character recognition using radon transformation and principal

8/10/2019 Character Recognition Using Radon Transformation and Principal

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Proceedings of the International Multiconference on ISBN 978-83-60810-14-9 o!"uter Science and Infor!ation #echnolog$% ""& 49' ( '00 ISSN 1896-7094

Abstract This paper describes the method of handwrittencharacters recognition and the experiments carried out with it.The characters used in our experiments are numeric charactersused in post code of mail pieces. The article contains basicimage processing of the character and calculation ofcharacteristic features, on basis of which it will be recognized.The main objective of this article is to use Radon Transformand Principal Component Anal sis methods to obtain a set of

features which are invariant under translation, rotation, andscaling. !ources of errors as well as possible improvement ofclassification results will be discussed.

I& I N#)*+, #I*N

. toda$/s s$ste!s of auto!atic sorting of the "ost!ails use the * ) *"tical haracter )ecognition

!echanis!s& In the "resent recogni2ing of addresses"articularl$ ritten $ hand the * ) is insufficient&

##he t$"ical s$ste! of sorting consists of the i!age

ac5uisition unit% ideo coding unit and * ) unit& #he i!ageac5uisition unit sends the !ail "iece i!age to the * ) forinter"retation& If the * ) unit is a le to "ro ide the sort ofinfor!ation re5uired this technolog$ has '0 "ercenteffecti eness for all !ails % it sends this data to the sortings$ste!% other ise the i!age of the !ail "ieces is sent to the

ideo coding unit% here the o"erator rites do n theinfor!ation a out !ail "ieces&

#he !ain "ro le! is that o"erators of the ideo codingunit ha e lo er through"ut than an * ) and induce highercosts 1 & #herefore the * ) !odule is i!"ro ing%

"articularl$ in the field of recognition of the characters&lthough% these satisfactor$ results ere recei ed for "rintedriting% the hand riting is still difficult to recogni2e& #a:ing

into consideration the fact% that !anuall$ descri ed !ail "ieces !a:e 30 "ercent of the hole !ainstrea!% it isi!"ortant to i!"ro e the "ossi ilit$ of seg!ent recogni2ingthe hand riting& #his "a"er "resents the "ro"osal of as$ste! for recognition of hand ritten characters% for reading

"ost code fro! !ail "ieceshe "rocess of character recognition "rocess can e

di ided into stages; filtration and inar$2ation%nor!ali2ation% )adon transfor! calculating% accu!ulatoranal$sis% Princi"al o!"onent nal$sis% feature ector

uilding% and character recognition stagehe first ste" of the i!age "rocessing is inari2ation& #he

colourful i!age re"resented $ 3 coefficients )ed%


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496 P)* ..+IN3&

#he i!age of character recei ed fro! the ac5uisition stageha e different distortion such as; translation% rotation andscaling& #he character nor!ali2ation is a""lied for standard-i2ation si2e of the character& I!ages there are translated% ro-tated and e>"anded or decreased& #he t$"ical solutions ta:esinto consideration the nor!ali2ation coefficients and calcu-late the ne coordinates gi en $;

[ x , y %1]=[ i , j %1]

[1 0 00 1 0

I J 1]

[mi 0 00 m j 00 0 1][cos sin 0 sin cos 00 0 1] 1

here; I,J is a center of gra it$ gi en $ ;

I =

i

jif i , j

i

j

f i , j J =

i

j

jf i , j

i

j

f i , j =

In the realit$ e ha en/t got this "ara!eters starting rightno % so e use ne coordinate s$ste! here center is e5ualsto center of gra it$ of the character& #he alue of angle rota-tion is according to !ain a>es of the i!age& #he alue ofscale coefficient is calculated $ !ean alue of ariation ofthe character& So the center of gra it$ of the character isgood candidate "oint of the center of i!age as a "roduct ofnor!ali2ation stage&

II& ) +*N # ) NSD*)M #I*N

In recent $ears the )adon transfor! ha e recei ed !uchattention& #his transfor! is a le to transfor! t o di!en-sional i!ages ith lines into a do!ain of "ossi le line "a-ra!eters% here each line in the i!age ill gi e a "ea: "osi-

tioned at the corres"onding line "ara!eters& #his ha e leadto !an$ line detection a""lications ithin i!age "rocessing%co!"uter ision% and seis!ic 3 18 & #he )adon #ransfor-!ation is a funda!ental tool hich is used in arious a""li-cations such as radar i!aging% geo"h$sical i!aging% nonde-structi e testing and !edical i!aging =0 &

#he )adon transfor! co!"utes "roHections of an i!age!atri> along s"ecified directions& "roHection of a t o-

di!ensional function f(x,y) is a set of line integrals& #he)adon function co!"utes the line integrals fro! !ulti"lesources along "arallel "aths% or ea!s% in a certain directionhe ea!s are s"aced 1 "i>el unit a"art& #o re"resent ani!age% the radon function ta:es !ulti"le% "arallel- ea!

