Random-Valued Impulse Noise Detection and Removal in Grayscale and Color Images

Transcription

1 Random-Valued Impulse Nose Detecton and Removal n Grayscale and Color Images Vladmr V. Khryashchev, Member, IAENG, Andrey M. Shemyaov, Olga N. Gushchna and Dan Falcon Abstract - The paper presents a comparatve analyss of random-valued mpulse nose detectors for grayscale and color mages. Expermental results demonstrate that vector medan flter wth drectonal detector outperforms other flters both n terms of objectve crtera and vsual appearance. The examples of reconstructed mages are provded. 1 Keywords - color mage restoraton, nose detecton, vector medan flter, peer group flter, random-valued mpulse nose I. INTRODUCTION In many practcal applcatons mages are corrupted by nose caused ether by faulty mage sensors or due to transmssons corrupton resultng from artfcal or natural phenomena. Transmsson nose, also nown as salt-andpepper nose n grey-scale magng, s modeled by an mpulsve dstrbuton. However, a problem n the study of the effect of the nose n the mage processng communty s the lac of commonly accepted multvarate mpulse nose model. A number of smplfed models have been ntroduced recently, to assst the performance evaluaton of the dfferent color mage flters [1, 2]. Based on trchromatc color theory, color pxels are encoded as three scalar values, namely, red, green and blue (RGB color space). Snce each ndvdual channel of a color mage can be consdered as a monochrome mage, tradtonal nonlnear mage flterng technques have nvolved the applcaton of scalar flters on each channel separately [3-5]. However, ths dsrupts the correlaton that exsts between the color components of natural mages. As such the color nose model should be consdered as a 3-channel perturbaton vector n color space [5]. Let x be the vector, characterzng a pxel of a nosy mage, v the vector descrbng mpulse nose model, z s the nose-free color vector, p mpulse nose probablty, then v, wth probablt y p x. z, wth probablt y 1 p Vladmr Khryashchev, PhD, P.G. Demdov Yaroslavl State Unversty, 14 Sovetsaya, Yaroslavl, Russa, (phone: ; e-mal: vhr@yandex.ru). Andrey Shemyaov, Graduate Student, P.G. Demdov Yaroslavl State Unversty, 14 Sovetsaya, Yaroslavl, Russa, (phone: ; e-mal: andrey.shemaov@gmal.com). Olga Gushchna, Graduate Student, P.G. Demdov Yaroslavl State Unversty, 14 Sovetsaya, Yaroslavl, Russa, (phone: ; e-mal: olyagushchna@gmal.com). Dan Falcon, M.ED, Pastuhov State Academy of Industral Management, 42 Respublansaya, Yaroslavl, Russa, (phone: ; e-mal: dfelcone@hotmal.com). Dependng on the type of vector v researchers consder ether fxed-valued or random-valued mpulse nose models [3-9]. In the case of fxed-valued mpulse nose v s characterzed by the followng expresson: G B T ( d, z, z ), wth probablt y p1 R B T ( z, d, z ), wth probablt y p 2 v, R G T ( z, z, d ), wth probablt y p3 T ( d, d, d ), wth probablt y p 4 where d - an mpulse value and p 1. 4 m1 Random-valued mpulse nose can be defned n several ways. In ths paper we use the followng model: G B T ( d1, z, z ), wth probablt y p1 R B T ( z, d 2, z ), wth probablt y p2 v, R G T ( z, z, d3), wth probablt y p3 T ( d1, d 2, d3), wth probablt y p4 where d 1, d2, d3 - unformly dstrbuted ndependent random numbers. The man approach for mpulse nose removng s to use medan-based flters [3]. However, these nonlnear flters also tend to modfy pxels that are not affected by the nose. In addton, when mpulse nose probablty s hgh, they are prone to edge jtter, so that detals and edges of the orgnal mage are usually blurred by the flter [6-11]. In order to mprove performance of medan-based flter approach, varous decson-based flters have been proposed, where possble mpulse nose pxels are frst dentfed and then replaced by usng medan flter. The examples of decson-based flters for