Switching Median Filter Based on Iterative Clustering Noise Detection

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1 Swtchng Medan Flter Based on Iteratve Clusterng Nose Detecton Chngakham Neeta Dev 1, Kesham Prtamdas 2 1 Deartment of Comuter Scence and Engneerng, Natonal Insttute of Technology, Manur, Inda 2 Deartment of Electroncs and Communcaton Engneerng, Natonal Insttute of Technology, Manur, Inda Abstract: In ths aer, a swtchng medan flter ncororated wth an teratve clusterng based nose detecton algorthm that effectvely restores mages corruted wth mulse nose s roosed to mrove the erformance of swtchng based medan flters. The roosed flter mechansm nvolves a nose detecton algorthm for mage restoraton that detects corruted xels by classfyng the xels nto three xel clusters teratvely. If the xel n consderaton falls under the mddle cluster n the last teraton, the xel s classfed as uncorruted otherwse t s detected as corruted. Corruted xels go through medan flterng leadng to restoraton of the nosy mage effectvely whle uncorruted xels reman unerturbed. Exermental results show that the roosed flter rovdes arecable qualty restored mages reservng mortant detals of the mage. Keywords: Imulse nose, nose model, nose detecton, mage restoraton, swtchng medan flters. 1. Introducton Images are often corruted by mulsve nose that leads to the degradaton of the qualty of the mage. Corruton by mulse nose s normally due to the errors generated n nosy sensors and communcaton channels [1], [2]. The subsequent mage rocessng oeratons such as mage comresson, mage edge detecton, mage segmentaton and object trackng etc. mght get worse erformances f the nose exsts n the nut mage wth hgh nose densty. Therefore, detectng nose and relacng the nose xel wth an arorate value s an mortant work for mage rocessng. One of the most oular mulse nose removal nonlnear flters s the medan flter [3] whch s well known for elmnatng the nose n the smooth regons n mage. But n the detal regons such as edge and texture, the medan mght smear the detal. Because the tycal medan flter s unformly aled across an mage, t s rone to modfy both nosy xels and nose-free good xels roducng a number of artfacts. Varous medan based mulse nose flters have already been roosed n [4], [5], [6], [7] to overcome mentoned roblems. 2. Related Work In the feld of mage rocessng, nonlnear medan flters have attracted much attenton of mage rocessng researchers n the ast decades. In 1995, Hwang and Haddad [4] roosed an Adatve Medan Flter. The Adatve Medan Flter (AMF) reserves the sharness of the mage whle havng a varable wndow sze for removng mulse nose whle reservng sharness. Wang and Zhang [6] roosed a rogressve swtchng medan flter (PSMF) n The PSMF ncororates a swtchng scheme. Along wth the swtchng scheme, the fltraton method rogress through several teratons to denose the corruted mage. Center weghted medan flter [7] erforms mage restoraton to a satsfable level for slghtly corruted mages but gves oor results for hghly corruted mages. Conventonal medan flters substtute the xel n consderaton wth the medan value wthout consderng whether the xel s corruted or not. And as such valuable mage detals are lost as nose-free xels also gets relaced by the medan value leadng to mage qualty degradaton. In order to overcome the dsadvantage of the conventonal medan flters, a swtchng scheme s emloyed to decde when to aly the medan flter as descrbed n [4], [5], [6], [7], [8], [9]. In swtchng based medan flters, the man ssue s desgn of an effcent nose detecton algorthm whch dstngushes nosy and nose-free xels. Sun and Neuvo [4] roosed the frst swtchng algorthm where corruted xels are assed through the medan flter whle the values of the uncorruted xels reman ntact by makng them ass through the dentty flter. The man dea behnd swtchng medan flter s the dentfcaton of corruted and uncorruted xels. A feasble soluton to ths s to mlement mulse-nose detecton algorthm ror to flterng