"roHections of the i!age fro! different angles $ rotating thesource around the centre of the i!age& #he Dig&3J sho s asingle "roHection at a s"ecified rotation angle&

#he )adon transfor! is the "roHection of the i!age inten-sit$ along a radial line oriented at a s"ecific angle& #he radialcoordinates are the alues along the x' -a>is% hich is ori-ented at degrees counter cloc: ise fro! the x -a>is& #heorigin of oth a>es is the center "i>el of the i!age &

Dor e>a!"le% the line integral of f(x,y) in the ertical di-rection is the "roHection of f(x,y) onto the x -a>isK the line in-tegral in the hori2ontal direction is the "roHection of f(x,y)onto the y -a>is& #he Dig&4J sho s hori2ontal and ertical

"roHections for a si!"le t o-di!ensional function&ProHections can e co!"uted along an$ angle , $ use

general e5uation of the )adon transfor!ation =3 =4 =' ;

R x ' =

f x , y xcos ysin x ' dydy 3

here ( ) is the delta function ith alue not e5ual 2eroonl$ for argu!ent e5ual 0% and;

x ' = xcos ysin 4 x' is the "er"endicular distance of the ea! fro! the originand is the angle of incidence of the ea!s& #he Dig& 'J il-lustrates the geo!etr$ of the )adon #ransfor!ation& #he

Dig 3& Single "roHection at a s"ecified rotation angle

Rotation angle

x

y

S o u r

c e f(x,y)

S e n s

o r s

x'

Dig =& Median filtering

155 164 164 247 247 164 164 155 155 91 155 155

164 164 164 164 164 164 164 155 91 82 91 155

164 164 164 164 164 164 164 91 155 91 155 164

164 164 247 164 164 164 155 91 91 91 164 164

164 164 247 164 164 155 155 91 91 155 164 164

164 164 164 164 164 155 91 91 91 164 164 164

164 164 164 155 164 91 155 91 155 164 247 164

247 247 164 164 164 91 82 91 164 164 164 164

247 247 164 164 155 91 82 155 164 164 164 247

164 164 164 164 155 91 91 164 164 164 164 247

155 155 155 91 91 91 155 164 164 164 164 164

155 155 91 91 82 91 155 164 164 164 164 164

164 155 91

164 91 155

164 91 82

164 155 91 164 91 155 164 91 82

82 91 91 91 155 155 164 164 164

155 164 164 247 247 164 164 155 155 91 155 155

164 164 164 164 164 164 164 155 91 82 91 155

164 164 164 164 164 164 164 91 155 91 155 164

164 164 247 164 164 164 155 91 91 91 164 164

164 164 247 164 164 155 155 91 91 155 164 164

164 164 164 164 164 155 91 91 91 164 164 164

164 164 164 155 164 155 155 91 155 164 247 164

247 247 164 164 164 91 82 91 164 164 164 164

247 247 164 164 155 91 82 155 164 164 164 247

164 164 164 164 155 91 91 164 164 164 164 247

155 155 155 91 91 91 155 164 164 164 164 164

155 155 91 91 82 91 155 164 164 164 164 164

164 155 91

164 155 155

164 91 82

sorting

Im"utImage

#ut"ut Image


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MI)*SL MI I E; ) #.) ). *tract lines cur es in general fro! er$ noise i!ages&)adon transfor! has so!e interesting "ro"erties relating tothe a""lication of affine transfor!ations& e can co!"utethe )adon transfor! of an$ translated% rotated or scaled i!-age% :no ing the )adon transfor! of the original i!age andthe "ara!eters of the affine transfor!ation a""lied to it&

#his is a er$ interesting "ro"ert$ for s$! ol re"resenta-tion ecause it "er!its to distinguish et een transfor!edo Hects% ut e can also :no if t o o Hects are related $an affine transfor!ation $ anal$2ing their )adon transfor!s

19 & It is also "ossi le to generali2e the )adon transfor! inorder to detect "ara!etri2ed cur es ith non-linear eha ior

