A Novel Fuzzy logic Based Impulse Noise Filtering Technique

Transcription

1 Internatonal Journal of Advanced Scence and Technology A Novel Fuzzy logc Based Impulse Nose Flterng Technque Aborsade, D.O Department of Electroncs Engneerng, Ladoke Akntola Unversty of Tech., Ogbomoso. Oyo-state. doaborsade@yahoo.com Abstract A novel fuzzy logc based flterng technque s proposed to restore mages corrupted by mpulse nose. The proposed scheme s n two phases namely the detecton of nosy pxels at all locatons n the mage usng fuzzy knowledge based and applcaton of recursve medan flter on the corrupted pxels to remove the mpulse nose. The performance of the proposed technque s tested on varous test mages corrupted at varous nose denstes and also compared wth some of the exstng flters. Expermental results show that the proposed technque exhbts superor performance than ther counterparts and s effcently capable of removng fxed-valued mpulse nose denstes, rangng from 5% to 40% n the mage whle at the same tme effectvely preservng the useful nformaton n the mage. Keywords: Impulse nose, Nonlnear flter, Fuzzy Logc, Defuzzfcaton, Recursve medan flterng, Peak Sgnal- to- nose Rato. 1. Introducton Dgtal mages are prone to mpulse nose as a result of errors n the mage acquston or transmsson process. Nose sgnfcantly degrades the mage qualty and cause great loss of nformaton detals n the mage. It also complcates further mage processng, such as mage segmentaton and edge detecton. Varous flterng technques have been proposed over the year, for removng mpulse nose. It s well-known that lnear flters could produce serous mage blurrng hence, nonlnear flters have been wdely exploted due to ther much mproved flterng performance, n terms of mpulse nose attenuaton and edge/detals preservaton. One of the most popular and robust nonlnear flters s the standard medan (SM) flter [1], whch explots the rank-order nformaton of pxel ntenstes wthn a flterng wndow and replaces the center pxel wth the medan value. However, the medan flter tends to blur mage detals and remove thn lnes even at low nose denstes. To avod the nherent drawbacks of the standard medan flter, the weghted medan flter [2] and the centerweghted medan flter [3], whch are modfed medan flters, have been ntroduced. These flters demonstrate better performance n preservng mage. However, applyng these flters uncondtonally across the entre mage wthout consderng whether t s uncorrupted or corrupted as practced n the conventonal schemes would nevtably remove the uncorrupted detal pxels, destroy the mage qualty, and cause addtonal blur. Many swtchng-based medan flterng approaches for locatng the dstorted pxels pror to flterng have been suggested n the past by many researchers [4]-[9]. Although satsfactory results have been obtaned n all these approach by ncorporatng nose detecton mechansm 79

2 Internatonal Journal of Advanced Scence and Technology nto the flterng framework, however the study reveals that n case of unformly dstrbuted mpulse nose, these technques do not perform well as the noses are dffcult to be detected and elmnated. Consderng the capablty of neural network and fuzzy logc based processng, n recent years, many researches have been done on ther applcatons n mage nose detecton/removal. Dfferent methods for fuzzy based mpulse nose removal have been proposed. In the work proposed by Zhang et al. [10], a fuzzy logc technque was used to detect and remove mpulse nose. Ther work was based on long-range correlaton wthn dfferent parts of the mage. Schulte et al. [11], [12] proposed a fuzzy dervatve estmaton for nose detecton and a fuzzy smoothng of neghborng pxels for nose removal. Lee et al. proposed a fuzzy mage flter based on the genetc learnng process [13]. These methods are vastly superor to the conventonal methods hence they ncur a very hgh computatonal cost. In ths paper a novel fuzzy logc based flterng scheme s proposed. The proposed scheme s smple but effcent and works alternatvely n two phases: detecton of nosy pxels followed by medan flterng of the corrupted pxels to overcome many of the shortcomngs observed n the exstng methods. Detecton operaton s carred out at all locatons but flterng s performed only at selected locatons. The overall block dagram of the combned flter structure s depcted n Fgure 1. The outlned of the paper s as follows: Secton II, revews mpulse nose model, Secton III, presents the novel fuzzy mpulse nose detecton and removal scheme. Secton IV, presents the expermental results, and Secton V conclude the paper. Choose next wndow Input Image 3x3 Sldng wndow Fuzzy knowledge base 0 Image defuzzfers 0 Non-nosy pxel Nosy pxel Replacement of corrupted (Nosy) pxel Adaptve medan flter 2. Impulse Nose Model Fg. 1. Block Dagram of the Proposed Scheme Impulsve nose s one such nose, whch may affect mages at the tme of acquston, transmsson or storage. The mage model contanng mpulse nose can be descrbed as follows [14]: 80

