Aptive Geometric Fetures Bse Filtering Impulse Noise in Colour Imges Zhengy Xu #1, Bin Qiu *, Hong Ren Wu #3 Xinghuo Yu #4 # School of Electricl n Computer Engineering, Pltform Technologies Reserch Institute, RMIT University VIC 3001, Austrli 1 zhengy.xu@rmit.eu.u 3 henry.wu@rmit.eu.u 4 x.yu@rmit.eu.u * Fculty of Informtion Technology, Monsh University, VIC 3800, Austrli bin.qiu@infotech.monsh.eu.u Abstrct An Aptive geometric fetures bse filtering (AGFF) technique with low computtionl complexity is propose for removl of impulse noise in corrupte color imges. The effective n efficient etection is bse on geometric chrcteristics n fetures of the corrupte pixel n/or the pixel region. A progressive restortion mechnism is evise using multi-pss non-liner opertions. Through extensive experiments conucte using wie rnge of test color imges, the propose filtering technique hs emonstrte superior performnce to tht of well-known benchmrk techniques, in terms of objective mesurements, the visul imge qulity n the computtionl complexity. I. INTRODUCTION Non-liner filtering techniques hve been extensively reserche in the lst ece ue to their importnce in restortion of noise corrupte color imges. The mein filter is usully use to remove impulse noise [1, [14. The most well known vector filters for color imge enoising inclue the vector mein filter (VMF) [, n the irectionl istnce filter (DDF) [3. Unlike the itive noise tht contmintes ll imge pixels, the impulse noise estroys only smll portion of n imge n leves other pixels noise free. Detection bse vector filtering techniques such s the ptive vector mein filter (AVMF) [6, the ptive vector LUM smoother (AVLUM) [8, moifie weighte vector mein filter (MWVM) [9, n the ptive selection center weighte vector irection filter (ACWVDF) [10, were specilly esigne to remove the impulse noise from color imges. They utilize series of weighte mein vector filters to perform the binry noise etection n switch the output between n ientity filter n weighte mein vector filter ccoring to the etection results. In this pper, fst ptive geometric fetures bse filtering technique (AGFF) with low computtionl complexity is propose for restortion of igitl color imges corrupte by the impulse noise. This new technique uses set of novel noise etection criteri for etection of the corrupte pixels, which re bse on two-imensionl geometric n imension fetures of the noisy pixel or the noisy region of the imges. Bse on the result of the estimtion, n ptive progressive filtering opertion is employe in combintion with optimize imension n shpe of processing winows. It is very useful for online pplictions for fst suppression of impulse noise in meium- n lrge-size color imges. The orgniztion of this pper is s follows. Section II resses the principles of the propose filtering technique. Experimentl results re presente in Section III. Finl conclusions re rwn in Section IV. II. PRINCIPLE OF AGFF TECHNIQUE The fst ptive geometric feture bse filtering technique (AGFF) is introuce s follows, for the restortion of colour imges corrupte by the impulse noise. A. Dimensionl n Geometric Fetures of the Impulse Noise A mjor problem in restortion of color imges to te is the estruction of etile imge structures ue to inbility of enoising filters to istinguish cluster of corrupte pixels from cluster of pixels presenting fine (etile) imge structures n the incorrect removl or moifiction of pixel segments. This section proposes novel technique, which etects, exctly n efficiently, impulses in color imges. Creful exmintions of vriety of color imges corrupte impulse noise moels revel tht most of uncorrupte pixels or pixel regions in nturl color imge lwys emonstrte certin egree of smoothness. This mens tht the color intensities of 8-neighbors[1 of pixel lwys chnge grully in ll irections (e.g., in smooth re), n t lest grully chnge in one (ege) irection (e.g., in bounry re). In contrst with norml pixels of imges, impulse noise corrupte pixels lwys show their fetures s n isolte spot or cluster by its very un-hrmonic colors, shpes n sizes compre with those of its neighborhoo. It is observe tht lmost ll impulses only hve shrp step eges n, in contrst, lmost no uncorrupte object hs this type of eges in its vicinity. The shpes of the noise regions my be n isolte point, short thin line, cross of two short thin lines or other smll roun-shpe blocks. In other wors, the shpe n the 978-1-444-95-1/08/$5.00 008 IEEE 47 MMSP 008 Authorize license use limite to: RMIT University. Downloe on July 01,010 t 04:4:37 UTC from IEEE Xplore. Restrictions pply.
