. In this section more resuts obtaine by the propose agorithm to show its abiity in Proc. of SPIE Vo

9 proucing ynamic range compresse images preserving the oca contrast an goo renition wi be given. Exampes given in Fig. 7. show that the propose enhancement agorithm is capabe of removing the shaes an proviing better resuts in terms of visua quaity. The oca contrast is preserve, even improve in a these exampes. The processe images are sharper than the origina ones. Fig 8. shows two exampes of the rea-wor scenes that vioate the gray-wor assumption. though the scenes are ominate by one coor channe (mosty-green), the propose enhancement agorithm can provie resuts that have very appeaing coor renition an the resuts o not suffer from graying-out of the uniform areas. 2v Fig 7. Image enhancement resuts by propose agorithm. Top: Origina images, bottom: Enhance Images 4 H 4 :. 48 fj4 Fig 8. Image enhancement resuts by propose agorithm. Left: Origina images, right: Enhance Images Proc. of SPIE Vo

10 Fig 9. Image enhancement resuts by propose agorithm. Left: Origina images, right: Enhance Images Two exampes for scenes that have very rich coor mixture are given in Fig 9. The iumination is aso baance in both scenes. Both enhancement resuts preserve the coor information we, proviing sharper resuts. The backgroun that has ow iumination in the first image becomes more visibe with reaistic an baance coors in the enhance image. Both enhance images are brighter than the origina ones. The main avantage of the propose agorithm is its spee. Since the convoutions which take most of the processing time are ony appie to approximation coefficients, the processing time is reuce to amost haf the processing time require for IRME which is known to be esigne for rea time vieo processing on PC patforms. The propose agorithm successfuy accompishes coor renition, ynamic range compression with oca contrast enhancement simutaneousy except for some pathoogica scenes that have very strong spectra characteristics in a singe ban. Two exampes for such scenes are given in Fig 10. though the enhance resuts are sharper than the origina images an the coors of the enhance resuts are consistent with the coors in the origina images, they are not the coors observe in rea-ife scenes. This rawback of the propose agorithm is share with INDNE an IRME as we, since these agorithms, ike the propose one, expoit ony the uminance component of the image to be enhance. The pathoogy in the origina image is inherite to the enhance image via inear coor restoration process. The agorithm is not coor constant. Coor constancy impies the observe scene is inepenent of the spectra characteristics of the iumination to some extent. The observe scenes in given exampes wou et the rea-wor coors be more visibe. 4. CONCLUSIONS waveet base fast image enhancement agorithm which provies ynamic range compression preserving the oca contrast an tona renition has been eveope to improve the visua quaity of the igita images. It is aso a goo caniate for rea time vieo processing appications. though the coors of the enhance images prouce by the Proc. of SPIE Vo

11 propose agorithm are consistent with the coors of the origina image, the propose agorithm fais to prouce coor constant resuts for some pathoogica scenes that have very strong spectra characteristics in a singe ban. The inear coor restoration process is the main reason for this rawback. Hence, a ifferent approach is require for the fina coor restoration process. new version of the propose agorithm which eas with this issue is presenty being eveope..1 I' iz Fig 12. Enhancement resuts of the Pathoogica images. Left: Origina images, right: Enhance Images REFERENCES [1] H. Kob, How the retina works, merican Scientist, Vo 91, No. 1, 2003, pp [2] S. M. Pizer, J. B. Zimmerman, an E. Staab, aptive grey eve assignment in CT scanispay, Journa of Computer ssistant Tomography, vo. 8, pp ,1984. [3] J. B. Zimmerman, S. B. Cousins, K. M. Hartze, M. E. Frisse, an M. G. Kahn, psychophysica comparison of two methos for aaptive histogram equaization, Journa of Digita Imaging, vo. 2, pp (1989). [4] S. M. Pizer an E. P. mburn, aptive histogram equaization an its variations, Computer Vision, Graphics, an Image Processing, vo. 39, pp ,1987. [5] K. Rehm an W. J. Daas, rtifact suppression in igita chest raiographs enhance with aaptive histogram equaization, SPIE: Meica Imaging III,1989. [6] Y. Jin, L. M. Faya, an. F. Laine, Contrast enhancement by mutiscae aaptive histogram equaization, Proc. SPIE, vo. 4478, pp , [7] E. Lan an J. McCann, Lightness an Retinex theory, Journa of the Optica Society of merica, vo.61, pp. 1-11, [8] E. Lan, n aternative technique for the computation of the esignator in the Retinex theory of coor vision, Proc. of the Nationa caemy of Science US, vo. 83, pp , [9] J. McCann, Lessons earne from monrians appie to rea images an coor gamuts, Proc. IS&T/SID Seventh Coor Imaging Conference, pp. 1-8, Proc. of SPIE Vo

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