random-valued mpulse nose removal from grayscale mages are: adaptve centerweghted medan flter [10] and drectonal weghted medan flter [11]. The most popular vector flter s vector medan flter (VMF). VMF s a vector processng operator that has been ntroduced as an extenson of scalar medan flter [4, 5]. To quantfy relatve magntude dfferences of nput samples, VMF utlzes ether the well-nown Eucldean dstance or the generalzed Mnows metrc. Neuvo and Ku proposed the frst peer group based flterng method [12]. Peer group flter (PGF) s based on the evaluaton of statstcal propertes of a sorted sequence of accumulated dstances used for the calculaton of vector medan of samples belongng to the flterng wndow. PGF output swtches between vector medan and the orgnal central pxel [13, 19, 20]. m

2 Fg. 1. The scheme of vector medan flter wth drectonal detector Camarena et al. [14] proposed a fast peer group based flterng method n whch a pxel s dentfed as noncorrupted when the sze of peer group s larger than a threshold n the fuzzy metrcs context. Morllas et al. [15] used a reduced orderng of color vectors to detect and replace the corrupted pxels for smultaneous reducton of mpulse noses and preservaton of the textured edges. Camarena et al. [16] further proposed a two-stage peer group flterng method to detect the corrupton status of a pxel [17]. In our prevous wor [18] we ntroduce a novel flter for the purpose of random-valued mpulse nose removal from RGB-color mages whch utlzes the advantages of both weghted vector medan and decson-mang fltraton schemes - vector medan flter wth drectonal detector (VMF-DD). Ths paper focused mostly on detaled comparson of random-valued mpulse nose detectors. New results of detectors and flters smulaton are presented for grayscale and color test mages. The rest of the paper s organzed as follows. In secton 2, we shortly descrbe the vector medan flter wth drectonal detector. Secton 3 focuses on comparson of random-valued mpulse nose detectors performance for grayscale mages. In secton 4, we present new expermental results for color RGB- mages. Secton 5 concludes the paper. II. VECTOR MEDIAN FILTER WITH DIRECTIONAL DETECTOR The processng of each mage pxel conssts of two stages: mpulse detecton and fltraton, as shown n fg. 1. The VMF-DD detector wors as follows. Let x be the current pxel of the dstorted mage wth coordnates (, j), y - the correspondng pxel of the processed mage. On the stage of detecton four basc drectons passng through the central pxel x are chosen nsde the flter sub-wndow. They are desgnated by ndexes For each drecton two sums are calculated: the sum of brghtness value dfferences dl drecton ( 1...4) between pxels lyng on the gven x and the central pxel x ;

3 the sum of angular dstances da ( 1...4) between pxels lyng on the gven drecton x and the central pxel x. The angular dstance between two pxels we defne as an angle between correspondng 3-channel vectors whch contan color component values of pxels [21]: x 1, x2 x 1, x2 arc cos x1 x 2. x11x21 x12x22 x13x23 arc cos x11 x12 x13 x21 x22 x23 The brghtness of a pxel s calculated from ts color component values by the followng formula: L( x ) 0.3R 0.59G 0. 11B, where R, G, B - are red, green, and blue component values of pxel x. Among all calculated sums dl the mnmum s found: rl mndl 1,..., 4. Smlarly we fnd the mnmum among all sums da : ra mn da 1,..., 4. The resulted values rl and ra are compared to threshold values TL and TA respectvely. If both rl TL and ra TA, then pxel x remans wthout changes. Otherwse, the current pxel s consdered dstorted and s replaced by weghted vector medan calculated nsde the flter s sub-wndow. III. SIMULATIONS ON GRAYSCALE IMAGES Detectors performance can be compared usng fve measures: recall, specfcty, precson, accuracy and F-measure [17]. Recall measure (R) shows the rato