A Framework for Reducing Ink-Bleed in Old Documents

Transcription

1 A Framwork for Rducing Ink-Bld in Old Documns Yi Huang Michal S. Brown Dong Xu Nanyang Tchnological Univrsiy; School of Compur Enginring; Rpublic of Singapor Naional Univrsiy of Singapor; School of Compuing; Rpublic of Singapor Absrac W dscrib a novl applicaion framwork o rduc h ffcs of ink-bld in old documns. This ask is rad as a classificaion problm whr raining-daa is usd o compu pr-pixl liklihoods for us in a dual-layr Markov Random Fild (MRF) ha simulanously labls imag pixls of h fron and back of a documn as ihr forground, background, or ink-bld, whil mainaining h ingriy of forground sroks. Our approach obains br rsuls han prvious work wihou h nd for assumpions abou ink-bld innsiis or xnsiv paramr uning. Our ovrall framwork is daild, including fron and back imag alignmn, raining-daa collcion, and h MRF formulaion wih associad liklihoods and inra- and inrlayr cos compuaions. 1. Inroducion Ink-bld is a srious problm commonly found in aging handwrin documns. Ink-bld occurs whn ink wrin on on sid of a pag pnras h papr o bcom visibl on h opposi sid. Th svriy and characrisics of ink-bld is rlad o a variy of facors including h ink s chmical makup, h papr s physical and chmical consrucion, h amoun of ink applid and h papr s hicknss (boh spaially varying), h documn s ag, and h amoun of humidiy in h nvironmn housing h documns. Figur 1-(a) shows xampls of ink-bld xhibiing various lvls of svriy and innsiy characrisics from four diffrn documns. Th documns ar from h sam archival collcion daing from Th obvious drawback of ink-bld is h rducion in h documn s lgibiliy. Th moivaion of our work is o provid a pracical approach o rduc ink-bld inrfrnc in imagd documns in ordr o improv lgibiliy as shown in Figur 1-(b). W also sriv for a soluion ha is applicabl in a ral-world sing ha considrs h widrang of ink-bld divrsiy as wll as pracical concrns, such as h abiliis of h nd usrs. brown@comp.nus.du.sg; {hu0005yi dongxu}@nu.du.sg (a) (b) Figur 1. (a) Closup of imag rgions from diffrn handwrin documns, circa , suffring ink-bld. (b) Our goal is o rain h original forground sroks o improv lgibiliy. [Conribuion] This papr dscribs a novl applicaion framwork o rduc ink-bld from imags of h fron and back of a documn. Th problm is rad as on of classificaion whr imag pixls ar labld as ihr forground, ink-bld, or background. This pixl labling is aidd by a dual-layr MRF wih smoohnss cos dsignd o rduc nois whil mainaining forground sroks in rgions whr forground and ink-bld ovrlap. Our approach opras on a wid-rang of ink-bld and dos no rquir assumpions abou h ink-bld innsiy or xnsiv paramr uning. All ncssary componns ndd for his applicaion ar prsnd, including fron and back imag alignmn, collcion of raining-daa, and h duallayr MRF sup wih associad liklihoods and inra- and inr-layr cos compuaions. Th rmaindr of his papr is organizd as follows: scion 2 discusss rlad work; scion 3 provids an ovrviw of our framwork; scion 4 dails h daa-cos compuaions and dual-layrd MRF formulaion; scion 5 prsns rsuls including comparisons agains ohr approachs; scion 6 provids a shor discussion and summary. 1

2 2. Rlad Work Thr is surprisingly lil prvious work arging complx ink-bld. This is likly du o h difficuly in obaining accss o oldr handwrin marials ha ar housd undr igh rgulaion. Much of h prvious work ha dos xis focuss on rlaivly simpl ink-bld ha can b rmovd using variaions of local or global hrsholding (.g. [1, 6, 10]). Drira al [5] prsnd a rcn approach arging complx ink-bld ha uss Principal Componn Analysis (PCA) o firs rduc h dimnsionaliy of an RGB inpu imag. Pixls hn ar classifid as forground and background by iraivly clusring h PCA daa ino wo groups via an adapiv hrshold. Tonazzini al [14] argd complx ink-bld using