size of impulse noise corrupte pixels epen on the noise rtio. Accoring to the bove observtion n nlysis of color, shpe n sizes of impulse noise corrupte pixels/regions, n the type of eges which form the borers of the noise regions, novel impulse noise etection metho is propose here bse on two imensionl geometric fetures of the impulses, in ste of the one imensionl rnk orere sttisticl informtion use by other well-known filtering techniques, to etermine more exctly n efficiently if ech pixel in color imge is corrupte or clen. One of the geometric properties of the impulse noise is the ege feture of its bounry. An ege cn be efine s locl iscontinuity in illumintion function n the ege orienttion is efine s eges of n octgonlly shpe object whose mplitue is higher or lower thn its bckgroun [1. Therefore, the propose criteri for ientifying the ege feture roun the pixel re bse on two types of erivtives, which re pproximte by ifferences in igitl color imges. Given tht C c = ( c c ) 1 c H,1 c } enote the pixel { 1, 1 W coorintes of color imge, where H n W re the height n with of the imge, respectively. If T x( c ) = [ xr (, xg (, xb ( is the illumintion function of color imge, the two specil types of erivtive re enote s x( n x(. x( is efine s follows, 1 1 i n, j n (1) 3 3 i + n, 4 4 j + n where, n >0, n the efult vlue of n is 1. When erivtive is only consiere in the igonl irection, x is efine s follows, 1 1 1 i n, j n i + n, j n () 3 3 3 i n, j + n 4 4 4 i + n, j + n where, n >0, n the efult vlue of n is 1. The enote erivtives, x( n x( will be use to mesure the ege feture (shrpness) n other geometric properties to etermine whether the center pixel t c ( j) is corrupte or not in the propose filtering technique. In etecting n removing impulse noise, filter cn mke ifferent types of mistkes. Type I error (miss) occurs when there is corrupte pixel, which the filter oes not etect. Type II error (flse lrm) hppens when the filter etects n impulse noise pixel, which is ctully clen. When the filter removes n impulse noise n replces it with vlue etermine by certin restortion strtegy, Type III error (over- or uner-correcting error) is efine s the ifference between the resultnt vlue fter restortion process n the true pixel vlue s the noise-free pixel ws. The propose technique, similr to other well-known benchmrk techniques n the so-clle switching filters [5,6,11,18, consists of two components, i.e., impulse etection n impulse removl. A key component of the propose filtering technique is novel impulse etection scheme bse on the two imensionl geometric informtion of the corrupte pixels. The novel criteri use by the propose filtering technique for noisy pixel etection re bse on combintion of the twoimensionl ege, geometric n size fetures of the noisy pixel/ region in the imges. They eprt from tritionl noise etection techniques use by other existing filters [5,6,,13, which only use some properties of the ege of noisy pixel or one-imensionl rnk orere sttisticl informtion roun the noisy pixel. First, we efine the ege feture-ientifiction threshol, T e, which represents the vlue of erivtive to istinguish the shrp step eges from other types of eges. Since very short thin lines usully form the impulse noise pixels, the length of line is lso use s feture to istinguish short noise line from fine line in color imges. The length threshol my be efine s T l ccoring to the noise rtio. Secon, in terms of the pixel coorintes of color imge, C, set of corrupte pixels is efine s S 1 = {c (( x( < (- T e )) ( x( <((- T e ))) (( x( > T e ) ( x( > T e )), N = {1,, 3, T m }, i n N, i=1,,4) (3) where T m = (T l +1)/. The efult vlue of T m is. This corrupte pixel set inclues iniviul impulse pixels, slnt noise lines with one-pixel with n the pixels of the lines only jcent to ech other in igonl irection within the efine length of T l. Thir, set of corrupte pixels, which inclue iniviul impulse pixels, stright noise lines with one-pixel with n the pixels of the lines being only 4-connecte[1 to ech other within the efine length of T l, is efine s S = {c (( x( < (-T e )) ( x( <(- T e ))) (( x( > T e ) ( x ) ( c > T e )), N = {1,, i 3, T m }, n N, i=1,,4} (4) where T m = (T l +1)/. The efult vlue of T m is. Finlly, set of corrupte pixels, which inclue noisy pixels/regions within 3-pixel with in ny irection except the noisy pixels c S 1 S, is efine s S 3. If S = {c (( x( < (-T e )) ( x( <(- T e ))) (( x( > T e ) ( x( > T e )), n = n = or 3 } (5) where the efult vlue for n n n is in (5). Thus, S 3 cn be represente s S 3 = S (S 1 S ) (6) 48 Authorize license use limite to: RMIT University. Downloe on July 01,010 t 04:4:37 UTC from IEEE Xplore. Restrictions pply.