between correctly deduced corrupted pxels and the overall number of corrupted pxels. Specfcty (S) s the relaton between the total number of pxels, correctly deduced as noncorrupted, and the number of non-corrupted pxels on the mage. Precson (P) s the proporton of true corrupted pxels wthn the deduced corrupted pxels. Accuracy (A) s the proporton of correctly deduced pxels wthn the total number of pxels on the mage. The F-measure (F) s the harmonc mean of the recall and precson measures. Let TP and TN be the number of pxels, correctly deduced as corrupted and non-corrupted respectvely. FP and FN denote respectvely the number of pxels that was falsely deduced as corrupted and non-corrupted. Usng the notaton, the measures can be gven by: TP R, TN S, TP P, TP FN TN FP TP FP TP TN A, 2. TP FP TN FN F 1 1 R P The grayscale test mages used are Peppers, Lena and Barbara. The resoluton of all mages s An mage s beng corrupted by random-valued mpulse nose. The corrupton s carred out wth dfferent nose probablty p, and the proposed flter s tested usng these ncreasngly corrupted mages. The flters used for comparson are: adaptve center-weghted medan flter (ACWMF) [10], sgnal-dependent ran-ordered-mean flter (SD-ROM) [8] and drectonal weghted medan flter (DWM) [11]. p Measure TABLE I COMPARISON OF DETECTORS PERFORMANCE FOR GRAYSCALE IMAGES Peppers Lenna Barbara ACWMF SD-ROM DWM ACWMF SD-ROM DWM ACWMF SD-ROM DWM R 91,46 90,46 4,06 90,54 89,60 5,32 86,38 86,04 5,65 S 99,03 98,19 98,86 99,27 98,03 98,79 94,42 90,51 96,57 0,1 P 91,28 84,78 27,71 93,27 83,47 32,84 63,18 50,21 15,46 A 98,27 97,42 89,36 98,40 97,19 89,45 93,61 90,07 87,47 F 91,33 87,50 7,07 91,80 86,38 9,16 72,94 63,38 8,28 R 85,10 86,57 5,62 85,40 86,44 5,43 81,05 83,13 5,72 S 98,88 97,70 98,85 98,85 97,24 98,78 94,08 88,92 96,55 0,2 P 95,02 90,41 54,87 94,98 88,72 52,59 77,44 65,28 29,31 A 96,12 95,47 80,19 96,16 95,08 80,10 91,47 87,76 78,37 F 89,77 88,44 10,19 89,90 87,56 9,84 79,18 73,12 9,57 R 80,60 85,24 5,98 80,30 84,68 5,89 76,37 81,93 6,21 S 97,76 96,11 98,81 97,99 95,78 98,74 93,05 86,62 96,61 0,3 P 93,99 90,39 68,29 94,56 89,60 66,72 82,52 72,39 43,94 A 92,61 92,85 70,96 92,68 92,45 70,90 88,05 85,21 69,50 F 86,77 87,74 10,99 86,85 87,07 10,83 79,32 76,86 10,88

4 Accordng to the results presented n Table 1, the followng conclusons can be made. In terms of recall the SD-ROM algorthm demonstrated the best results, slghtly outperform ACWMF. Low recall of DWM caused by the huge number of false negatve errors. All of the detectors have about the same specfcty (except hghly detaled mage Barbara, for whch the worst performance shows SD-ROM detector). The ACWMF has sgnfcantly hgher precson. However precson s depend on the test mage and for all detectors precson s lower for hghly detaled mages. In terms of accuracy and F-measure the results of ACWMF and SD-ROM detectors are comparable and much lower for DWM (whch s also caused by the huge number of false negatve errors). Presented results show that ACWMF and SD-ROM detectors outperform DWM detector. Fg. 2 shows the restoraton results for grayscale Lena mage n terms of pea sgnal to nose rato (PSNR). The ACWMF outperforms other two flters for nose probablty p<0.15, whle the DWM has better performance for p>0.15. IV. SIMULATIONS ON COLOR IMAGES In ths secton, we provde the smlar analyss of mpulse nose detectors for color RGB-mages. The color test mages used are Peppers and Baboon. Each vector pxel s of 24 bts, wth 8 bts for every channel. The resoluton of all mages s The flters used for comparson are: drectonal weghted medan flter, appled for each color channel; peer group flter, and vector medan flter wth drectonal detector. The smulaton results presented n Table 2. Based on the smulaton results, the followng conclusons can be made. The VMF-DD has sgnfcantly hgher recall (because of the less number of false negatve errors). For hghly detaled mages the PGF has the mnmum number of false postve errors and respectvely the hgher specfcty. Meanwhle the DWM has hghest specfcty for lowdetaled mages. Accordng to the results presented n Table 2, PGF outperforms other detectors for hghly detaled and low-detaled mages n terms of remanng three crtera. Fg. 3 shows the restoraton results for color Peppers mage n terms of PSNR. For low mpulse nose probablty p<0.1 the proposed VMF-DD algorthm wns aganst PGF 2-4 db n terms of PSNR metrc. For the ncreased mpulse nose probablty p>0.1 the values of PSNR metrc, measured for mages processed by the proposed VMF-DD flter, are 1-2 db hgher than for mages fltered by PGF. Let s consder vsual results of test mages restoraton. Test mage Caps and ts corrupted verson wth randomvalued mpulse nose probablty p = 0.15 are presented n fg. 4. Normalzed color dfference (NCD) crteron [22-23] was used for restored mages qualty assessment. TABLE II COMPARISON OF DETECTORS PERFORMANCE FOR COLOR IMAGES «Peppers» «Baboon» p Measure DWM PGF VMF-DD DWM PGF VMF-DD R 44,01 73,71 86,11 40,14 82,68 83,66 S 88,98 89,98 73,58 99,21 95,89 94,72 0,1 P 30,74 44,97 26,59 85,02 69,36 63,51 A 84,48 88,35 74,83 93,30 94,67 93,51 F 36,19 55,86 40,63 54,54 75,85 71,83 R 44,20 70,22 86,85 40,40 80,43 83,00 S 88,83 90,80 70,08 99,16 95,35 93,04 0,2 P 49,73 65,61 42,05 92,34 81,23 74,89 A 79,9 86,68 73,43 87,41 92,37 91,03 F 46,81 67,84 56,67 56,21 80,83 78,74 R 44,35 67,08 88,01 40,09 75,70 83,42 S 88,67 91,84 65,38 99,11 95,69 89,85 0,3 P 62,66 77,89 52,14 95,12 88,29 77,90 A 75,38 84,41 72,17 81,41 89,69 87,92 F 51,94 72,08 65,49 56,41 81,51 80,56

5 Fg. 2. Restoraton performance (PSNR, db) vs. probablty of random-valued mpulse nose for the grayscale Lena mage Fg. 3. Denosng performance (PSNR, db) vs. probablty of random-valued mpulse nose for the color Peppers mage (a) NCD = 0 (b) NCD = Fg. 4. Test mage Caps : (a) orgnal mage, (b) mage corrupted by mpulse nose (p = 0.15) Fg. 5 shows enlarged fragments of test mage Caps after ther processng by dfferent algorthms. After DWM fltraton restored mages turn out to be less blurred but they stll contan some amount of mpulse pxels. Better restoraton results are acheved by the applcaton of PGF algorthm whch preserves mage detals and almost completely removes mpulses from an mage. The proposed VMF-DD algorthm demonstrates vsual results close to that of PGF algorthm excellng the least n mage edges preservaton and the number of removed mpulses. The values of NCD qualty metrc, presented n fg. 5, corroborate the conclusons drawn after the analyss of vsual data. Thus, from shown fltraton results t s possble to draw a concluson that VMF-DD algorthm, appled to randomvalued mpulse nose removal from color RGB-mages, allows to acheve a sgnfcant ncrease of restored mage qualty n terms of both objectve and subjectve qualty assessment crtera. Moreover experments show that computatonal complexty of the proposed VMF-DD flter s lower than computatonal complexty of DWM and PGF flters. (a) NCD = 12.2 (b) NCD = 11.2 (c) NCD = 8.3 Fg. 5. Zoomed restoraton results of test mage Caps correspondng to Fgure 4: (a) DWM output, (b) PGF output, (c) VMF-DD output

6 V. CONCLUSIONS The followng conclusons can be drawn based on the obtaned smulaton results. The ACWMF and SD-ROM algorthms acheve better detecton ablty for grayscale mages. Meanwhle, the DWM flter demonstrates better mage restoraton abltes n terms of PSNR. The PGF algorthm s effectve n nose detecton for color RGB-mages. Besdes, earler proposed VMF-DD algorthm outperforms PGF n terms of PSNR and NCD. Vsual results of restored mages prove the results of objectve qualty assessment. The expermental results demonstrate the possblty for further mprovement of the flters wth detectors