Vector Median Filter with Directional Detector for Color Image Denoising

Transcription

1 Proceedngs of the World Congress on Engneerng 0 Vol II WCE 0 July London UK Vector Medan Flter wth Drectonal Detector for Color Image Denosng Vladmr V Khryashchev Member IAENG Dens K Kuyn and Alna A Studenova Abstract In ths paper a new approach to the problem of mpulse nose removal from color mages s presented The proposed method s based on nose detecton algorthm and weghted vector medan flter The results of ts analyss compared to other nown medan-based vector flters are presented The analyss shows that the proposed algorthm s more effcent n random-valued mpulse nose removal from color dgtal mages than other consdered flters Inde Terms color mage processng mpulse nose removal vector medan flter order statstc genetc algorthm optmzaton I I INTRODUCTION MAGE nose reducton wthout structure degradaton s perhaps the most mportant low-level mage processng tas [ ] Faulty sensors optc mperfectness electroncs nterference and data transmsson errors may ntroduce nose to dgtal mages In consderng the sgnal-to-nose rato over practcal communcaton meda such as mcrowave or satellte lns there can be degradaton n qualty due to low receved sgnal power Based on trchromatc color theory color pels 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 often nvolved the applcaton of scalar flters on each channel separately [3-5] However ths dsrupts the correlaton that ests 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 [6 7] The nose encountered n dgtal mage processng applcatons cannot always be descrbed n terms of commonly used Gaussan model Very often t can be characterzed n terms of mpulse sequences whch occur n the form of short duraton hgh energy spes attanng large ampltudes wth probablty hgher than those predcted by Gaussan densty model Transmsson nose also nown as salt-and-pepper nose n grayscale magng s modeled by an mpulsve dstrbuton [4 5 7] Ths wor was supported by the Russan Mnstry of Educaton and Scence under Grant /7067 The development of nonlnear theory of sgnal and mage processng n rado engneerng and communcatons Vladmr Khryashchev s wth the Image Processng Laboratory PG Demdov Yaroslavl State Unversty 4 Sovetsaya Yaroslavl Russa (phone: ; e-mal: vhr@ yanderu) Dens Kuyn s Post-Graduate Student PG Demdov Yaroslavl State Unversty 4 Sovetsaya Yaroslavl Russa (phone: ; e-mal: densuyn@ gmalcom) Alna Studenova s Post-Graduate Student PG Demdov Yaroslavl State Unversty 4 Sovetsaya Yaroslavl Russa (phone: ; e-mal: alnastudenova@ gmalcom) There are many types of mpulse nose Let be the vector characterzng a pel 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 probablty p z wth probablty p Dependng on the type of vector v researchers consder ether fed-valued or random-valued mpulse nose models [4-6] In the case of fed-valued mpulse nose v s characterzed by the followng epresson: G B T ( d z z ) wth probablty p R B T ( z d z ) wth probablty p v R G T ( z z d ) wth probablty p3 T ( d d d ) wth probablty p4 where d - an mpulse value and p 4 m Random-valued mpulse nose can be defned n several ways In ths paper we use the followng model: G ( d z z ) R ( z d z R G ( z z d ( d d d B T B T ) wth probablty p v T 3) wth probablty p3 T 3) wth probablty p4 d m wth probablty where d d 3 - unformly dstrbuted ndependent random numbers The man approach for mpulse nose removng s to use medan-based flters [3 8-0] However these nonlnear flters also tend to modfy pels 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 [-3] In order to mprove performance of medan-based flter approach varous decson-based flters have been proposed where possble mpulse nose pels are frst dentfed and then replaced by usng medan flter The eamples of decson-based flters for random-valued mpulse nose p ISBN: ISSN: (Prnt); ISSN: (Onlne) WCE 0