where T m = for S 1 n S in (8). Since n impulse noise rtio p <1, n C, where n = 3, in the current cse. T e in I S i i=1 (3), (4) n (5) coul be set in ifferent vlues. Since the shpes n the sizes of corrupte pixels epen on the noise rtio, n the restortion of the corrupte pixels requires the sttisticl informtion bout the noise ensity, the estimtion of noise rtio n noise type is importnt in orer to minimize both Type I n Type II errors. The criteri for clssifying the egree of impulse noise in the propose filtering technique re the rtio n the size of the lrgest noise corrupte region, n the vles of corrupte pixels. The strtegy of the progressive restortion for the propose filtering technique is first to restore corrupte iniviul pixels or noise regions of smll size. If it me either Type II or Type III error, it shoul not introuce ny new impulse noise region of bigger size thn the existing ones. Then, further opertions re crrie out roun big noise corrupte regions, to restore res of the imges ssocite with big noise regions more relibly. In orer to mke use of merits of the mein filter n to voi its rwbcks (cusing number of rtifcts for uncorrupte pixels) [14, etection scheme escribe in this section is employe before the mein filtering for restortion. As result, the propose restortion metho bse on the restricte mein cn keep the imge unchnge when the filter processing winow moves cross the uncorrupte imge etils. A novel progressive multi-pss filtering lgorithm/process with low computtionl complexity is propose, in orer to implement the principles of propose filtering technique. The restortion technique use in this work is bse on the moifie mein where the estruction of uncorrupte imges (i.e., Type II error) increses with the increse of the processing winow size, while ecreses with the increse of the ege feture threshol T e. In orer to chieve the best performnce of the propose filter, in terms of both visul qulity n objective mesurements, the esign of the processing winows hs to epen on the shpes n sizes of corrupte pixels/pixel regions. A principle for esigning the following opertions is to use s smll size of the winows n s less number of the psses s possible, s long s the impulse noise cn be remove (to ensure perceptul imge qulity). The number of psses ws etermine to remove noise region bse on the worst cse scenrio within the estimte mximl size of the noise region. Actully, the ptive filter is very robust n tolernt to the estimtion evitions for impulse noise rtio of corrupte imges. For the propose filter (AGFF), in contrst with other filters, only comprison n ition/subtrction opertions re involve, n the computtionl complexity of the AGFF is minly epenent on the restortion opertions. Although the propose filter uses multi-pss opertion n the time consume by the filter is epenent on the noise rtio, the computtionl complexity of its lgorithm is ctully very low. III. EXPERIMENTS Without losing generlity, the recommene the efinition of the corrupte pixel sets in color imges were teste by experiments using typicl test imges, which inclue ifferent types of rel-life imges [17. Tble I presents the experimentl results for etection of rnom impulse noise using S 1, S n S 3 on vriety of originl clen (without corruption) rel life imges, which inclue well-known stnr test imges such s, Airplne, Bots, Flower, Girl, Golhill, Moon, Pen, Soccer, Zel, n Ycht with n imge resolution of 500x36 or 51x51 or 787x576 or 70x576 or 768x51 or 1986x1986 pixels. In Tble 1, FA (flse lrm) stns for Type II error, n FA(S 1 ), FA(S ) n FA(S 3 ) enote flse lrm rtios (the number of flse lrm to the number of pixel for the teste color imge) by S 1, S n S 3, respectively. The flse lrming rtios re very low for the test imges, especilly for the high resolution color imges. The propose filtering technique hs been evlute by n extensive rnge of tests n its performnce is compre with number of prior-rt filtering techniques in the re of removing impulse noise from color imges. Severl objective criteri re use in the tests to mesure the istortion in restore imges. The objective criteri inclue the Men Squre Error (MSE) n the Men Absolute Error (MAE) efine in the RGB color spce [4,10, n the Normlize Color Difference (NCD) [4,10 which mesures the color istortion in perceptul uniform CIELUV color spce. All impulse corruptions were generte ccoring to the noise moel in [11, using the rnom impulse noise or the slt-n-pepper noise, n noise rtio p I [11 vrie from 0% to 0%. The evlution of impulse suppression ws conucte using three 4-bit RGB imges [17, Len, Prrots n Peppers, with imge resolutions of 56x56, 51x51, n 1536x104 pixels, respectively, which hve been wiely use by prior-rt impulse filtering techniques ue to their representtive color chrcteristics n imge structure. The filters re use in the impulse suppression tests inclues the stte-of-the-rt techniques recently evelope for the impulse n the mixe noise suppression, incluing AVMF, MWC[16, SAA[19, AVLUM, ACWVDF, SCWVDF[10, ACWMF[15, SWVDF[0, HBTM[7, SAHVF[5 n PBTVM[11. Besies the excellent objective performnce mesurements, the propose filter lso chieve consistently better performnce in perceptul imge qulity thn other impulse filtering techniques. Figures 1 hve emonstrte the performnce of the propose AGFF compre with other typicl n stte-of-the-rt techniques. A test imge Len with 0% rnom impulse corruption generte by noise moel in [11 ws selecte to revel the etil preservtion cpbility of the propose filter (see Fig.1) 49 Authorize license use limite to: RMIT University. Downloe on July 01,010 t 04:4:37 UTC from IEEE Xplore. Restrictions pply.