3 4 ' &

III& P)IN IP C *MP*N.N#S N C SIS

P is !athe!aticall$ defined 6 7 8 as an orthogonallinear transfor!ation that transfor!s the data to a ne coor-dinate s$ste! such that the greatest ariance $ an$ "roHec-tion of the data co!es to lie on the first coordinate called

the first "rinci"al co!"onent % the second greatest arianceon the second coordinate% and so on& P is theoreticall$ theo"ti!u! transfor! for a gi en data in least s5uare ter!she !ain idea of using P for character recognition is toe>"ress the large 1-+ ector of "i>els constructed fro! =-+character i!age into the co!"act "rinci"al co!"onents ofthe feature s"ace =1 &

P can e used for di!ensionalit$ reduction in a data set $ retaining those characteristics of the data set that contri -ute !ost to its ariance% $ :ee"ing lo er-order "rinci"alco!"onents and ignoring higher-order ones& Such lo -orderco!"onents often contain the O!ost i!"ortantO as"ects ofthe data&

Dor all r digital i!ages f(x,y) fro! the nor!ali2ation stageis creating colu!n ector X k $ the concatenate o"eration%

here k=( ,!!!,r) & Dor that "re"ared i!ages e can calculate!ean of rightness intensit$ " % difference ector R andco ariance !atri> # &

" k =1r k = 1

r

X k '

Rk = X k " k 6

= 1r k = 1r

R k R k t

7 here;

X =[ X 1 X =& X r ] 8

" =[ " 1 " =& " r ] 9

x

y

f(x,y)

Projection onto the x-axis

P

r o j e c

t i o n o n

t o t h e y - a x

i s

x

y

f(x,y)

y' x'

x'

R (x')

x'

R (x') R (x ')

x '

Dig 4& ori2ontal and Gertical ProHections of a Si!"le Dunction

Dig '&


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498 P)* ..+IN #! #heeigen ectors $ l are nor!ali2ed% sorted in order eigen alue%highest to lo est and trans"oned% to o tain transfor!ation!atri> & % here is the nu! er of di!ensions in the di-!ensionall$ reduced su s"ace calculated $;

i = 1

'

%i

i = 1

l

%i

11

here; is assu!ed as threshold =1 & #he !atri> & is gi en $;

& =

[$ 1

1&&& $ 1

'

& &&& &

$ l 1

&&& $ l '

] 1=

fter i!age "roHection into eigen ectors s"ace e do notuse all eigen ectors% ut these ith !a>i!u! eigen alues%this gi es the co!"onents in order of significance& #heeigen ector associated ith the largest eigen alue is one thatreflects the greatest ariance in the in"ut data& #hat is% thes!allest eigen alue is associated ith the eigen ector thatfinds the least ariance& #he$ decrease in e>"onential fash-ion% !eaning that the roughl$ 90 of the total ariance iscontained in the first ' to 10 of the di!ensions =1 &

#he "roHection of X into eigen ectors s"ace is gi en $;

= & X " 13 here;

=[ 1 =& r ] 14 #he final data set ill ha e less di!ensions than the origi-

nal 8 % after all e ha er colu!n- ector for each in"ut i!-age ith alues *

k = y 1% y=%&&& , y t

1'

#he P !odule in "ro"osal s$ste! generate a set ofdata% hich can e used as a features in uilding feature

ector section& Dor instance hen e use in"ut !atri> 8>8fro! )adon transfor!ation stage% as a result e o tained

= 8 alues ector% using attell/s criterion 9 &

IG& D. #,). G . #*)

# o sets of data recei ed fro! the P !odule and accu-!ulator anal$sis stage are used to create ector of features ofcharacter& #he a!ount of data fro! )adon transfor!ationde"ends fro! the i!age of character si2e and nu! ers of

"roHections& Dor e>a!"le% e use i!age ith si2e 1=8>1=8

"i>els and ste" e5uals one degree& ith those "ara!eterse can retrie e accu!ulator !atri> ith 180 idth and 18'

height cells& #o "roduce feature ector e don/t use all al-ues fro! the accu!ulator& #he reduction the accu!ulatordata is "ossi le $ the resi2ing o"eration - hen generall$si2e of !atri> is !ost co!!onl$ decreased& #he !ost :no nscaling techni5ues are; !ethod used ith Pi>el art scaling al-gorith!s% Bicu ic inter"olation% Bilinear inter"olation% Canc-

2os resa!"ling% S"line inter"olation% Sea! car ing 10 111= & In our research e !a:e tests ith Cinear% Bicu ic andBilinear !ethods& #he results ith other !ethods as er$si!ilar and do not ha e influence on the recognition rate of

"ro"osed s$ste!& s a result of resi2e o"eration in our s$s-te! is a !atri> 8>8 ele!ents as in Dig&7J&