blind signal sparaion via Indpndn Componn Analysis which linarly dcomposs an RGB imag ino hr signals assumd o b forground, background, and ink-bld. Wolf [16] rcnly xndd his ida using non-linar blind sparaion via an MRF framwork ha could spara h forground and inkbld from ihr RGB or grayscal imags. Thrsholding and sourc sparaion approachs produc good rsuls whn h ink-bld and forground hav clarly disinguishabl graylvl innsiis or RGB signaurs. Boh chniqus, howvr, suffr whn h ink-bld and forground hav similar innsiis as shown in som of h xampls in figur 1-(a). Thrsholding chniqus mak a furhr assumpion ha h ink-bld innsiy is always lighr han h forground, an ofn invalid assumpion. In addiion, hs chniqus us a singl imag only which provids limid informaion. On obvious sragy o obain mor informaion is o us imags from boh h fron and back sid of a documn. Sharma [9] dmonsrad a succssful wo-imag show hrough rducion approach for us in xrox imaging. Show-hrough, howvr, assums global blding bwn h fron and back imags whr ink-bld ypically varis spaially making i mor difficul o modl. Th mos significan wo-imag approach arging ink-bld ar h wavl-basd approachs inroducd by Tan al [12] and Wang al [15]. Ths chniqus firs globally align h fron and back imags from which an iniial classificaion of h forground and ink-bld sroks is mad using h magniud of h imag diffrnc. Iraiv filring of h wavl cofficins is usd o dampn ink-bld whil sharpning forground pixls. Whil his chniqu producs good rsuls, six paramrs mus b und pr xampl, including hrsholds for h diffrnc-imag, dampning and sharpning cofficins, h numbr of wavl scal-lvls, and h numbr of iraions. Our approach is uniqu from prvious work in svral disinc ways. Firs, whil prvious work prforms wll for xampls ha m hir assumpions, our approach opras on a largr rang of inpus wihou xplici hrsholding or xnsiv paramr uning. Our approach also simulanously corrcs boh h fron and back imags, whr ohr wo-imags approachs ( [15, 12, 9]) procss ach sid individually. Lasly, w prsn a compl framwork, including ovrlookd componns such as h nd for localalignmn of h fron and back imags, as wll as an asy way o collc raining-daa. 3. Framwork Ovrviw Our ovrall framwork is discussd, including fron and back imag alignmn, h faur usd for classificaion, and raining-daa collcion. Dails o h labling MRF ar givn in scion 4. A brif dscripion of our applicaion s usag is prsnd firs Applicaion Usag This work is don in parnrship wih h Naional Archivs of Singapor which houss hundrds of volums of govrnmnal ldgrs, circa , ha suffr from ink-bld. Many of hs ldgrs hav bn imagd o grayscal microfilm whil ohrs ar imagd upon rqus. Rsarchrs of hs ldgrs ar mos ofn lawyrs and lgal aids who sill rly on hs documns in lgal dispus. Only digial imags of h original marials ar mad availabl o usrs. Our applicaion srvs as a pos-procssing ool o hlp mak h documns mor lgibl. Whil mos usrs ar compur-lira hy hav lil o no background in compur vision or imag procssing Sp-by-sp Procdur Our framwork sars wih wo high-rsoluion imags ( 2K 3K) of h wo sids of a pag. Imags obaind from microfilm ar grayscal, whil ohrs ar RGB scans of h original marial. Th pags in hs volums ar ypically bound and as a rsul ar no complly prssd fla whn imagd. This non-planar imaging compoundd wih small 3D surfac variaions ha ar ypical of hs oldr documns maks i impossibl o align h fron and back imags wih a singl global ransform. Whil flaning chniqus can rmov hs 3D surfac variaions (.g. [4, 8, 13]), such approachs rquir addiional 3D scanning quipmn no availabl in mainsram imaging sups and canno b usd on xising microfilmd documns. As a rsul, a local alignmn procdur in addiion o global alignmn is ndd. Considring our inpu imags our ovrall procdur is as follows: 1) imag alignmn wih local rfinmn; 2) raining-daa collcion via minimal usr-assisanc; 3) pixls labling using h dual-layr MRF framwork; 4) oupu imag gnraion. 2