2 Proceedngs of the World Congress on Engneerng 0 Vol II WCE 0 July London UK removal from grayscale mages are: adaptve centerweghted medan flter [4] and drectonal weghted medan flter [5] These flters are good n locatng the nose even n the case of hgh nose probablty The most popular vector flter s vector medan flter (VMF) VMF s a vector processng operator that has been ntroduced as an etenson of scalar medan flter [6 7] To quantfy relatve magntude dfferences of nput samples VMF utlzes ether the well-nown Eucldean dstance or the generalzed Mnows metrc To mprove detalpreservng characterstcs of VMF the smple basc dea has been modfed and etended VMF-based flters [6-8] were desgned The famly of vector drectonal flters (VDF) represents a dfferent type of vector processng flters These flters operate on the drectons of mage vectors amng to elmnate vectors wth atypcal drectons n the color space [6] Weghted vector drectonal flters (WVDF) etend the fleblty of VDF-based desgns and provde a powerful color mage flterng tool capable of tracng varyng sgnal and nose statstcs Recently developed 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 pel [8] In ths paper 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 The rest of the paper s organzed as follows In secton we ntroduce the proposed vector medan flter wth drectonal detector (VMF-DD) Secton 3 focuses on the genetc algorthm optmzaton of the VMF-DD parameters In secton 4 we present epermental results of applyng of the proposed flter Secton 5 concludes the paper II VECTOR MEDIAN FILTER WITH DIRECTIONAL DETECTOR The proposed flter utlzes a decson-mang scheme to mprove the effcency of mpulse nose removal algorthm The processng of each mage pel conssts of two stages: mpulse detecton and fltraton as shown n fg The VMF-DD detector wors as follows Let be the current pel of the dstorted mage wth coordnates ( j) y - the correspondng pel of the processed mage On the stage of detecton four basc drectons passng through the central pel are chosen nsde the flter subwndow They are desgnated by ndees 4 Fg The scheme of vector medan flter wth drectonal detector ISBN: ISSN: (Prnt); ISSN: (Onlne) WCE 0

3 Proceedngs of the World Congress on Engneerng 0 Vol II WCE 0 July London UK For each drecton two sums are calculated: the sum of brghtness value dfferences dl ( 4) between pels lyng on the gven drecton and the central pel ; the sum of angular dstances da ( 4) between pels lyng on the gven drecton and the central pel The angular dstance between two pels we defne as an angle between correspondng 3-channel vectors whch contan color component values of pels [6]: arc cos arc cos The brghtness of a pel s calculated from ts color component values by the followng formula: L( ) 03R 059G 0 B where R G B - are red green and blue component values of pel Among all calculated sums dl the mnmum s found: rl mn dl 4 Smlarly we fnd the mnmum among all sums ra mn da 4 da : The resulted values rl and ra are compared to threshold values TL and TA respectvely If both rl TL and ra TA then pel remans wthout changes Otherwse the current pel s consdered dstorted and s replaced by weghted vector medan calculated nsde the flter s sub-wndow III FILTER PARAMETERS OPTIMIZATION From the descrpton of VMF-DD algorthm presented above t follows that the effcency of ts wor depends on the choce of threshold values TL and TA and also on the choce of vector medan flter weghtng coeffcents w w 9 Thus there s a problem of mentoned above parameters optmzaton relatve to one of restored mage qualty estmaton crtera In our wor ths problem has been solved by the utlzaton of classcal genetc algorthm (GA) [9] whch scheme s shown n fg In order to solve the problem of VMF-DD algorthm parameters optmzaton we use chromosomes representng an element vector whch conssts of real values Frst 9 elements of ths vector represent the values of vector medan flter weghtng coeffcents; the 0th element contans the threshold value TL ; the th element the threshold value TA w w TL TA H 9 Mean square error (MSE) between the orgnal mage and the restored mage s used as a ftness functon MSE s calculated by the followng formula []: where Z N 3 ( Z Y ) Z Y MSE 3N Y - -th component value of -th pel n the orgnal mage and the restored mage respectvely N the total number of pels n an mage Durng the process of genetc algorthm operaton the value of ftness functon gradually decreases whle the number of generatons grows Ths process for test color mages Lena and Arplane [0 ] s demonstrated n fg 3 The analyss of presented dependences shows that durng the process of genetc algorthm operaton and hence durng the growth of the number of generatons the value of ftness functon gradually decreases reachng appromately 0% relatve to ts ntal value And t s possble to acheve ths result after only 5-0 generatons Performed eperments show that optmzed parameters of the flter averaged on several runs of genetc algorthm dffer nsgnfcantly from each other for dfferent test mages Further for VMF-DD flter we use optmzed parameters acqured on test mage Lena IV SIMULATIONS ON COLOR IMAGES The color test mages used are Peppers Lena and Parrots Each vector pel s of 4 bts wth 8 bts for every channel The resoluton of all mages s 5 5 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: medan flter (MF) [3] appled for each color channel; drectonal weghted medan flter (DWM) [5] appled for each color channel; vector medan flter (VMF) [6]; weghted vector drectonal flter (WVDF) [6]; peer group flter (PGF) [8] and the proposed vector medan flter wth drectonal detector (VMF-DD) ISBN: ISSN: (Prnt); ISSN: (Onlne) WCE 0