and classfy the xels as corruted or uncorruted. The corruted xels are then assed to the flterng rocess whle the uncorruted xels reman undsturbed. The frst stage s for nose detecton, whle the second stage s for nose suresson. Ng et. al. [8] roosed the boundary dscrmnatve nose detecton algorthm to determne whether the current xel s a corruted xel or a nose-free xel. Accordng to the nose detecton algorthm two boundares that forms three clusters- lower ntensty mulse nose, uncorruted xels and hgher ntensty mulse nose are determned and each xel s classfed whether t s corruted or uncorruted. Then, the corruted xel s assed through medan flter to erform the restoraton rocess. Sorted Swtchng Medan Flter (SSMF) roosed by [9] conssts of three hasesdetectng stage, the sortng stage and the flterng stage, the SSMF. Ths aer resents an teratve clusterng based swtchng medan flter that reserves mage detals whle effectvely suressng mulse nose. The roosed flter mechansm nvolves a nose detecton algorthm that detects the center Paer ID:

2 xel wthn the consdered wndow as corruted or uncorruted. The nose detecton algorthm detects between corruted and non-corruted xels by classfyng the xels nto three clusters teratvely. If the xel n consderaton falls under the mddle cluster n the last teraton, the xel s classfed as uncorruted otherwse t s detected as corruted. Corruted xels go through medan flterng leadng to restoraton of the nosy mage effectvely. Exermental results show that the roosed flter rovdes good qualty restored mages reservng mortant detals of the mage. The aer s dvded nto fve sectons as follows. Secton 1 as already seen gves a bref ntroducton. Secton 2 descrbes how and why a swtchng medan flter s mortant. Secton 3 descrbes the nose models. Secton 4 descrbes roosed mulse nose detecton algorthm and swtchng medan flter. Secton 5 resents the exermental results showng the erformance evaluaton of the roosed flter. Secton 6 concludes the aer gvng a bref summary of the aer. 3. Nose Models Nose models are assocated wth detecton and fltraton of mulse nose. Varous nose models can be develoed but the general models [8] used normally are descrbed n ths secton. Two of the nose models have been mlemented and used for carryng out the evaluaton rocess of the roosed flter. In all the models, for each mage xel at locaton (x,y), wth ntensty value x,y, n x,y reresents the corresondng xel of the nosy mage; and reresent the nose denstes. 1) Nose Model 1: In ths frst model, nose s modelled as salt and eer nose wth equal robablty where xels are randomly corruted by fxed extreme values 0 and 255. The robablty densty functon s as follows:, n 0 2 f ( n) 1, n (1), n Here, reresents the total nose densty. 2) Nose Model 2: The dfference between Nose Model 2 and the Nose Model 1 s that each xel mght be corruted wth unequal robabltes by ether salt or eer. The robablty densty functon s: 1, n 0 2 f ( n) 1, n (2) 2, n and total nose densty s gven by ) Nose Model 3: Another realstc aroach to modelng mulse nose s to adot two fxed ranges of length l each, and then the nose could take any values wthn the range. The robablty densty functon wll be:, 0 n l 2l f ( n) 1, n, 255 l n 255 2l where s the total nose densty. 4) Nose Model 4: The only dfference wth Model 3 s that denstes of low and hgh ntensty nose are unequal as gven: 1, 0 n l 2l f ( n) 1, n (3) (4) 2, 255 l n 255 2l and the total nose densty s gven by Proosed Algorthm 4.1 Nose Detecton Algorthm Before an mage s fltered, ts xels need to be classfed as nosy or nose-free. The followng roosed algorthm detects whether the current xel centred at the wndow s corruted or not and s somewhat smlar to [6], [8]. The orgnal mage s transformed n ths nose detecton rocess nto mage sequences where are the mage sequences generated where denotes the xel centred at coordnate (x,y) and btma sequence of same dmenson as s obtaned at each teraton n. All the values of Btma sequence are set to 0 s. The btma sequences are generated usng the followng stes: 1)Consder an 11 x 11 wndow centred on the current xel n consderaton. 