3 Fr oni mag Backi mag ( mi r r or d) h various fron-back configuraions, including siuaions whr h ink-bld innsiy is darkr or lighr han h opposi pag s forground pixls. Difficulis can aris whn h ink-bld and forground hav similar innsiis, rsuling in a raio clos o h valu 1, a valu ha can also occur in faurs whr boh fron and back pixls ar background or forground. Inr-layr coss in our dual-layr MRF will b usd o disambigua his siuaion. Whil his is a simpl faur, i provd o b h bs discriminan ovr ohr all availabl informaion including faur from pixl innsiy (including RGB whn availabl), pixl diffrncs, and combinaions of hs ha also includd raio. Local di spl acmn s ( wi hou ) ( wi h) 50% opaci yoff r onandbackshown wi handwi houl ocalal i gnmn. Figur 2. Local displacmns compud bwn h fron and back imags. A zoomd ins shows fron rgions (black-crosss) machd o hir corrsponding locaions in h back imag (whicrosss). Ovrlappd imag rgions wih and wihou local alignmn ar shown wih 50% opaciy. Ghosing, visibl from misalignmn, is rmovd wih h local alignmn procdur Training Daa Collcion Du o h ink-bld divrsiy, raining-daa nds o b obaind for ach imag pair. This rquirs usr assisanc which is kp o a minimum using a wo sp procdur. Th usr firs draws simpl color-codd sroks on h fron and back imags, labling a fw xampls of forground, background, and ink-bld. Th iniial usr labld raining sampls ar oo spars for pracical us and unbalancd in rms of numbr of labls, wih gnrally many mor background xampls providd han forground and ink-bld. To nlarg h raining-ss, a K-NN classifir basd on h raio faur s disanc from h spars usr-labld daa is usd o labl h nir imag, whr K is h squar roo of h siz of h usr-labld daa. Pixl-wis confidnc scors ar compud as discussd in Eq (2) in Scion 4.1. Th 10% mos confidn pixls for ach class ar slcd o dfin h nlargd raining-ss. Figur 3 shows his raining-daa collcion procdur Imag Alignmn wih Local Rfinmn Whil inpu imags ar alrady coarsly alignd hy sill rquir an iniial global alignmn. To do his, h back imag is mirrord and h locaion of h maximum corrlaion scor of h fron and mirrord back imag ovr a [ 20, 20] pixl rang in h horizonal and vrical dircion is hn akn b h global displacmn. For our xampls, a ranslaion alignmn suffics, howvr, a full affin alignmn could b asily incorporad. Local displacmns ar compud by dividing h fron imag ino local windows (60 60 for our xampls). Corrlaion is prformd bwn ach fron imag window wih is corrsponding back locaion ovr a [ 10, 10] pixl rang in h horizonal and vrical dircion. Th locaion of h maximum corrlaion scor for ach window is akn o b h local displacmn. If h maximum scor is blow a minimum hrshold, i is assumd ha hr is no local chang. Using h local displacmns, hin-pla-splin (TPS) inrpolaion [2] is usd o warp h back pag o align wih h fron. Figur 2 shows his local-alignmn procdur. Th fron and back imag rgions ar shown ovrlappd wih 50% opaciy. Ghosing from misalignmn is visibl whn local alignmn is no prformd; his is rmovd afr TPS warping. R d=f or gr ound Gr n=i nkbl d Bl u=ba c kgr ound 3.4. Raio Faur A good faur is crucial for classificaion. Givn h C alignd imags, a raio faur is dfind as ρp = C p0, p whr Cp and Cp0 ar h innsiis of fron imag pixl p and corrsponding back imag pixl p0 rspcivly. Th back imag faur, ρp0, is h rciprocal of h fron faur. This raio faur salinly capurs h diffrnc in Figur 3. Iniial raining-daa is providd via minimal usr markup in h form of color sroks or poins drawn ovr forground (rd), ink-bld (grn) and background (blu) xampls in h fron and back imags (markup is nlargd for clariy). Th raining-daa is nlargd using highly confidn pixls labld via h iniial usr markup. 3

4 Fron Imag Back Imag MRF Nod p MRF Nod p Nod Edgs V1 MRF Nod q V2 MRF Nod q Figur 4. Our MRF nwork wih associad nods and dgs. 4. MRF formulaion Afr raining-daa collcion, ach imag pixl is labld as on of hr classs: Forground, Ink-bld and Background dnod as {F, I, B}. This ask is formulad as a discr labling MRF whr ach pixl, p is assignd a labl l p, whr l p {F, I, B} (s [7] for dails o MRF formulaions). Th opimal labl assignmn is found by minimizing h following nrgy rms: E = E d + λe s, (1) whr E d rprsns h daa-cos nrgy associad wih h liklihoods of assigning a l p o ach pixl and E s is a smoohnss nrgy basd on h MRF s prior cos for assigning nighboring pixls diffrn labl valus. Th scalar wigh λ is s o on in our work. Whil his nrgy funcion is sandard for all MRFs, h associad liklihood (daa cos) and h prior (smoohing cos) ar uniqu for ach problm. Dails of E d ar givn in scion 4.1. Our smoohnss rm E s is composd of inra-layr dg coss, V 1 (l p, l q ), ha compus h cos of assigning nighboring pixls h labls l p and l q and inr-layr dg coss (bwn layr), V 2 (l p, l p ), ha compus h cos of assigning a labl combinaion o pixl p and is corrsponding pixl on h opposi layr p. Inra-layr dgs ar s for boh h fron and back imag, hus w also hav dgs V 1 (l p, l q ) as shown in figur 4. Inra-layr dg coss ar dsignd o ncourag consisn labls basd on faur and color similariy. Th inr-layr dg coss ar dsignd o avoid invalid labl configuraions and aid in rsolving rgions wih ovrlapping ink. This dual-layr combinaion provs significanly mor ffciv a mainaining forground sroks compard wih using h inra-layr alon. Dails o E s ar givn in scion Daa Cos Enrgy E d Th daa-cos E d is dfind for boh h fron and back imag. Only h fron is dscribd hr for xampl. Th 1- dimnsional raio faur is normalizd o b zro cnrd wih sandard dviaion of on bfor h following procdur. For spdup, h dns raining-daa is clusrd by V1 K-mans, wih clusr cnrs of ach class rprsnd as {ρ F i } L i=1, {ρi j } M j=1 and {ρb k } N k=1. Whil choosing h opimal numbr of clusr cnrs is an opn problm, w s L = M = N as 10% of h siz of h smalls raining-s. For ach pixl p, w compu h Euclidan disancs (L2-norm) bwn ρ p and all h L + M + N clusr cnrs and hn slc h op-k closs cnrs whr K is s as L + M + N. Th op-k cnrs ar dnod as {ρ m } K m=1 and ar furhr dividd ino hr indx ss π F,π I and π B according o hir labls. Th disanc bwn ρ p and h m-h clusr cnr ρ m is compud by d pm = ρ p ρ m. W also dno d 2 p as h man squard disanc o h op-k cnrs. Th similariy of pixl p o ach class is dfind as: S F = xp( d 2 pm/d 2 p) m π F S I = xp( d 2 pm/d 2 p) (2) m π I S B = xp( d 2 pm/d 2 p). m π B Th daa-cos rm, E d, for ach labl is dfind as: E d (l p = F) = E d (l p = I) = E d (l p = B) = S I + S B 2 (S F + S I + S B ) S F + S B 2 (S F + S I + S B ) S F + S I 2 (S F + S I + S B ). Eq (3) rsuls in E d ranging bwn zro and on, and E d (l p = F) + E d (l p = I) + E d (l p = B) = Smoohnss rm E s As prviously sad, h prior rm E s is compud as dg coss wihin a layr and bwn layrs giving ris o: E s = V 1 (l p, l q ) + V 2 (l p, l p ), (4) p,q N p,p M whr p, q N ar h wihin layr dgs and p, p M ar h bwn layr dgs. Ths wo rms ar wighd qually Inra-Layr Edg Coss Inra-layr coss ar basd on h innsiy diffrnc or raio diffrnc bwn wo inra-layr nighbors p and q. W dfin d ρ pq = ρ p ρ q as h disanc bwn p and q raio faur. Similarly w dfin d c pq = C p C q as h disanc bwn p and q pixl innsiy. W normaliz d ρ pq and d c pq o rang bwn zro and on. To impos a smoohnss consrains in h inra-layr whil prsrving (3) 4

5 h dgs bwn diffrn classs, h inra-layr cos is xprssd as: V 1 (l p, l q ) = (ξ pq ) 2, (5) whr ξ pq is dfind in h following abl: l q l p Forground Ink-Bld Background Forground d ρ pq d c pq Ink-Bld d ρ pq d ρ pq Background d c pq d ρ pq I is worhwhil o no ha w us d c pq o dfin h inra-layr cos in Forground-Background configuraion bcaus w obsrv ha h innsiy from h forground and background pixls diffr mor han ha of h raio faur. In ohr configuraions, w us h dfaul raio faur. Morovr, if h nighbors hav h sam labl, w us zro cos o nforc h smoohnss consrain (h hr in h diagonal clls rsul in a zro cos) Inr-Layr Edg Coss Inr-layr coss, V 2 (l p, l p ), ar dfind as: l p l p Forground Ink-Bld Background Forground Ink-Bld 0 Background 0 2ω In h abov abl, w hav a condiional consrain for h Background-Background configuraion. W s ω as 1 if (C p < Cavg 1 and C p < Cavg), 2 0 ohrwis, whr Cavg 1 and Cavg 2 ar h avrag innsiis of h forground pixls in h fron and back imags rspcivly. Th background pixls ar usually h brighs pixls in h whol documn, hus w assum ha boh fron and back pixl ha hav lowr innsiy (i.. darkr) ar no likly o b a Background-Background configuraion and a small wigh of 2 is usd as pnalizaion. W us hr infiniy pnalis in h abov abl bcaus hs hr cass will nvr happn. If on pixl is labld as ink-bld in on sid, h corrsponding pixl in h opposi imag can only b forground. All ohr configuraions ar possibl and ar hrfor assignd a zro cos Minimizing h Objciv Funcion Enrgy W us h Graph-cus approach dscribd by Boykov and Kolmogorov [3] o minimiz our global objciv funcion sad in Eq (1). Th Middlbury s MRF cod providd by [11] is modifid o incorpora our dual-layr configuraion. In all of our xprimns, h opimizaion convrgs wihin 5-6 iraions. 5. Rsuls W compard our approach wih h singl-imag adapiv hrsholding approach [5] 1, h fron and back imag wavl-basd approach [15], and a singl-layr MRF basd on our daa-cos and inra-layr cos formulaions. Markup varis pr xampl, bu gnrally consiss of 5 15 sroks or poins drawn on boh h fron and back imags. Procssd imags ar roughly 2K 3K in rsoluion. Pixls labld as forground ar shown wih h inpu imags innsiy, all ohr pixls ar s o h man innsiy of h background raining-labls. Figur 5 shows sub-rgions from four xampls ha rprsn a rasonably divrs rang of ink-bld. Shown ar h fron and back inpu and our rsuls, as wll as a comparison of h ohr approachs on h fron imag only which ar combind ino a singl imag pariiond as follows: (op) singl-imag adapiv hrsholding, (middl) singl layr MRF and (boom) wo-imag wavl approach. Figur 6 shows a full-pag xampl wih comparisons of slcd rgions shown a h boom. For all xampls our approach provids subjcivly h bs rsuls. Th wavl approach [15] producs comparabl rsuls in som cass bu rquirs six-paramrs o b und pr xampl. Quaniaiv rsuls wr obaind by couning h numbr of rrors obsrvd in h oupu imags. Errors ar considrd any forground word no dcd corrcly or any background/ink-bld dcd as forground. Sinc ground-ruh is no availabl, our quaniaiv rsuls ar sill subjciv as rrors ar dcidd by a human obsrvr. Howvr, in a bs ffor for fairnss w found ha our mhod had a prcision accuracy of 85.96%, compard o 63.70% for [5], 71.94% for [15], and 75.00% for h singl-layrd MRF. Prcision is dfind as (W W F )/(W +W B ), whr W is h oal numbr of forground words, W F is h numbr of incorrcly classifid forground words, and W B ar h numbr of srok-siz background or ink-bld rgions ha wr classifid as forground. Prcision was compud for 10 full-pag imags wih a oal of 4896 words. 6. Discussion and Summary Our rsuls dmonsra h ffcivnss of our approach for rducing ink-bld. As wih all suprvisd larning chniqus raining-daa is ndd. Our wo sp procdur for labling daa rquirs minimal usr markup. Whil markup diffrs from inpu o inpu, only a dozn or so quickly drawn sroks ar ypically usd pr imag. I is arguabl ha usr-assisd markup is similar o sing paramrs or hrsholds, bu w no ha i is much asir for h domain usr o spcify imag xampls in liu of uning algorihmic paramrs. Furhrmor, in a long-rm work- 1 Th PCA sp of his algorihm is omid for grayscal inpu imags. 5

6 Ex. I Ex. II Ex. III Ex. VI (a) (b) (c) (d) () Figur 5. [Exampls I-II ar from microfilm; Exampls III-IV ar from RGB scans.] (a-b) Fron and back wih markup. Th back markup is mirrord for clariy. (c-d) Oupu obaind using our dual-layrd MRF approach. () Comparisons wih adapiv hrsholding [5], singl layr MRF and wavl [15] in op-middl-boom forma. Rd lins spara h diffrn rsuls. No ha sub-rgions ar chosn o show som markup, howvr, h nir markup is no shown. ing scnario i should b possibl o us prviously collcd raining-daa on nw pags wih similar ink-bld. Th documns argd in our work hav h sam color ink hroughou a pag, howvr, our framwork can b usd on ohr yps of documns xhibiing diffrn background and forground characrisics (.g. muli-colord ink). Furhrmor, diffrn faurs for diffrn documn yps and vn classifirs (.g. SVM) could b usd in h liklihood compuaion wih h sam ovrall framwork and dual-layr MRF sup rmaining inac. Many old documns xhibi problms in addiion o ink-bld;.g. h war-sains in Figur 5. Our classificaion approach is inhrnly mor robus o hs yps of problms. Lasly, w no ha addiional smanic informaion such as srok dircion or characr characrisics wr no usd in our MRF. This was purposly don o circumvn ailoring our soluion o h xampls a hand. Incorporaion of highr-lvl smanics ino his framwork undoubdly dsrvs furhr considraion. In summary, w hav prsnd a novl framwork for rducing ink-bld. This framwork provids a pracical approach o ink-bld rmoval ha can arg a wid rang of xampls and is suiabl for us in a ral-world sing. Acknowldgmns W grafully acknowldg h suppor of our collagus from h Naional Archivs of Singapor. This work was suppord by h ASTAR SERC Gran No: Rfrncs [1] J. Bscos. Imag procssing algorihms for radabiliy nhancmn of old manuscrips. Elcronic Imaging, 1: , [2] F. Booksin. Principal warps: Thin-pla splins and h dcomposiion of dformaions. IEEE Trans. PAMI, 11(6): , Jun [3] Y. Boykov and V. Kolmogorov. An xprimnal comparison of min-cu/max-flow algorihms for nrgy minimizaion in vision. IEEE Trans. PAMI, 26(9): , [4] M. Brown and W. B. Sals. Imag rsoraion of arbirarily warpd documn. IEEE Trans. PAMI, 26(10): , [5] F. Drira, F. L. Bourgois, and H. Empoz. Rsoring ink bld-hrough dgradd documn imags using a rcursiv unsuprvisd classificaion chniqu. In Documn Analysis Sysms (DAS 06), pags 38 49, [6] F. C. M. al. Toward on-lin, worldwid accss o vaican library marials. IBM Journal of Rsarch and Dvlopmn, 40(2): , March [7] S. Li. Markov Random Fild Modling in Imag Analysis (2nd Ediion). Springr-Vrlag, [8] M. Pilu. Undoing papr curl disorion using applicabl surfacs. In CVPR 01. [9] G. Sharma. Show-hrough cancllaion in scans of duplx prind documns. IEEE Trans. on Imag Procssing, 10(5): , [10] Z. Shi and V. Govindaraju. Hisorical documn imag nhancmn using background ligh innsiy normalizaion. In ICPR 04. 6

7 Figur 6. A full pag xampl (RGB scan) wih only h fron is shown (op) wih h compl usr markup. Comparisons wih ohr chniqus ar shown for hr slcd rgions. Our dual-layr MRF approach producs h bs rsuls. [11] R. Szliski, R. Zabih, D. Scharsin, O. Vkslr, V. Kolmogorov, A. Agarwala, M. Tappn, and C. Rohr. Comparaiv sudy of nrgy minimizaion mhods for markov random filds. In ECCV 06. [12] C. L. Tan, R. Cao, and P. Shn. Rsoraion of archival documns using a wavl chniqu. IEEE Trans. on PAMI, 24(10): , Oc [13] C. L. Tan, Z. Li, Z. Zhang, and T. Xia. Rsoring warpd documn imags hrough 3d shap modling. IEEE Trans. PAMI, 28(2): , [14] A. Tonazzini, L. Bdini, and E. Salrno. Indpndn componn analysis for documn rsorion. Inrnaional Journal on Documn Analysis and Rcogniion, 7:17 27, [15] Q. Wang, T. Xia, L. Li, and C. Tan. Documn imag nhancmn using dircional wavl. In CVPR 03. [16] C. Wolf. Documn ink bld-hrough rmoval wih wo hiddn markov random filds and a singl obsrvaion fild. In Tchnical Rpor RR-LIRIS , 2006/