3 Internatonal Journal of Advanced Scence and Technology X j N j, Yj, wth p wth 1- p where Yj and Nj denotes the gray level of the orgnal mage and nose substtutng for the orgnal gray scale value at pxel locaton (, j) respectvely. There are two cases of nose dstrbutons for mpulse nose: fxed valued mpulse nose and random-valued mpulse nose. For fxed-valued mpulse nose whch s also known as the salt-and-pepper, values of the corrupted pxels are equal to nmn or nmax wth equal probablty [8]. For random-valued mpulse nose, however, the corrupted pxel values are unformly dstrbuted between nmn and n max [11]. For gray-level mages wth 8 bts per pxel (.e., n mn 0 and n max 255), the nose value N j of the frst case corresponds to a fxed value of 0 or 255 wth equal probablty p / 2, whle that of the second case corresponds to a random value unformly dstrbuted n the range 0, 255. In ths paper, fxed-valued mpulse nose was adopted as the nose model to test the system robustness. 3. Proposed Technque A. Impulse Nose Detecton and Fuzzy Rules In ths paper, at frst for each pxel n the mage the ntensty dfference between the center pxel and the neghborng pxels n a sldng wndow of 3 3 shown n Fgure 2 s calculated. Snce gray-scale mages havng ntensty values n the range 0, 255 are beng consdered, thus, the values s n the range 255, 255 and s denoted by, 2 P P 1,, -1 D abs 0 N (2) where N 3, 5, 7,, dependng on the wndow sze. By consderng the ntensty dfference method and a fuzzy dea, four computed values are used to form a fuzzy knowledge base whch n turn s used to detect whether a gven pxel s nose or not. Many membershp functons have been ntroduced n the lterature. In the proposed scheme, trapezodal membershp functons are defned for the fuzzy system nputs. To appled ths functon, frst D s mapped to the range of [ 0 100]. The mapped values are classfed nto two fuzzy parttons (regons) D L and D H as shown n Fgure 3. The regon, D L consttutes the pxels that acqure low ntensty dfference value and the regon, D H consttutes the pxels that acqure hgh ntensty dfference value. To separate dfferent D classes two dfferent thresholds 1 and 2 are used such that f D value s n the range of [ 0 2 ], the correspondng pxel s classfed to D L, and for the range of [[ 1 100], the pxel s classfed to D H. The output of fuzzy system explans to how extent a pxel could be nosy. By the defned fuzzy rules, the output o varable has two fuzzy sets, L and H, where L and H correspond to pxel wth low and hgh probablty values belongng to non-nose and nosy (1) 81

4 Internatonal Journal of Advanced Scence and Technology pxel respectvely. The membershp functons correspondng to o are shown n Fgure 4. Sxteen fuzzy decson rules shown n Table 1 are used n the proposed fuzzy system. Fg. 2. Appled Mask to Compute Intensty Dfferent D 0 DL DH L H D Fg. 3. Classes Membershp Functon Fg. 4. Output Membershp Functon B. Defuzzfcaton The fuzzy sets output comng from the FKB are fed to the defuzzfer blocks. The defuzzfer defuzzfes the nput fuzzy set and converts t nto a sngle scalar value. Defuzzfcaton s done usng the followng equaton: o o( j) C ) (3) Fnal ( j where o( j) s the pxel membershp value n j ' th class, and C j s the output class center. o Fnal s the probablty used for fnal pxel classfcaton as nosy or non-nosy. An optmum threshold level n the range of 0.6 to 0.95 s determned through experments to bnarze the output mage produced through the defuzzfer.e., 1, o Fnal (4) 0, 0.6 Thus, a pxel wth probablty greater than the threshold of 0. 6 s classfed as nosy whle that wth probablty less than the threshold s not. C. Recursve Medan Flterng Algorthm To process the corrupted mage pxel, recursve medan flter s appled. The twodmensonal medan flter s realzed by passng a ( 2N 1) wndow over each pont of the 2 mage sgnal, rankng the values n the wndow, and replacng each pont wth the output of the recursve medan flter on that partcular pont before shftng the wndow to the next poston. In mage processng applcatons, t s necessary to apply the recursve medan flter 82