2)The xels n the wndow are sorted n ascendng order n Vector V whose elements are denoted by v where ranges from 0 to n. 3)The medan M s comuted for the sorted vector V. 4)Agan, the medan M l for the lower half of the vector V s calculated. 5)The maxmum ntensty dfference between the ars of xels of the lower half tll M l s comuted. The lower bound B l s gven by the corresondng xel. 6)Smlar to ste (4) and ste (5), M h s comuted and uer bound B h s found out usng the same rocedure. 7)If the current xel falls wthn the values of B l and B h, t s consdered as uncorruted and s set to 0 else t s classfed as corruted and s set to 1. Paer ID:

3 The above algorthm stes grous the xels nto three clusters {v 0,B l }, {B l, B h } and {B h,v n }. Thus, the btma at teraton n has values 0 for the xels whch fall n the mddle cluster whch are classfed as uncorruted grou of xels whle the xels that fall n the other two clusters are termed as corruted and values are set to 1. Image s oerated usng the btma generated n the above stes to generate ts next mage sequence usng the gven relaton n1 n1, 1 n m f b a (5) n1 n1 a, f b 0 where s the medan of the wndow centred at (x,y), over the nosy mage. The stes descrbed n the algorthm are reeated for n=1, 2, 3 to generate a fnal mage sequence and a corresondng btma ndcatng the corruted and non corruted xels. For colour RGB mages, btma sequences for each channel are used and the algorthm s run for each channel. 4.2 Swtchng Medan Flterng The revous secton descrbed about nose detecton algorthm whch lays a major role n desgnng a swtchng based medan flter. After the detecton of the corruted xel, flterng rocess s carred out. The flterng art s dscussed n ths secton. The fnal btma s checked for gettng the nformaton whether the xel s corruted or not at. After the xel has been classfed as nosy, the xel s assed through medan flter wth a maxmum wndow sze of 5 x 5. The medan value of a wndow for gray level mages of sze W can be calculated usng O med I ( s, t) W (6) xy, xsy, t O reresents the outut xel and I reresent xels that artcated n the rankng of xels to comute the medan wthn the wndow W. Consderng colour mages, for each xel vector v, ts L 1 - norm dstances wth resect to other xel vectors s comuted ndvdually and summed together by usng N S v v (7) j for = 1, 2, 3,..., N j1 Each corruted xel s relaced the vector medan corresondng to the mnmum value of S. 5. Exermental Results For the exermental urose n order to smulate the erformance of the roosed flter, Nose Model 1 has been used. The frst ste n mage restoraton s detecton of nosy xels. The smulatons of the roosed flter gve the followng Mss Detecton ercentage and False Alarms shown n table 1. It can be seen from the table that the roosed flter gves low mss detecton and false alarms. The mages show the smulaton results whch wll be dscussed n detals later n ths secton. Nose Model 1 usng equaton (1) has been used for the njecton of salt and eer nose to the orgnal mage shown n fgure 1. The mages after the njecton of the nose at varous densty levels 20,40,70,80 usng Nose Model 1 have been shown n the fgures. The corresondng fltered mages after the detecton of corruted xels and subsequent medan flterng are shown sde by sde of the nosy mages. Table 1: Mss Detecton and False Alarm for the Proosed Iteratve Clusterng Nose Detecton based Swtchng Medan Flter usng Nose Model 1 Nose Percentage Mss Detecton False Alarm The mages wth low nose denstes 20% and 40% are fltered very effectvely as shown n fgure 1. The roosed flter rovdes very good result for low nose denstes. Images njected wth hgh nose denstes 70% and 80% shown n fgure 2 gve satsfable fltered results as can be seen from the mages. The evaluaton of the erformance of the roosed flter s done n terms of Peak Sgnal to Nose Rato (PSNR). usng the formula PSNR 10 log db 10 (8) MSE where Mean Square Error (MSE) s 1 X Y 1 j 1 2, j, j MSE f o (9) XY Here, X and Y denote the total number of mage xels n the horzontal and vertcal dmensons; and reresent the orgnal and fltered xels of the mage resectvely. Another ont consdered s the non-ncluson of the corruted xel for rankng whle calculatng the medan value. That s, f the current xel s classfed as corruted, t wll be excluded from the rocess of rankng; that s only nose-free xels wthn the wndow are consdered for the rankng rocess. Ths rovdes better results leadng to less dstorton. Paer ID:

4 6. Concluson Fgure 1: Orgnal mage alongwth nose nduced mages wth nose densty 20% and 40% and ther subsequent medan fltered mage sde by sde In ths aer, an teratve clusterng nose detecton based swtchng medan flter s roosed. The roosed flter ncororates a nose detecton algorthm whch effectvely classfes xels as corruted or uncorruted. The roosed flter rovdes low mss detecton and false alarm values. After the classfcaton of the xel as corruted or uncorruted, the corruted xel goes through medan flterng rocess leadng to restoraton of the nosy mage. The uncorruted xel remans undsturbed reservng the mortant mage detals. The roosed flter s comared wth conventonal medan flter and smf flter, the results are found to be arecable n comarson wth them. The roosed flter rovdes good qualty results as shown n the mage fgures. References Fgure 2: Nose nduced mages wth nose densty 70% and 80% and ther subsequent medan fltered mage sde by sde The PSNR values obtaned for the roosed Iteratve Clusterng Swtchng Nose detecton based Medan Flter usng Nose Model 1 where the nose densty ranges from low densty to hgh densty s shown n table 2. From the values shown, t can be sad that the roosed flter rovdes good results n comarson wth tradtonal medan flter (MF) and Progressve Swtchng Medan Flter (PSMF). Table 2: Psnr Values for Dfferent Nose Denstes Usng Nose Model 1 Nose Model 1 Nose Densty (%) PSNR (Db) Salt/ Peer MF PSMF Proosed Flter 10/ / / / / / / / [1] T. Chen, H.R. Wu, Sace varant medan flters for the restoraton of mulse nose corruted mages, IEEE Transactons on Crcuts and Systems-II: Analog and Dgtal Sgnal Processng Vol. 48, No. 8, , [2] R. Lukac, B. Smolka, K. Martn, K.N. Platanots, A.N. Venetsanooulos, Vector flterng for color magng, IEEE Sgnal Processng Magazne Vol. 22, No. 1, 74 86, [3] RC Gonzalez, RE Woods, Dgtal Image Processng, Thrd Edton, Pearson, [4] T. Sun, Y. Neuvo, Detal-reservng medan based flters n mage rocessng, Pattern Recognton Letters, Vol. 15, No.4, , [5] H. Hwang, R.A. Haddad, Adatve medan flters: new algorthms and results, IEEE Transactons on Image Processng Vol.4, No.4, , [6] W. Zhou, Z. Davd, Progressve swtchng medan flter for the removal of mulse nose from hghly corruted mages, IEEE Transactons on Crcuts Systems-II: Analog and Dgtal Sgnal Processng Vol.46, No.1, 78 80, [7] T Chen, HR Wu, Adatve mulse detecton usng center-weghted medan flters, IEEE Sgnal Process Let, Vol. 8, No. 1, 1-3, [8] P.E. Ng, K.K. Ma, A swtchng medan flter wth boundary dscrmnatve nose detecton for extremely corruted mages, IEEE Transactons on Image Processng Vol 15,No. 6, , [9] Sh-Jnn Horng, Lng-Yuan Hsu, Tanru L, Shaoje Qao, Xun Gong, Hsen-Hsn Chou, Muhammad Khurram Khan, Usng Sorted Swtchng Medan Flter to remove hgh-densty mulse noses, Elsever Journal of Vsual Communcaton and Image Reresentaton, Vol.24, No. 7, , Author Profle Chngakham Neeta Dev comleted her B.E from Manur Insttute of Technology, Manur and M.Tech from The Oxford College of Engneerng, Bangalore. She s currently workng as Assstant Professor n Comuter Scence and Engneerng Deartment of Natonal Insttute of Technology, Manur. Paer ID:

5 Kesham Prtamdas comleted hs B.E from PGP College of Engneerng and Technology and M.E from Sr Krshna College of Engneerng, Chenna. He s currently workng as Assstant Professor n Electroncs and Communcaton Engneerng Deartment of Natonal Insttute of Technology, Manur. Paer ID: