Detailing a Quantitative Method for Assessing Algorithms to Remove Back-to-Front Interference in Documents

Transcription

1 Journal of Universal Compuer Science, vol. 14, no. 2 (2008), submied: 15/6/06, acceped: 17/11/07, appeared: 28/1/08 J.UCS Deailing a Quaniaive Mehod for Assessing Algorihms o Remove Back-o-Fron Inerference in Documens Rafael Dueire Lins (Universidade Federal de Pernambuco, Recife, Brazil rdl@ufpe.br) João Marcelo Mone da Silva (Universidade Federal de Pernambuco, Recife, Brazil joaommsilva@gmail.com) Fernando Mário Junqueira Marins (Universidade do Minho, Braga, Porugal fmm@di.uminho.p) Absrac: Documens wrien on boh sides on ranslucen paper make visible he ink from one side on he oher. This arefac is called back-o-fron inerference, bleeding or showhrough. The direc binarizaion of documens wih such inerference yields unreadable documens. The lieraure presens several algorihms for suiably removing such arefac. This paper presens a quaniaive mehod o assess algorihms o remove back-o-fron inerference. Keywords: Documen engineering, Back-o-fron inerference, Show hrough, Bleeding Caegories: H Inroducion Whenever a documen is yped or wrien on boh sides and he opaciy of he paper is such as o allow he back prining o be visualized on he fron side, yielding differen hues of paper and prining whenever compared o documens wrien on a single side a shee of he same paper wih he same ink. This phenomenon, firs addressed in he lieraure by [Lins, 95], was called back-o-fron inerference. If he documen is scanned eiher in rue-color (Figure 1) or gray-scale (Figure 2) he human eye is able o filer ou ha sor of noise keeping documen readabiliy. The direc binarizaion of such documen overlaps he wrien or prined par of boh sides producing an unreadable documen for he human reader and drasically degrading he performance of auomaic ools such as OCRs. Thus, i is imporan o find beer segmenaion echniques o suiably solve ha problem. Binarized images (black and whie images) claim less sorage space, allow for faser nework ransmission, and are suiable o be processed by mos commercial OCR ools. Image processing environmens (such as Jasc Pain Shop Pro [Adobe, 07]) offer a grea variey of binarizaion filers. However, he use of such sofwares requires a specialized operaor and ha is no feasible o handle large quaniies of documens. Besides ha, he palee reducion algorihms provided by sandard

2 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod commercial ools whenever applied o documens wih back-o-fron inerference yield unreadable images, even for humans. Figure 1 provides an example of a documen wih back-o-fron inerference and Figure 2 is he gray-scale version of he same documen. The binarized version of his documen generaed by he direc applicaion of he binarizaion algorihm by using Jasc Pain Shop Pro version 8 (Palee componen: Grey values, Reducion componen: neares color, Palee weigh: non-weighed) is compleely unreadable, as one may observe in Figure 3. Figure 1: Hisorical Documen wih back-ofron inerference. Figure 2: Gray-scale version of Figure 1. Figure 3: Binarized documen of Figure 1. In a documen such as he one presened in Figure 1, one expecs o find hree color clusers corresponding o he ink in he foreground, he paper background and he respassed ink (he back-o-fron inerference). Unforunaely, despie he effors of several researchers in over a decade of work, no image represenaion provided such clusering o allow he easy filering ou of he back-o-fron inerference. Several papers in he lieraure addressed he back-o-fron inerference problem. Some auhors use waerflow models [Oha, 05], oher researchers have used wavele filering [Tan, 02], bu he echnique of mos widespread used is hresholding [Kavallieraou, 05], [Leedham, 02] and [Wong, 01]. The mos successful echniques for filering ou back-o-fron inerference are based on he enropy [Abramson, 63] of he grey-scale documen [Mello, 00] and [Mello, 02]. Alhough recen advances were made in finding efficien algorihms ha yield good qualiy images [Silva, 06], a final soluion o he filering of back-o-fron inerference is sill sough off. Visual inspecion of he filered images provides a weak quaniaive assessmen of he performance of he algorihms under comparison. Analyzing he qualiy of images produced by filering algorihms is far from being a rivial ask. Subjeciviy mus be avoided by every means. Thus, a quaniaive mehod o measure he qualiy of algorihms for binarizing documens wih back-o-fron inerference is inroduced

3 268 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod... here. The mehod presened herein generalizes and provides beer comparison grounds han he one presened in [Lins-b, 06], deailing furher he resuls presened in reference [Lins, 07]. This aricle is organized as follow. Secion 1 presens his inroducion. Secion 2 presens eigh hreshold-based algorihms used o demonsrae he mehod described in secion 3. The resuls obained are discussed and analysed in secion 4. Finally, secion 5 presens he conclusions of he mehod inroduced herein and draws lines for furher work. 2 Threshold Techniques The survey paper by Sankur and Sezgin [Sankur, 04] presens a comprehensive overview and comparison of hresholding algorihms, clusering hem according o heir naure. Tha survey does no address he back-o-fron inerference, however. From he almos fory algorihms presened six schemes have shown suiable o work in such documens: Pun [Pun, 81], Kapur-Sahoo-Wong [Kapur, 85], Johannsen-Bille [Johannsen, 82], Yen-Chang-Chang [Yen, 95], Wu-Songde-Hanquing [Wu, 98], and Osu [Osu, 79]. The firs five algorihms are based on he enropy of he image, whereas he las one makes discriminaor analysis. Those six algorihms were no designed o filer back-o-fron inerference. Besides hose algorihms, wo algorihms based on enropy ha were creaed in he scope of he Nabuco Projec [FUNDAJ, 07] o filer ha inerference are presened: he Mello and Lins s algorihm [Mello, 00][Mello, 02] and he Silva, Lins and Rocha s algorihm [Silva, 06]. The use of gray-scale images wih 256 levels as an inermediae sep owards image binarizaion has shown o be a valuable simplificaion. Thus, he firs processing sep is generaing grey-scale documens from he rue-color ones by using he sandard equaion o calculae he gray level value of he new pixel: grey = 0.299r g b where r, g, and b are he red, green and blue values of he original pixel. In general, enropy-based algorihms ake he image hisogram and normalize each of is enries by he oal number of pixels in he image, yielding a disribuion of probabiliies provided by relaive frequencies. Thus, ni pi =, 0 i 255 N P p i i0 where n i is he number of pixels wih grey level i (0 o 255), N is he oal number of pixels in he image, {p 0, p 1,, p 255 } is he probabiliy disribuion of he pixel graylevels aking ino accoun heir relaive frequencies, and P is he adding of all probabiliies up o enry. All of he algorihms presened here were implemened in sandard C using he dev-c++ v program. (1) (2) (3)

4 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod Pun s Algorihm In he algorihm proposed by Pun [Pun, 81], he gray levels are considered like saisically independen 256-symbol source. Pun considers he raio of he a poseriori enropy wih he source enropy where H b and H w are: H '( ) =Plog( P) (1 P)log(1 P) H( ) H ( ) H ( ) b w (4) (5) and p(i) = p i given by equaion (2). Pun shows ha where H ( ) b H ( ) w i0 255 i1 p( i)log( p( i)) p( i)log( p( i)) H'( ) log P ( ) log[1 P ( )] Fe( ) = + (1 ) H log[max( p,..., p )] log[max( p,..., p )] H b ( ) H (6) (7) (8) (9) The hreshold is obained by he value ha saisfies he equaion (9), where is he argumen ha maximizes Fe(). 2.2 Kapur, Sahoo and Wong The algorihm by Kapur, Sahoo and Wong [Kapur, 85] considers he foreground and background images as wo disinc sources, such ha whenever he addiion of he wo enropies reach a maximum, is argumen reaches he opimal value. The disribuion of he objec A and he disribuion of he background B are given by: pi A: p( i), P 0 i pi B : p( i), 1 i P The values of he enropies H w and H b are calculaed hrough equaions (6) and (7), wih p(i) given by equaions (10) and (11). (10) (11)

5 270 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod Johannsen and Bille The algorihm proposed by Johannsen and Bille [Johannsen, 82] aims a minimizing he funcion: S () = S 1 b() + Sw() = log( P) + [ Ep ( ) + EP ( 1) P ] + + log(1 P 1 1 ) + [ E( p) (1 ) (1 ) + E P P ] where E(p)p.log(p), and p i and P are provided by equaions (2) and (3), respecively. The value of ha minimizes S() is is opimal value. 2.4 Yen, Chang and Chang The algorihm by Yen, Chang and Chang [Yen, 95] follows he same idea as he one by Kapur and his colleagues in respec o he foreground and background disribuions. An enropic correlaion is defined as p i p i TC() = Cb() + Cw() =log log i= 0 P i= + 1 1P and he hreshold is he argumen ha maximizes ha expression. The funcions C b () and C w () are known as Ranyi enropy [MahWorld, 07], wih = Wu, Songde and Hanquing This algorihm calculaes he same enropies evaluaed by he Kapur, Sahoo and Wong s algorihm. Bu, insead of maximizing he addiion of heses, Wu, Songde and Hanquing [Wu, 98] minimize he difference given by: F() = H () H (). b w (12) (13) (14) 2.6 Osu s Algorihm The algorihm by Osu [Osu, 79] does no belong o he class of algorihms based on enropy. I is included here because i is one of he mos ofen used algorihms in image segmenaion. Osu s algorihm makes discriminaor analysis for defining if a grey level will be mapped ino objec or background informaion. This algorihm works o maximize he beween-class variance () given by: where ( ) ( )( ) 2 () () 2 1 () 2 B = P b T + P w T (15) () b p p, i = i, 255 i w() = i i= 0 P i=+ 1 1P 255 T = ip.. i i= 0 (16) The hreshold is he argumen ha maximizes he beween-class variance ().

6 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod Mello and Lins The algorihm by Mello and Lins [Mello, 00][Mello, 02] looks for he mos frequen gray level of he image and akes i like iniial hreshold o evaluae he values H b, H w and H by equaions (6), (7) and (5), respecively, bu he enropies mus be calculaed wih he logarihm o he base N. The enropy H deermines ow weighs m b and m w : If H 0.25, hen m w = 2 e m b = 3. If 0.25 < H < 0.30, hen m w = 1 e m b = 2.6. If H 0,30, hen m w = 1 e m b = 1. And he hreshold is direcly calculaed by 256( m H m H ). * b b w w (17) (18) 2.8 Silva, Lins and Rocha The main idea behind his algorihm is o consider he hisogram disribuion as he 256-symbol source (a priori source) disribuion. One may assume he hypohesis, as in Pun [Pun, 81], ha all symbols are saisically independen. In he case of real images one knows ha his hypohesis does no hold. However, his largely simplifies he algorihm and yields good resuls. Thus, he enropy of he a priori source is given by: 255 H = pilog 2( pi) i= 0 where p i is provided by equaion (2). As he resuling image is binarized, he disribuion of is hisogram may be seen as a disribuion of a binary source (a poseriori source). The enropy of he a poseriori source is given by: H' ( ) h( P ) (19) (20) where h(p)p.log 2 (p)(1p).log 2 (1p) is he enropy funcion [Abramson, 63] and P is provided by equaion (3). One makes an exension of a binary source o represen wihou losses all he 256 symbols of he a priori source. This new binary source is called a priori binary source. The value of he enropy of his new source is given by: H H H apriori = = binary source log (256) 8 One looks for a value of such ha he enropy of he a poseriori source were as close as possible o he value of he enropy of he a priori binary source, ha is, one looks for he following equaliy: H' ( ) 2 H a priori binary source This argumen maps he disribuion of he a poseriori source ono he disribuion of he a priori binary source. (21) (22)

7 272 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod... Applying equaions (20) and (21) o (22), one obains H h( P ) (23) 8 One should consider he behavior of he enropy funcion. For ha purpose one mus ake ino accoun ha he arge images are of documens, wih a much higher frequency of background (paper) pixels han objec (prin or wriing) ones. Thus, i is reasonable o work wih he argumen of P wihin inerval [0, 0.5]. In his inerval, he enropy funcion is injecive, hus here is only one value of P ha saisfies he equaion, unless if p i is zero. In such case i would no maer if he calculaed limi were i or i 1. The arge of he proposed algorihm is o filer ou he back-o-fron inerference in binarizaion. Due o is feaures, he inerference raises he value of he a priori source s enropy. A loss facor (H a priori binary source ) (24), experimenally deermined, is inroduced o reduce he presence of he inerference. 3 Hapriori if Hapriori < bs.. bs.. ( Hapriori) = (24) bs.. Ha priori 0.2 if Ha priori 0.7 bs.. bs.. Thus, he following relaion holds: H'( ) ( H ) H a b. priori s. b a. priori s. Once he bases of he algorihm are presened, is seps are now deailed: (25) 1. one calculaes H, he enropy of he image hisogram. 2. one scans he levels, calculaing of each of hem he disribuions {P, 1 P }, while P 0.5, and he enropy associaed wih ha disribuion H ()=h(p ); 3. one deermines he opimal limi ha minimizes e() given as: H'( ) e( ) ( H /8). H 8 (26) 3 Assessmen Mehod In his secion a new mehod o assess algorihms used o binarize documen images wih back-o-fron inerference is presened. The proposed mehod is divided ino wo seps: Synhesis of image wih inerference: based on wo images wihou back-ofron inerference. Calculaing he qualiy facors: hree qualiy facors ha ogeher inform he qualiy of binarized documen are proposed.

8 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod Synhesis of Images wih Inerference This secion presens how es images wih back-o-fron inerference are generaed. The basic idea is o inroduce such inerference in a well conrolled way, hus one is able o really know which pixels ough o be removed and which should no be removed in he filered image. The mismaching pixels from he reference and filered images will be used o calculae hree qualiy facors of he algorihm, allowing a fair comparison beween he resuls obained. As in [Lins-b, 06], he image generaion process is deailed. Fron (S) Back (I) Figure 4: Documens wihou back-o-fron inerference from Nabuco s beques. 1) The firs sep is ake wo 256-grayscale images wihou back-o-fon inerference, such as he ones presened in Figure 4. S he image ha plays he role of he fron of he documen (signal image); and I he image ha plays he role of back (back-o-fron inerfering image). 2) The second sep is o synhesize a hird image, called G, by overlapping he S image wih a d version of he I image, as follows: One s he I image, producing he I image given by i l i( m, n), l, if l 255 ( m, n), 255, if l 255 (27) where he i(m,n) and i (m,n) are he inensiy values in he pixel (m,n) from he I and I images, respecively, and is he brighness offse applied. Noice ha he maximum value of he sum is 255. Finally, he overlapping process merges he S and I images, selecing he darker pixel beween s(m,n) and i (m,n), hen,

9 274 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod... g s( m, n), if s( m, n) i ( m, n) ( m, n), i ( m, n), if s( m, n) i ( m, n) (28) where s(m,n), i (m,n) and g (m,n) are he inensiy values in he pixel (m,n) from he S, I and G images, respecively. To assess he filering capabiliy of algorihms assumes values from 0 o 255. The effec of variaion on he final synhesized documen generaed from he documens presened in Figure 4 wih I mirror-refleced is presened in Figure 5. = 0 = 30 = 50 = 70 = 100 = 130 = 150 = 170 Figure 5: Pieces of synhesized images for differen values. 3.2 Calculaing The Qualiy Facors Firs one akes as reference he S (manual) image, which is obained from S by manually searching a hreshold ha yields a good qualiy binary image (vide Figure 6). Afer, one binarizes he G images by he applicaion of he algorihm k, generaing he (k) G images. Than, one calculaes he hree qualiy facors for each G image, in (k) oher words, each algorihm will have hree qualiy facor values for each value. Before he definiions of he qualiy facors one needs o define ex area and non ex area : The Tex Area is he area formed by ex in he reference image, in oher (manual) words, i is he black pixels in he S image. The number of pixels in his area is defined as N. "ex area" The Non Tex Area is he area formed by he par of he reference image (manual) ha has no ex, in oher words, i is he whie pixels in he S image. Now one defines he hree qualiy facors: a) Qualiy Facor 1: Tex Error The Tex Error of he G image is defined as (k)

10 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod q n (Tex Error) w,"ex area", k, N"ex area" where n is he number of whie pixels in he (k) w,"ex area" G image ha are presened in he ex area, defined by reference image. b) Qualiy Facor 2: Paper Error The Paper Error of he G image is defined as (k) (29) Figure 6: Reference Image S Threshold value chosen by he operaor. Figure 7: Synhesized Image wih =80. q (Paper Error), k n b,"non ex area",paper, N "ex area" (k) where n is he number of black pixels in he b,"non ex area",paper G image ha are presened in he non ex area, defined by he reference image, supplied by he paper. c) Qualiy Facor 3: Inerference Error The Inerference Error of he G image is defined as q (k) n (Inerf. Error) b,"non ex area",inerf., k, N"ex area" (30) (31) (k) where n is he number of black pixels in he b,"non ex area",inerf. G image ha are presened in he non ex area, defined by he reference image, supplied by he back-o-fron inerference.

11 276 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod... The second and hird qualiy facors defined abouve adoped he same normalizaion facor as he firs, because i is of ineres o know he amoun of dir, brough by he paper and inerference, in relaion o he size of he ex area. The hree qualiy facors examined ogeher provide informaion of he filered image: Tex Error shows how much ex has been erased; Paper Error measures he quaniy of dir here is in he image due he paper pixels; and Inerference Error saes how much of he original inerference is presened in he resuling image. For a synhesized image using he pair of images in Figure 4, a binary image of accepable qualiy, provides qualiy facors values less han 40%, 50% and 10% for he Tex Error, Paper Error and Inerference Error, respecively. The firs limi depends on he widh and gradien of he foreground documen, he second depends on he disribuion of he paper pixels and he hird depends on he inerference locaion in he documen image. 4 Resuls and Analysis The proposed assessmen mehod was applied o he eigh algorihms presened here. For he eigh se of 256 binarized images, one for each algorihm, he hree qualiy facors inroduced were measured and heir graphics were ploed. This experimen was made for weny pairs of images from he Nabuco s beques. The resuls of applying he proposed mehod using he pair of images shown in he Figure 4 are presened in his paper. Figure 8 presens eigh graphs, one for each algorihm, ha conain hree curves generaed by he hree qualiy facors. Noice ha he range of he qualiy facor axis is differen for each algorihm. Figure 9 presens hree graphs; each of hem brings he same qualiy facor for all of he algorihms. Noice ha he range of he qualiy facor axis is from 0 o 100 in he hree graphs. The analysis of he graphs in Figure 8 and 9 allows one o observe ha he Johanssen-Bille algorihm always produced he highes values of he Paper Error and Inerference Error facors. The Tex Error facor always was zero, bu his can no help i. One can see in Figure 10a he resul of applying Johanssen-Bille algorihm on he image shown in Figure 7, ha was synhesized wih =80, one of he mos frequen values of back-o-fron inerference in he Nabuco s beques. Algorihm Tex Error (%) Paper Error (%) Inerf. Error (%) Johanssen-Bille 0 1, Pun Yen-Chang-Chang Kapur-Sahoo-Wong Osu Mello-Lins Wu-Songde-Hanqing Silva-Lins-Rocha Table 1: Values of he hree qualiy facors (=80).

12 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod (k) Table 1 shows he values of he qualiy facors for all binarized image ( G ), 80 ha is he resul of applying algorihm k o he G image presened in Figure The performance of Pun s algorihm, alhough far superior han Johanssen and Bille s, as may be observed from he plos in Figures 8 and 9, yields unsaisfacory images (see Figure 10b).

13 278 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod...

14 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod Figure 8: Graphs of he hree qualiy facors for each algorihm.

15 280 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod... According o he assessmen mehod proposed herein six algorihm of he eigh algorihms analyzed are suiable o remove he bleeding noise in documens. Their performances vary according o he srengh of back-o-fron inerference. The graphs in Figure 8 and 9 show ha he algorihms by Yen-Chang-Chang and Kapur-Sahoo-Wong only produce reasonable filering for images wih medium-oweak back-o-fron inerference (110). In he mos frequen noise region (80) hese algorihms are unable o filer ou significan amoun of he back-ofron inerference, as shown in Figure 10c and 10d. Analyzing he graphs shown, Silva-Lins-Rocha, Mello-Lins and Osu algorihms are able o filer images wih greaer han 70, 90 and 100, respecively, enhancing heir performances as he noise weakens. The resuling images from he Osu and Mello-Lins algorihms are shown in Figure 10e and 10f. For images wih srong noise (3060), he algorihm proposed by Wu-Songde-Hanqing has good chances of performing well in back-ofron noise removal, however i ends o be greedy and remove par of he foreground informaion as one can evidence by is Tex Error values in he Figures 8 and 9 and Table 1. Figure 10g presens he resul of applying ha algorihm wih = 80.

16 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod Figure 9: Graphs of he hree qualiy facors for all algorihms. (a) Johansen-Bille (b) Pun (c) Yen-Chang-Chang (d) Kapur-Sahoo-Wong (e) Osu (f) Mello-Lins (g) Wu-Songde-Hanqing (h) Silva-Lins-Rocha Figure 10: Filered images by he algorihms presened in secion 2 (=80).

17 282 Dueire Lins R., da Silva J.M.M., Marins F.M.J.: Deailing a Quaniaive Mehod... The seadies good performance in filering ou he bleeding noise is provided by Silva-Lins-Rocha algorihm, whose may be seen in Figure 10h. As one can see in Figures 8 and 9, he Inerference Error curve of he Silva-Lins-Rocha sands below he curve of Wu-Songde-Hanquing; however, he Tex Error curve of he Silva-Lins- Rocha decreases while he curve of Wu-Songde-Hanquing increases. Alhough he six suiable algorihms have worked well in he cases of images wih very low back-o-fron noise (>120), i is imporan o say ha in he mos of he experimens, Osu s algorihm worked beer hen he ohers. 5 Conclusions and Lines for Furher Work A quaniaive mehod o assess he qualiy of binarizaion algorihms for images wih back-o-fron inerference was inroduced. The resuls obained wih his assessmen mehod are consisen wih he obained by visual inspecion of filered documens. The qualiy facors inroduced herein are able o inform wheher he applicaion of an algorihm yields a readable or unreadable binary documen. An imporan poin of he proposed mehod is ha i is able o spo which algorihm is more likely o perform beer a filering ou he bleeding noise by analyzing he feaures of he documen. This aribue may allow he auomaic choice of he bes suiable algorihm o filer a specific documen, hus permiing o be incorporaed ino an auomaic documen processing environmen such as BigBach [Lins-a, 06]. The assessmen mehod proposed here did no ake ino accoun he color of he background as a conrolled parameer. Work on progress are widening he scope of his work o model aged background, giving complee conrol of all documen parameers. Acknowledgemens Research repored herein was parly sponsored by CNPq Conselho Nacional de Pesquisas e Desenvolvimeno Tecnológico, Brazilian Governmen. The auhors are graeful o he Joaquim Nabuco Foundaion for graning he permission o use he images from Nabuco s beques. References [Abramson, 63] N. Abramson, Informaion Theory and Coding, McGraw-Hill Book Co, [Adobe, 07] Adobe Sysems Inc. hp:// [FUNDAJ, 07] FUNDAJ Fundação Joaquim Nabuco: hp:// [Johannsen, 82] G. Johannsen and J. Bille, A hreshold selecion mehod using informaion measures, ICPR 82, pp (1982). [Kapur, 85] J. N. Kapur, P. K. Sahoo and A. K. C. Wong, A New Mehod for Gray-Level Picure Thresholding using he Enropy of he Hisogram, C.Vision, Graph. and Im.Proc., 29(3), 1985.

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