TABLE I THE PERFORMANCE OF THE PROPOSED THE DEFINITION OF THE CORRUPTED PIXEL SETS FOR DETECTING RANDOM IMPULSE NOISE IN A VARIETY OF ORIGINAL COLOR IMAGES Imges Airplne Bots Flower Girl Golhill Prrots Moon Pen Soccer Ycht Zel FA(S 1 )10-3 0.009 0.003 0.001 0.001 0.034 0.09 0.06 0.000 0.003 0.007 0.003 FA(S )10-3 0.00 0.051 0.019 0.018 0.119 0.076 0.1 0.05 0.094 0.104 0.01 FA(S 3 )10-3 0.056 0.007 0.008 0.00 0.047 0.06 0.081 0.056 0.065 0.064 0.0 TABLE II The impulse suppression performnce of the propose AGFF filter compre with other techniques. () Color imge Peppers corrupte by ifferent levels of rnom impulse[11. Filters 5% 10% 0% MSE MAE NCD MSE MAE NCD MSE MAE NCD SAA 17.5 0.511 0.0045 33.5 0.89 0.0086 73.0 1.78 0.0185 AVLUM.1 0.465 0.004 44.6 0.96 0.0083 93. 1.875 0.0178 HBTM 19.3 0.466 0.0039 36.4 0.880 0.0078 73.4 1.70 0.017 AVMF 5.6 0.556 0.0045 38.8 0.999 0.0089 89. 1.98 0.0189 ACWVDF 1.1 0.693 0.007 59.7 1.1 0.017 180..774 0.096 SCWVDF 0.5 0.666 0.0070 5.8 1.110 0.010 145.5.361 0.054 SWVDF 18.1 0.96 0.014 43.1 1.381 0.0196 13.5.615 0.0314 PBTVM 16.8 0.476 0.0044 3.5 0.869 0.008 65.4 1.65 0.0167 SAHVF 9.8 0.946 0.0074 48.8 1.40 0.0104 74.9.191 0.0171 AGFF 18.0 0.451 0.0041 30. 0.804 0.0054 45.9 1.30 0.0088 (B) COLOR IMAGE PARROTS CORRUPTED BY DIFFERENT LEVELS OF SP(SALT-AND-PEPPER) IMPULSE. Filters 5% 10% 0% MSE MAE NCD MSE MAE NCD MSE MAE NCD AVMF.659 0.540 0.0004 3.34 0.614 0.0005 5.16 0.769 0.0008 DDF 3.95 0.609 0.0004 4.496 0.668 0.0005 7.65 0.81 0.0008 HBTM 0.586 0.061 0.0001 1.06 0.11 0.000.434 0.55 0.0004 MWC.731 0.61 0.0004.5 0.393 0.0007 4.9 0.517 0.0011 FAGFF 0.346 0.040 0.0001 0.63 0.081 0.000 1.368 0.169 0.0004 ) Originl imge Len b) 0% rnom corruption DDF output ) HBTM output e) ACWMF output f) AGFF output Fig. 1. The reconstruction of propose filter compre with other techniques, where the test imge Len is corrupte by rnom impulse with p I =0% [11. 50 Authorize license use limite to: RMIT University. Downloe on July 01,010 t 04:4:37 UTC from IEEE Xplore. Restrictions pply.
IV. CONCLUSION A geometric fetures bse filtering technique with very low computtionl complexity is propose for removing impulse noise in corrupte igitl color imges. The specil contribution of the propose filtering technique is its novel impulse etection, which uses two imensionl geometric fetures (shpe n ege type) n size of the impulse pixel/pixel region, in ste of one imensionl sttisticl informtion, to ientify the impulse in more exct n efficient mnner. The other novelty of the propose filtering technique is its progressive ptive restortion mechnism to recover the corrupte pixels step by step in relible wy through multi-pss process with low computtionl complexity. Through extensive experiments conucte using wie rnge of nturl color imges, the propose filtering technique hs emonstrte superior performnce to tht of well-known benchmrk techniques, in terms of stnr objective mesurements, visul imge qulity n the computtionl complexity, in removing ifferent types of impulse noise commonly consiere in color imge restortion. The types of impulse noise inclue the slt-npepper n the rnom impulse noise. It is very useful for online pplictions to suppress impulse noise especilly for meium n lrge size color imges. REFERENCES [1 I. Pits n A. N. Venetsnopoulos, Nonliner Digitl Filter: Principles n Applictions. Norwell, MA: Kluwer, 1990. [ J. Astol, P. Hvisto, n Y. Neuvo, Vector mein filter Proc. IEEE, vol. 78, no. 4, pp. 678-689, Apr. 1990. [3 D. G. Krkos n P. E. Trhnis, Combining vector mein n vector irection filters: the irectionl-istnce filter in Proc. IEEE int. Conf. Imge Processing (ICIP 95), vol. 1, Wshington DC. Oct. 1995, pp. 171-174. [4 R. Lukc n K.N. Pltniotis, A txonomy of color imge filtering n enhncement solutions, In `Avnces in Imging n Electron Physics, (e.) P.W. Hwkes, Elsevier, vol. 140, pp.187-64, 006. [5 Z. M, H. R. Wu, n B. Qiu, An structure ptive hybri vector filter for the restortion of igitl color imges, IEEE Trns. Imge Processing, vol. 14, no. 1, pp 1990-001, Dec. 005. [6 R. Lukc, Aptive vector mein filtering, Ptt. Recogn. Lett., vol. 4, no. 1, pp. 1889-1899, Aug. 003. [7 Z. M n H. R. Wu, A histogrm bse ptive vector filter for color imge restortion, in Proc. IEEE ICICS-PCM 03 Singpore, Dec. 15-18, 003, pp. 1A3.4.1-5. [8 R. Lukc n S. Mrchevsky, Aptive vector LUM smoother, in Proc. IEEE int. Conf. Imge Processing, vol. 1, Oct. 001, pp. 878-881. [9 B. Smolk, M. Szczepnsk K. N. Pltniotis n A. N. Venetsnopoulos, On the moifie weighte vector mein filter, in Proc. IEEE int. Conf. Digitl Signl Process. Vol. 1, Sntorin Greece, July 00, pp. 939-94. [10 R. Lukc, Aptive colour imge filtering bse on center weighte vector irection filters, Multiimentionl Syst. Signl Process, vol.15, no., pp. 169-196. Apr. 004. [11 Z. M, H. R. Wu, D. Feng, Prtition bse vector filtering technique for suppression of noise in igitl colour imges, IEEE Trns. on Imge Processing, vol. 15, no. 8, pp 34-34, Aug. 006. [1 Miln Sonk, Vclv Hlvc n Roger Boyle, Imge processing, Anlysis, n Mchine Vision, Brooks/Cole, 001. [13 S. Schute, V. D. Witte, M. Nchtegel, D.V. Weken n E.E. Kerre, Fuzzy two-step filter for impulse noise reuction from colour imges IEEE Trns. on Imge Processing, vol. 15, no. 11, pp 3568-3579, Nov. 006. [14 Rymon H. Chn, Chung-W Ho n Mil Nikolov, Slt-npepper noise removl by mein-type noise etectors n etilpreserving regulriztion IEEE Trns. on Imge Processing, vol 14, no. 10, pp 1479-1485, Oct. 005. [15 T. Chen n H. Wu, Aptive impulse etection using centerweighte mein filter, Signl Processing Lett., Vol.8 no. 1pp. 1-3, Jn. 001. [16 E. S. Hore, B. Qiu, n H. R. Wu, Preiction bse imge restortion using multiple winow configurtion, Opt. Eng., vol.41, no. 8 pp. 1855-1865, Aug. 00. [17 http://www.hlevkin.com. [18 P. Ng n K.K. M, A Switching Mein Filter with Bounry Discrimintive Noise Detection for Extremely Corrupte Imges", IEEE Trnsctions on Imge Processing, vol. 15, no. 6, pp. 1506-1516, June 006. [19 B. Smolk, A. Chyzinsk K. Wojciechowsk K. N. Pltniotis, n A. N. Venetsnopoulos, Self-ptive lgorithm for impulsive noise reuction in color imges, Ptt. Recogn., vol. 35, no 8, pp. 1771-1784, Aug 00. [0 R. Lukc, B. Smolk, K. N. Pltniotis, n A. N. Venetsnopoulos, Selection weighte vector irectionl filter, Comput. Vis. Imge Unerst., vol. 94, no. 1 3, pp. 140 167, Apr. 004. 51 Authorize license use limite to: RMIT University. Downloe on July 01,010 t 04:4:37 UTC from IEEE Xplore. Restrictions pply.