5 Internatonal Journal of Advanced Scence and Technology teratvely. By observng the functonal optmzaton propertes of recursve medan flterng, the process of repeated applcatons of recursve medan flterng s gven by ˆ ( t) ˆ ( t1) ˆ ( t1) Y ( k) medan Y ( k N ),, b ( k),, Y ( k N ) (5) (0) where the superscrpt t s the teraton ndex and Yˆ b ( k). Ths process can also be descrbed by the followng pseudo-c code. Here, we assume that the total number of sgnal ponts s L and at both ends of the sgnal, N ponts are appended to allow the flter to reach the edges of the sgnal. Algorthm 1 Re cursve-medan-flter for ( k 1; k L; k ) Y ( k) do {success 0; for ( k 1; n L; k ){ ( whle(success L);} ( ){ ( k); m medan Y ( k N),, b ( k),, Y ( k N) f ( m Y ( k)) success Y ( k) m;}} b That s, the orgnal sgnal s used n the mddle of the operaton wndow throughout the whole process, nstead of usng the output of the prevous pass. From the functonal optmzaton propertes of recursve medan flterng, t can be easly understood that ths operaton has the propertes of smoothng the sgnal and hence features such as thn lnes and sharp edges can be better preserved. 4. Smulaton Results The proposed scheme n ths paper s expermented upon to see how well t can remove the mpulsve noses. The performance of the scheme as been examned on a varety of mpulse nose-corrupted testng mages corrupted wth nose densty rangng from 5% to 40%. The peak sgnal-to-nose rato (PSNR) defned as PSNR 10log 10 MSE (6) s used as a quanttatve performance ndcaton, where MSE s the mean squared error, whch s defned as M N 1 2 MSE Y(, j) Yˆ(, j) MN 1 j1 (7) where M and N are the total number of pxels n the horzontal and the vertcal dmensons of the mage. Y and Ŷ denote the orgnal and fltered mage, respectvely. For comparson, the corrupted expermental mages are subjected to flterng by the proposed schemes along wth many other dfferent standard methods namely standard medan flters MF ( 3 3), MF ( 5 5), progressve swtchng medan flter [7], Prescanned mnmax center-weghted flters (PMCWF). All flterng schemes ncludng the proposed scheme operate on a 3-by-3 sldng wndow. 83

6 MSE PSNR n db Internatonal Journal of Advanced Scence and Technology The proposed method has been appled on varety of test mages whch are shown n Fg. 5. Table 2 show the quanttatve comparson of the proposed method and the exstng methods wth respect to mages corrupted wth fxed-valued mpulse nose. The PSNR and MSE thus obtaned wth varous nose levels are plotted n Fg. 6 and Fg. 7. From all the smulaton results t could be observed that the proposed method exhbts much better performance than other methods n terms of PSNR and vsual aspect. It s clearly seen that the proposed method successfully removes the nose from the mage as well as at the same tme effcently preserves the useful mage detals. 5. Concluson A novel fuzzy logc based mpulse nose detecton and flterng technque s presented. The fundamental superorty of the proposed technque over most of the exstng methods s t effcency n detecton of corrupted pxel and suppresson of the detected mpulse nose from dgtal mages wthout dstortng the useful nformaton wthn the mage. Extensve smulaton experments have been conducted on a varety of standard test mages to demonstrate and compare the performance of the proposed method wth many other well known technques. As can be seen from the plots the proposed technque s far better than many other exstng methods. The proposed technque s smple and easy to mplement PSM MF(3x3) MF(5x5) PMCWF PROPOSED Nose densty (%) Fg. 6. PSNR Plot for Test Image 5(a) Corrupted wth Dfferent Nose Densty PSM MF(3x3) MF(5x5) PMCWF PROPOSED Nose densty (%) Fg.7. MSE Plot for Test Image 5(a) Corrupted wth Dfferent Nose Densty 84