4 Proceedngs of the World Congress on Engneerng 0 Vol II WCE 0 July London UK Fg GA optmzaton of the VMF-DD parameters 5 5 Best Ftness Value 05 Best Ftness Value Generaton Number Generaton Number (а) (b) Fg 3 Convergence of the GA-VMF-DD optmzaton: (a) test mage Lena (b) test mage Arplane Followng the tradtonal practce of mage qualty evaluaton n the area of color mage processng pea sgnal to nose rato (PSNR) mean absolute error (MAE) and normalzed color dfference (NCD) crteron [7] were used for restored mages qualty assessment Whle both PSNR and MAE are defned n RGB doman NCD crteron s defned n CIE LUV color space [ ] Thus NCD crteron s useful for the evaluaton of color chromatcty dfferences between color vectors and t allows us to quantfy the error n the unformly perceved color space On the other hand MAE and PSNR are commonly accepted n mage processng communty as the measures of sgnal-detal preservaton and nose attenuaton respectvely For convenence the values of NCD crteron were multpled by 0 3 Table I lsts the performance of varous flters appled to the tas of random-valued mpulse nose removal from varous color test mages ISBN: ISSN: (Prnt); ISSN: (Onlne) WCE 0

5 Proceedngs of the World Congress on Engneerng 0 Vol II WCE 0 July London UK TABLE I COMPARISON OF PRESENTED ALGORITHMS USING IMPULSIVE NOISE CORRUPTION p Qualty measure Peppers Lena Parrots MF DWM VMF WVDF PGF VMF- DD MF DWM VMF WVDF PGF VMF- DD MF DWM VMF WVDF PGF VMF- DD PSNR db MAE NCD PSNR db MAE NCD PSNR db MAE NCD PSNR db MAE NCD PSNR db MAE NCD The results presented n table show that the proposed VMF-DD algorthm appled to the problem of randomvalued mpulse nose removal acheves the best performance relatve to any of consdered qualty assessment crtera and for all color test mages used For low mpulse nose probablty p the proposed VMF-DD algorthm wns aganst PGF -4 db n terms of PSNR metrc and provdes 30-60% smaller error relatve to NCD crteron For the ncreased mpulse nose probablty p the values of PSNR metrc measured for mages processed by the proposed VMF-DD flter are - db hgher than for mages fltered by PGF In terms of NCD crteron the advantage of VMF-DD algorthm at the same mpulse nose probablty range s about 0-40% Same dependences are observed concernng MAE crteron Fg 4 shows enlarged fragments of test mage Parrots after ther processng by dfferent algorthms The applcaton of medan flter to each color channel leads to almost complete removal of nose but t also ntroduces sgnfcant mage blur and causes the appearance of artfacts n the form of pale color regons on restored mages After DWM fltraton restored mages turn out to be less blurred but they stll contan some amount of mpulse pels The applcaton of VMF also lead to sgnfcant mage blur Among algorthms that don t contan nose detector hgh qualty of restored mages s demonstrated by WVDF algorthm But after WVDF fltraton separate mpulse nose pels whch are vsble for human percepton reman on an mage 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 ecellng the least n mage edges preservaton and the number of removed mpulses The values of NCD qualty metrc presented n fg 4 corroborate the conclusons drawn after the analyss of vsual data Thus from shown results t s possble to draw a concluson that VMF-DD algorthm appled to randomvalued mpulse nose removal from RGB color mages allows to acheve a sgnfcant ncrease of restored mage qualty n terms of both objectve and subjectve qualty assessment crtera V CONCLUSION The followng conclusons can be drawn based on obtaned smulaton results The proposed VMF-DD flter shows best results for all three test mages evaluated both by classcal qualty metrcs (PSNR and MAE) and by NCD metrc whch s specalzed for color mages The presence of detector allows reducng the level of dstortons ntroduced nto an mage by fltraton algorthm due to the reducton of the number of pels drectly subjected to changes Vsual results of test mages restoraton prove the results of the analyss held on the bass of objectve qualty assessment metrcs Eperments show that computatonal complety of the proposed VMF-DD flter s comparable to that of VMF and WVDF flters and s lower than computatonal complety of DWM and PGF flters Thus the effcency of VMF-DD flter appled to random-valued mpulse nose removal from color mages has been shown ISBN: ISSN: (Prnt); ISSN: (Onlne) WCE 0

