A New Metric for Quality Assessment of Digital Images Based on Weighted-Mean Square Error 1

Transcription

1 A New Metrc for Qualty Assessment of Dgtal Images Based on Weghted-Mean Square Error Proceedngs of SPIE, vol. 4875, 2002 Kawen Zhang, Shuozhong Wang, and Xnpen Zhang School of Communcaton and Informaton Engneerng, Shangha Unversty E-mal: or Phone: or Fax: Abstract: In ths paper, an mage qualty measure, termed pxel-based correlaton weghted-mean square error (WMSE), s presented. The proposed dstorton measure depends not only on the mean square error n the dstorted mage, but also on correlaton between pxels n a predefned neghborhood. Expermental results are gven to show the advantage of the descrbed method. Keywords: mage qualty metrc, mean square error (MSE) Ths wor was supported by the Natonal Natural Scence Foundaton of Chna ( ), and Key Dscplnary Development Program of Shangha.

2 Kawen Zhang, Shuozhong Wang, and Xnpeng Zhang. Introducton Image qualty assessment s an mportant but dffcult ssue n mage processng applcatons such as compresson codng and dgtal watermarng. For a long tme, mean square error (MSE) and pea sgnal-to-nose rato (PSNR) are wdely used to measure the degree of mage dstorton because they can represent the overall gray-value error contaned n the entre mage, and are mathematcally tractable as well. In many applcatons, t s usually straghtforward to desgn systems that mnmze MSE or PSNR. MSE wors satsfactorly when the dstorton s manly caused by contamnaton of addtve nose. However the problem nherent n MSE and PSNR s that they do not tae nto account the vewng condtons and vsual senstvty wth respect to mage contents. Wth MSE or PSNR, only gray-value dfferences between correspondng pxels of the orgnal and the dstorted verson are consdered. Pxels are treated as beng ndependent of ther neghbors. Moreover, all pxels n an mage are assumed to be equally mportant. Ths, of course, s far from beng true. As a matter of fact, pxels at dfferent postons n an mage can have very dfferent effects on the human vsual system (HVS). In order to mae more comprehensve mage qualty evaluaton, and to meet dfferent requrements n a wde range of applcatons, varous qualty measures have been proposed. Wang and Bov [8,9] showed some examples n whch MSE faled to provde correct results n evaluatng qualty of certan dstorted mages. They proposed a new metrc, Q, termed the unversal mage qualty ndex, for evaluaton of mage dstorton, and showed that some MSE assessments were n apparent contradcton wth subjectve judgments, and ths could be corrected by usng Q. There are many other measures that, accordng to the technques used, can be classfed nto pxel dfference-based [-4], correlaton-based [5], edge-based, spectral-based, context-based, and HVS-based [6,7], etc. Although a great deal of efforts have been made n the past, t s stll necessary to develop new technques for objectve evaluaton of mage qualty that can easly be mplemented and are truly adapted to the HVS. In ths paper, a weghted-mse metrc that taes nto account propertes n the neghborhood of each pxel s descrbed. Experments show that the proposed qualty metrc can overcome some dffcultes encountered when usng some exstng measures, and provde a useful means to evaluate degrees of mage dstorton n applcatons such as mage restoraton and dgtal watermarng. 2. Defnton of Weghted MSE As mentoned n the prevous secton, although MSE has ts merts and s wdely accepted n mage processng research, t only measures gray-level dfference between pxels of the deal and the dstorted mages wthout consderng correlaton between the neghborng pxels. Dstorted mages wth equal MSE or PSNR may have sgnfcantly dfferent vsual qualty. A human observer always vews an mage as an entrety, rather than just a collecton of solated pxels, therefore correlaton between neghborng pxels plays a role n the subjectve judgment of mage qualty. As a result, dfferent types of sgnal processng procedures and nose nterference can cause dfferent perceptual effects, and the vsual judgment s sometmes heavly dependent upon the degree of dstorton. For example, salt-pepper nose s generally more annoyng than Gaussan nose n cases of slght degradaton. If the degradaton becomes severe, however, the stuaton may be reversed. In vew of ths, a new qualty metrc that ncorporates pxel correlaton s ntroduced as follows. Let I and Î be the orgnal and the dstorted mages respectvely, szed M N. A weghted-mse s defned as WMSE = M N MN = j= ) 2 α I(, I (, () j 2