Dig 7& Scaling o"eration

#he ne>t ste" of ector features "re"aring is concatenate o"-eration and Princi"al o!"onent nal$sis of resi2ed !atri>fro! )adon #ransfor!ation% see on Dig&8J&

s a result of P is 8 ele!ent ector + +- of !ain al-ues fro! in"ut data% hich ill e used to feature ectorhe second set of data are; code of :no n character ./ as a,nicode 13 and nu! er of local !a>i!u! +0 fro! the

ccu!ulator nal$sis stage& #he feature ector consists a 10alues Dig&9J&

G& P).CIMIN ) C SSIDI #I*N

#he ai! of the "reli!inar$ classification is to reduce thenu! er of "ossi le candidates for an un:no n character% toa su set of the total character set& Dor this "ur"ose% the se-lected do!ain is categori2ed into si> grou"s ith nu! er oflocal !a>i!u! as in Dig&10J&

$ $ $ $ $ $ $ $

$ $ % & $ $ $ $

' ( % % ( ' ) ' * ' ) % % ) % + * &

* ' & + ' + ( , ( - ' - ' ( , *

, * ' + ( & ( , ' % ' * & , * '

( ( - + ( - ' + & & % % * % + * ( +

$ $ + , * $ % $ $ $

$ $ $ $ $ $ $ $

Dig 8& reating ector X $ concatenate o"eration&

Dig 9& reating feature ector in "ro"osed s$ste!

ZN L1 L2 L3 L4 L5 L6 L7 L8

4 8 2 4 32 55 8 - 1 21 29 0 1 3 11 7 - 2 76 86 0 1 6 61 30 2 21 97 - 59 38 4 - 3 81 01

LP

.NIC#D/

Number ofma0imum

PCA data


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MI)*SL MI I E; ) #.) ). *"eri!ents% e e>tracted so!e digit datafro! arious "a"er docu!ents fro! different sources eg&!ail "ieces "ost code% an: che5ue etc& In total% the training

datasets contain the digit "atterns of a o e 130 riters& ol-lected 9=0 different digits "atterns for training set and 300digits for test set& .ach "attern is re"resented as a feature

ector of 10 ele!ents&o!"aring results for hand ritten character ith other re-

searches is a difficult tas: ecause are differences in e>"eri-!ental !ethodolog$% e>"eri!ental settings and hand ritingdata ase& Ciu and Sa:o 1' "resented a hand ritten charac-

ter recognition s$ste! ith !odified 5uadratic discri!inantfunction% the$ recorded recognition rate of a o e 98 &Eauf!an and Bun:e 16 e!"lo$ed idden Mar:o Modelsfor digits recognition& #he$ o tained a recognition rate of 87

& issaoui and aouari 14 using Nor!ali2ed Dourier +e-scri"tors for character recognition% o tained a recognitionrate a o e 96 & Bellili using the MCP-SGM recogni2eachie es a recognition rate 98 for real !ail 2i" code digitsrecognition tas: 17 & In this e>"eri!ent recognition rate 94

as o tained& #he detailed results for indi idual testingsets as "resented in #a le I&

GIII& *N C,SI*NS

#he selecting of the features for character recognition can e "ro le!atic& Moreo er fact that the !ail "ieces ha e dif-ferent si2es% sha"es% la$outs etc& this "rocess is !ore co!"li-cated& #he "a"er descri es often used the character i!age

"rocessing such as i!age filtration% inar$2ation% nor!ali2a-tion and the )adon #ransfor!ation calculatinghe character recognition algorith!s ere "ro"osed& In

connection ith this or: the a""lication included the algo-rith!s is in "rogress& So far the a""lication reached recogni-tion s"eed 30 characters?sec ithout an$ o"ti!i2ation&

In the future or: is "lanning to use another statistical!ethodolog$ such as R+ ?C+ & Moreo er the ill e u"-graded to re!aining all al"hanu!erical signs and s"ecialsigns often "laced on regular "ost !ails&

) .D.).N .S1


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'00 P)* ..+IN4? - encodin6 form, 45e >4? - encodin6 sc5eme! , S#ransfor!ation Dor!at 8%J defined in nne> + of IS*?I.10646;=003% technicall$ e5ui alent to the definitions in the ,nicodeStandard% =003&

14 & issaoui% Nor!alised Dourier oefficients for ursi e ra icScri"t recognitionJ% ,ni ersite Moha!ed% Morocco% 1999&

1' & Ciu and & Sa:o% Perfor!ance e aluation of "attern classifiersfor hand ritten character recognitionJ% International Jo

character recognition using radon transformation and principal

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