6 Proceedngs of the World Congress on Engneerng 0 Vol II WCE 0 July London UK (a) NCD = 35 (b) NCD = 7 (c) NCD = 9 (d) NCD = 4 References [] R Szels Computer Vson: Algorthms and Applcatons Sprnger 00 [] R Luac Computatonal Photography: Methods and Applcatons CRC Press / Taylor & Francs 00 [3] I Ptas A Venetsanopoulos Nonlnear Dgtal Flters: Prncples and Applcatons Boston MA: Kluwer 990 [4] J Astola P Kuosmanen Fundamentals of Nonlnear Dgtal Flterng Boca Raton FL: CRC 997 [5] G Arce Nonlnear Sgnal Processng: A Statstcal Approach John Wley & Sons New Jersey 005 [6] J Astola P Haavsto Y Neuvo Vector medan flters Proceedngs of the IEEE vol pp [7] 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 005 pp [8] 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) 005 pp I-7 - I- 0 [9] I Apalov V Khryashchev A Prorov P Zvonarev Adaptve swtchng medan flter wth neural networ mpulse detecton step Lecture Notes n Computer Scence (LNCS 3696) Sprnger- Verlag 005 pp [0] L Yn R Yang M Gabbouj Y Neuvo Weghted medan flters: a tutoral IEEE Trans Crcuts Systems vol pp 57-9 [] D Kuyn V Khryashchev I Apalov Modfed progressve swtched medan flter for mage enhancement n Proc of the 9th Int Conf on Computer Graphcs and Vson (GraphCon) 009 pp [] 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) 995 vol 4 pp [3] R Chan C Hu M Nolova An teratve procedure for removng random-valued mpulse nose IEEE Sgnal Processng Letters 004 vol pp 9-94 [4] T Chen H Wu Adaptve mpulse detecton usng centerweghted medan flters IEEE Sgnal Processng Letters 00 vol 8 pp -3 [5] Y Dong S Hu A new drectonal weghted medan flter for removal of random-valued mpulse nose IEEE Sgnal Processng Letters 003 vol 4 pp [6] R Luac Adaptve color mage flterng based on centerweghted vector drectonal flters Multdmensonal Systems and Sgnal Processng 004 vol 5 pp [7] K Platanots D Androutsos A Venetsanopoulos Adaptve fuzzy systems for multchannel sgnal processng Proceedngs of the IEEE 999 vol 87 pp 60-6 [8] B Smola Peer group flter for mpulsve nose removal n color mages Lecture Notes n Computer Scence (LNCS 597) Sprnger-Verlag 008 pp [9] D Goldberg Genetc Algorthms n Search Optmzaton and Machne Learnng MA: Addson-Wesley 989 [0] Sgnal and Image Processng Image Database Avalable: [] Koda Lossless True Color Image Sute Avalable: (e) NCD = 94 (f) NCD = 7 Fg 4 Zoomed restoraton results of test mage Parrots : (a) MF output (b) DWM output (c) VMF output (d) WVDF output (e) PGF output (f) VMF-DD output ISBN: ISSN: (Prnt); ISSN: (Onlne) WCE 0