7 Internatonal Journal of Advanced Scence and Technology Table1: Fuzzy Rules Table2: Comparatve Results n PSNR of Dfferent Algorthms Appled to Test Image Fgure 5(a) Corrupted by Varous Rates of Fxed-Valued Impulse Nose References [1] Ptas and A. N. Venetsanopoulos, Order statstcs n dgtal mage processng, Proc. IEEE, vol. 80, no. 12, pp , Dec [2] D. R. K. Brownrgg, The weghted medan flter, Commun. ACM, vol. 27, no. 8, pp , Aug [3] S. J. Ko and Y. H. Lee, Center weghted medan flters and ther applcatons to mage enhancement, IEEE Trans. Crcuts Syst., vol. 38, no. 9, pp , Sep [4] T. Chen, K. K. Ma, and L. H. Chen, Tr-state medan flter for mage de-nosng, IEEE Trans. Image Processng, vol. 8, no. 12, pp , Dec [5] T. Chen and H. R. Wu, Impulse nose removal by mult-state medan flterng, n Proc. Int. Conf. Acoust., Speech, Sgnal Processng, Jun. 2000, vol. 4, pp [6] H. L. Eng and K. K. Ma, Nose adaptve soft-swtchng medan flter, IEEE Trans. Image Process., vol. 10, no. 2, pp , Feb [7] S. Zhang and M. A. Karm, A new mpulse detector for swtchng medan flters, IEEE Sgnal Process. Lett., vol. 9, no. 11, pp , Nov

8 Internatonal Journal of Advanced Scence and Technology [8] Z. Wang and D. Zhang, Progressve swtchng medan flter for the removal of mpulse nose from hghly corrupted mages, IEEE Trans. Crcuts System II, Analog Dgt. Sgnal Processng, vol. 46, no. 1, pp , Jan [9] P. E. Ng and K. K. Ma, A swtchng medan flter wth boundary dscrmnatve nose detecton for extremely corrupted mages, IEEE Trans. Image Processng, vol. 15, no. 6, pp , Jun [10] D. Zhang and Z.Wang, Impulse nose detecton and removal usng fuzzy technques, Electron. Lett., vol. 33, no. 5, pp , Feb [11] S. Schulte, M. Nachtegael,V. DeWtte, D.Van derweken, and E. E.Kerre, A fuzzy mpulse nose detecton and reducton method, IEEE Trans. Image Process., vol. 15, no. 5, pp , May [12] S. Schulte, V. De Wtte, M. Nachtegael, D. Van der Weken, and E. E. Kerre, Fuzzy random mpulse nose reducton method, Fuzzy Sets Syst., vol. 158, no. 3, pp , Feb [13] C. S. Lee, S. M. Guo, and C. Y. Hsu, Genetc-based fuzzy mage flter and ts applcaton to mage processng, IEEE Trans. Syst.,Man Cybern.,B, Cybern., vol. 35, no. 4, pp , Aug [14] H. Hwang and R.A. Haddad, Adaptve Medan Flters: New Algorthms and Results, IEEE Transactons On Image Processng, Vol. 4, No. 4, Aprl (a) (b) (c) (d) (e) (f) (g) (h) () 86

9 Internatonal Journal of Advanced Scence and Technology (j) (k) (l) Fgure 5: Test Images (a), (d), (g), (j) and correspondng nosy mage corrupted by 10%,15%, 20%, and 25% fxed value mpulse nose (b), (e), (h), and (k) respectvely and (c), (f), (), (l) are fltered mage of (b),(e),(h), and (k) respectvely. Authors Aborsade, Davd. O receved the B.Eng. degree n Electronc and Electrcal Engneerng Technology from Federal Unversty of Technology, Owerr, n He receved M.Eng. and Ph.D. degrees n Electrcal Engneerng from Unversty of Ilorn, n 1995 and 2006, respectvely. He s currently a Senor Lecturer wth the Department Electronc and Electrcal Engneerng, Ladoke Akntola Unversty of Technology, Ogbomoso. Hs research nterests nclude computer vson, pattern recognton, mage and sgnal processng, neural networks, and fuzzy logc. 87

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