3 A New Metrc for Qualty Assessment of Dgtal Images where α,j s a weght representng correlaton of pxels wthn a rectangular wndow W centered at (, : ) [ I (, ) ][ (, ) ˆ j I I j I ] W α, j = (2) 2 ) ) [ I (, ) ] [ (, ) ] 2 j I I j I N N w where N w s the number of pxels wthn the wndow. It s clear that MSE s a specal case of the descrbed WMSE snce WMSE approaches MSE when α,j tends to one. In calculatng α,j, the gray values are multpled wth a properly chosen taper functon β so that pxels wthn the wndow are gven dfferent mportance: w I (, = β (, I (, (3) Clearly, the value of β should decrease wth radus. As WMSE ncorporates correlaton between adjacent pxels n ts defnton, t s lely to provde qualty assessment close to human perceptve judgment. Ths has been verfed n the experments as wll be shown n the followng. 3. Characterstcs of WMSE A good objectve qualty measure should truly reflect the degree of mage dstorton due, for nstance, to blurrng, nose contamnaton, compresson codng, nadequacy of the sensor specfcaton, and so forth. It should possess the followng attrbutes: ) Conformty wth subjectve judgment: The metrc should provde a quanttatve evaluaton of mage dstorton that, n general, conforms to subjectve assessment. In other words, a vsually superor mage should have a qualty measure representng a lower dstorton. A reasonable mage qualty metrc should also be monotonc wth respect to the degree of dstorton. 2) Mathematcal tractablty: A practcally useful qualty metrc should be easy to calculate wthout tang excessve computatonal resources. 3) Consstency over dfferent mages: Ths means that an deal objectve qualty metrc should be able to provde correct assessment for all types of mages, and not to fal for any subset of mages MSE Q WMSE MSE Q WMSE MSE Q WMSE 00 MSE Q WMSE qualty= σ= Fg. Qualty metrcs vs. JPEG qualty factor Fg.2 Qualty metrcs vs. degree of blurrng 3

4 Kawen Zhang, Shuozhong Wang, and Xnpeng Zhang In order to study the propertes of WMSE, a test mage Lena was JPEG compressed at varous qualty factors, and blurred wth a 3 3 Gaussan ernel characterzed wth a standard devaton, σ. Fgs. and 2 show curves of WMSE together wth those of MSE and P=300( Q) where Q was ntroduced n [8] aganst JPEG qualty factor and σ, respectvely. It s observed from these fgures that WMSE satsfes conformty wth vsual judgment. Smlar results were obtaned by usng other test mages. From the defnton, one can see that WMSE s mathematcally tractable although t requres more computaton than the smple MSE. Snce WMSE s a modfcaton of MSE, and MSE can relably measure mage dstorton (or error) n a monotonous order, WMSE should also be monotonous wth dfferent degrees of mage dstorton. Also, snce WMSE manly depends on the dfference between pxel values of the orgnal and dstorted mages and, to a much less extent, on the pxel values of the orgnal mage, t s expected that, unle Q that depends on propertes of partcular mages, WMSE can gve consstent evaluaton to dfferent types of mage. 4. Expermental Results and Dscusson In the experments, a two dmensonal Gaussan functon (σ = 0.77) s used as the taper functon β. A number of mages ncludng Lena, Baboon and Couple were tested. These test mages were degraded n a varety of ways such as mpulsve salt-pepper nose nterference, addtve Gaussan nose, blurrng, and JPEG compresson. Fg.3 shows some of the test samples. It s confrmed from Fg.3 that dfferent sgnal manpulatons and contamnaton by dfferent nose types have dfferent effects upon the HVS. At low nose levels, salt-pepper nose s consdered more harmful than Gaussan nose, whereas at hgh nose levels, the reverse s true. The bloc effects due to JPEG codng s usually less annoyng than blurrng processng, etc. (a) the orgnal mage (b) MSE=80 Gaussan nose (c) MSE=80 salt-pepper nose (d) MSE=225 Gaussan nose (e) MSE=225 salt-pepper nose (f) MSE=8 JPEG 4

5 A New Metrc for Qualty Assessment of Dgtal Images (g) MSE=82 blurrng (h) Q=0.906 Gaussan nose () Q=0.9 salt-pepper nose Fg. 3 In order to mae comparson between WMSE and the other two metrcs, we produced two groups of degraded sample mages usng mpulsve salt-pepper nose and addtve Gaussan nose, referred to as S and G, respectvely. MSE, Q, and WMSE of each par of sample mages were calculated, denoted MSE(G ), MSE(S ), Q(G ), Q(S ), WMSE(G ), and WMSE(S ), where refers to dfferent sample mages. The levels of salt-pepper and Gaussan nose were chosen such that each par of sample mages had dentcal MSE values wth a tolerance of. Defne the followng quanttes: M ( ) = [ MSE( G ) + MSE( S )] (4) 2 Q ( ) = Q(G ) Q(S ) ( ) = WMSE(G ) WMSE(S ) (6) WMSE In Fg.4, Q s plotted aganst M. Snce all Q values are negatve n a wde range of dfferent degrees of dstorton, the metrc Q always gves the judgment that Gaussan nose s less annoyng. Ths, of course, does not conform to the experences of most observers. (5) Q vs. M WMSE vs. M Q M=5~300 Fg.4 Q vs. M WMSE M=5~300 Fg.5 WMSE vs. M 5

6 Kawen Zhang, Shuozhong Wang, and Xnpeng Zhang Fg.5 shows the relatonshp between WMSE and M, n whch one can see that, at low nose levels, salt-pepper nose s worse than Gaussan nose, whle at hgh nose level, Gaussan nose s worse. Ths ndcates the advantage of WMSE over Q and the smple MSE. The transton pont, whch s M=200 n the plot, depends on the choce of parameters such as the sze of wndow and the shape of β, and the partcular mage tested. Experments on other types of degradaton such as blurrng and JPEG codng produced smlar results. 5. Conclusons A weghted-mse qualty metrc for assessment of dstorton n dgtal mage has been proposed. It s not just based on gray-value dfferences of ndvdual pxels le the smple metrc MSE, but also on correlaton between neghborng pxels. Ths leads to a better performance than MSE as verfed n the experments carred out on mages degraded by mpulsve salt-pepper nose and addtve Gaussan nose. Satsfactory performance can be obtaned by choosng an approprate wndow sze and a proper functon β. The optmal choce may depend on specfc mages. However, WMSE s not meant to replace other mage qualty metrcs, but to provde a useful alternatve method. It s beleved that, snce the HVS s too complex to be matched wth any exstng objectve metrc, no sngle quantty at present can serve as a truly unversal measure that can gve accurate assessment to all mages n whatever applcatons. In ths area, further studes are needed. References: [] H. de Rdder, Mnowsy Metrcs as a Combnaton Rule for Dgtal Image Codng Imparments, n Human Vson, Vsual Processng, and Dgtal Dsplay III, Proc. SPIE, 666, 7-27, 992. [2] Internatonal Commsson of Illumnaton (CIE), Recommendatons on Unform Color Spaces, Color Dfference Equatons, Psychometrc Color Terms, Publcaton CIE [3] V. V. Staravotov, C. Köse, B. Sanur, Generalzed Dstance Based matchng of Nonbnary Images, Internatonal Conference on Image processng, Chcago, 998. [4] V. Dgesu, V. V. Staravotov, Dstance-based Functons for Image Comparson, Pattern Recognton Letters, 20(2), , 999. [5] A. M. Escoglu, P. S. Fsher, Image Qualty Measures and Ther Performance, IEEE Trans. Commun., 43(2), , 995. [6] Marcus J. Nadenau, Stefan Wnler, Davd Alleysson and Murat Kunt, Human Vson Models for Perceptually Optmzed Image, [7] T. Frese, C. A. Bouman, and J. P. Allebach, A Methodology for Desgnng Image Smlarty Metrcs Based on Human Vsual System Models, Tech. Rep. TR-ECE 97-2, Purdue Unversty, West Lafayette. [8] Z. Wang and A. C. Bov, A Unversal Image Qualty Index, IEEE Sgnal Processng Letters, Vol. 9, No. 3, March [9] 6