dealng wth random-valued mpulse nose removal from color mages. Because of ts low computatonal complexty, the proposed VMF-DD algorthm can be ntegrated n real-tme denosng systems. ACKNOWLEDGMENTS Ths wor was supported by the Russan Mnstry of Educaton and Scence under Grant 2.1.2/7067 The development of nonlnear theory of sgnal and mage processng n rado engneerng and communcatons. Olga Gushchna was also supported by Google Anta Borg Memoral Scholarshp REFERENCES [1] R. Szels, Computer Vson: Algorthms and Applcatons. Sprnger, [2] R. Luac, Computatonal Photography: Methods and Applcatons. CRC Press / Taylor & Francs, [3] I. Ptas, A. Venetsanopoulos, Nonlnear Dgtal Flters: Prncples and Applcatons. Boston, MA: Kluwer, [4] J. Astola, P. Haavsto, Y. Neuvo, Vector medan flters, Proceedngs of the IEEE, vol. 78, 1990, pp [5] R. Luac, B. Smola, K. Martn, K. Platanots, A. Venetsanopoulos, Vector flterng for color magng, IEEE Sgnal Processng Magazne, Specal Issue on Color Image Processng, vol. 22, 2005, pp [6] I. Apalov, V. Khryashchev, A. Prorov, P. Zvonarev, Image denosng usng adaptve swtchng medan flter, n Proc. of the IEEE Int. Conf. on Image Processng (ICIP), 2005, pp. I I-120. [7] L. Yn, R. Yang, M. Gabbouj, Y. Neuvo, Weghted medan flters: a tutoral, IEEE Trans. Crcuts Systems, vol. 43, 1996, pp [8] E. Abreu, Mtra S, A sgnal-dependent ran ordered mean (SD-ROM) flter - a new approach for removal of mpulses from hghly corrupted mages, n Proc. of the Int. Conf. on Acoustcs, Speech, and Sgnal Processng (ICASSP), 1995, vol. 4, pp [9] R. Chan, C. Hu, M. Nolova, An teratve procedure for removng random-valued mpulse nose, // IEEE Sgnal Processng Letters, 2004, vol. 11, pp [10] T. Chen, H. Wu, Adaptve mpulse detecton usng center-weghted medan flters, IEEE Sgnal Processng Letters, 2001, vol. 8, pp [11] Y. Dong, S. Hu, A new drectonal weghted medan flter for removal of random-valued mpulse nose, IEEE Sgnal Processng Letters, 2003, vol. 14, pp [12] Y. Neuvo, W. Ku, Analsys and dgtal realzaton of pseudorandom gaussan and mpulse nose source, IEEE Transactons on Communcatons, vol. 23, 2003, pp [13] B. Smola, Peer group flter for mpulsve nose removal n color mages, Lecture Notes n Computer Scence (LNCS 5197). Sprnger-Verlag, 2008, pp [14] J.G. Camarena, V.Gregor, S. Morllas, A. Sapena, Fast detectons and removal of mpulsve nose usng peer groups and fuzzy metrcs, Journal of Vsual Communcatons and Image Represenaton, vol. 19, 2008, pp [15] S. Morllas, V. Gregor, G. Pers-Fajarnes, Isolatng mpulsve nose pxels n color mages by peer group technques, Computer Vson and Image Understandng, vol. 110, 2008, pp [16] J.G. Camarena, V.Gregor, S. Morllas, A. Sapena, Some mprovements for mage flterng usng peer group technques, Image and Vson Computng, vol. 28, 2010, pp [17] Y. La, K. Chung, W. Yang, C. Chen, L. Ln, Novel Peer Group Flterng Method Based on the CIELAB Color Space for Impulse Nose Reducton, Proc. 21 st Internatonal Conference on Computer Graphcs and Vson, P [18] V. Khryashchev, D.K. Kuyn, A.A Studenova, Vector medan flter wth drectonal detector for color mage denosng, Proc. World Congress on Engneerng, V. 2. P [19] J. Y. F. Ho, Peer regon determnaton based mpulse nose detecton, Proceedngs of Internatonal Conference on Acoustcs, Speech and Sgnal Processng ICASSP, vol. 03, 2003, pp [20] B. Smola, A. Chydzns, Fast detecton and mpulsve nose removal n color mages, Real- Tme Imagng, vol. 11, 2005, pp [21] R. Luac, Adaptve color mage flterng based on center-weghted vector drectonal flters, Multdmensonal Systems and Sgnal Processng, 2004, vol. 15, pp [22] K. Platanots, D. Androutsos, A. Venetsanopoulos, Adaptve fuzzy systems for multchannel sgnal processng, Proceedngs of the IEEE, 1999, vol. 87, pp [23] K. N. Platanots, A.N. Venetsanopoulos, Color Image Processng and Applcaton. Sprng-Verlag, Berln, 2000.