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& ) : -8 * KI9I 3 M + G <= 4-7M 3 @8F80880888088088088088088808808808808824, 5-8,H% -+ 4! $ #! KI I /+ $/7'!!0 7#-% 2 =?# + 0 & 3 -.!&$/- 8 80888088088088088088808808808808824!, -8! +! )B <7' 3 =3( = $/7 8 808824!* -8 5@ + ()@ + - %@-4&&! 0 = +! = 88088088808808808808824 % -8 5. $/ 7 + )&+ -) # $/ + ) @ B+ $/7#-.! ) G #% + A,*!,!HH +! 8 J %'L J L ' )B / 3((# ) ;!G3 9J + L;6J ) L ' )* / 3( # =) (!-888088808808808808824 % -8 4 H! +! & B)'3 / $/7 () $E) : 86880880888088088088088088808808808808824 5-8 4!4. $/ 7 + )&+ -) # $/ + ) @ 3 +! <- $/ G #% + A4% '% *; +!. 9 8 + # 6) 0 : A 8< J + L(9J 'L H )* & 3(# ) ;! 3( =$/- 88088088088088088808808808808824 H -8 4,! +! )B3 9 $/7 ) $N A 2 % ) : ' E8& +! =3( =77' =( C' 7- @8;808808824!, -8 4. $/ 7 + )&+ -) # $/ + ) KI9I. % = $/7. % +! = <. $/ G #% + 0 %'% * H +! 8;; + # ; - &) 8 J %'L;9J L % )' ( ;3(B# &) A! ;3 &$/- G 3 6J + L J ) L ' 3( # =) ( 7# 7' 8 824!* -8 4 MP $/7 A0 $/7 :(J -G %'L 2 % /*.@,%'#-B $, G J + G 'L# * 0 & &7.*(! -, GJ G) L &.> -, G'J!-G 'L# & 3 &.(I < 7' + %@#7'-, GBJ G L / &.(, %%, G@ J 4'G L 0 &87. #; +, 8;P = $/7 ) $/ @868808808824 % & PAS

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& ) ) 2 & &* ) 2 2 8 4,M, # ) )! -3 3( $&.! &/?-# + 0 )A) # 2 + 808808808808824!* 58 4,R% -+ 4! $ ) KI I=. % >- + -. 2 +! = <- $=8988088088088088808808808808824% H 58, 4-! KI I +! < $=8@8088808808808808824%, 58 & 9) $/)( :/J L,*J %'L, 8& 3. + $&% 9) :J + L,AJ 'L 0,9;. $/ < # & 7!6 :9J + L,; J 'L, 8R80880880888088088088088088808808808808824% 58, % -+ 4! $)- BKI I=. % 0 > + -. ) B +!. < $=8888088088088088088808808808808824% 5 58 * * =!$/ / ) : J -L09 3. &+ $&%, G J %'L / 3. + $0%, G*J + L, 8 % + 4$/ 4/ 0 #!/7' 8808808808824 4 58 / $/ A 7 + 3!= /+ -) # $/ + @) :;J -L'D'#. B+ +. $/- G-J %'L'Q( <!. = =+ +. $/- 8MA #$&%' &) +! 24,5%!H/ -+ 3!H!*/+ + $/7 7!!,&+ +. $/- 8M88808808808808824 % 58 (3( % -+ 4 # )/ 3( E7 E%#! #! KI I ) :1J L '&. I= K,I9I=,, G J %'L & &.K,I=,, 8@0 3(3( & $/ + +. $/- /%#- 5* M3 5@ )?-# + 88088088088088808808808808824!* 58 93( 7 = #! KI9I ) :EJ L #& '. I= K,I9I=,, G*J %'L & &.;K,I=,, 8 ) # = + + +. $/- 8-88088808808808808824!* 58 5 93( 7 = #! KI9I ) :EJ L #& '. I= K,I9I=,, GJ %'L & &.'K,I=,, 8 9;+ + +. $/- * &2 <-!/-#$0%@ )B 2 & #$&%' )B!$/ 88808808808824 ' PAS S S

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ecdij2-o5k VG5C ( +?-# $/7- ; & + $/7' 3 = $/! 0 $/ 4-&3 + = + %' %<M#! =) # 9 7+ ) 7 % $=8M $/!/3 M & ) $/ M 66?# + 9) ). # 2 + # % )!&/ 9I= 4 2=$/- 8(,( $/ -+ )0 6 @G / +?# = ) = + +. $/- ' +?-# G' + + 3 = ( 7 %<& 7-. =7 #! = MI 4 2$/- ( + M7 & + + = )A2 #+ + 8 & ^_Y [Z Y3Z &_^ ) 3! + %#- ;)@ + 7 & @G@ -#+ 9 3 ) @: > + 9) # 9+ C. + =! $=8

+ < H< + HQB?A4 IJQBCE9 5CD4 QAGV?ACD@ (3 <-7@ / ) ) # & $/7 $/ 0 6 9. + %'+ # 2, % +3 :;! % ) $/ &) # #+ # @) # 8! l _AbE^Bl7] \ ^BÈZ d _A\ c(^] Y _A` d [^] ae\ [Z A 7 A $/ - + %'(+ # 2(, % +B3( #! 3(. $/ D'# B 7@ + #$1 )@ $/ &7@?# 2 8;$/ - # 0 3(. $/ ') # 2 + = =+! = G 7 + $/ G @8 ) # (2 + ;+ &%@# /%<& ; 3 &B3 & $/7 GB 2 (3(!. 7' 0 + A# 0A% 2 0?-# + G) 2 +?-# @G- & I= 4 2=$/- 8! p ] \ aeij] ae\ ^Bl3d [^] ae\ [Z (3 5* #+ # A) # & &7 6 =. @8A, #!0 $/;) () # B ;4-3 && 2(%' &# %@ ) G + $0% &)@2 #A) # ; /! () # 2 + + = + + $/!0% </3 ) # 7+ 8 + < H< F L 4 @B@BK 5ID4 QAK 0HO. L M703?AK QA256! + <G* 6I 4 26$/- 2/%' 6 #+ + ) # <677 + + 3( 6 +! @8& 0 6 $/7 $/ 3( ). ) 977 + 9 )/ EI= 4 2 $/- +! + # 2 3 ( /, % + $/-# + 7- :B $/- + $/ ;77 + 7 = + $/ 77 + @8! p fe[c(_dxe[l3xey Z i\ Y c(y È^B`J]^BmEmE\ _A^Bijf &77 + %# &= MI 4 2M$/- () & + 3( M >- + @8 2 % 2 =7 @G3 + 7 3 3 @G@ 0$/ +!/ + &! + 9$/- A + + # = 3 = $/! ( C' /3 / + 3 3 $/- '! 2 & $/ > $0#$ + 8

! p p fe[me^] f XEY Z i\ Y c(y È^B`J]^BmEmE\ _A^Bijf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

Chapter 1 Chapter 2 Chapter 3 Segmentation-Based/ character-model Technique Chapter 4 Segmentation-Free/ word-model Technique Chapter 8 Chapter 5 Chapter 6 Chapter 9 Chapter 7 Chapter 10 T ( % & % & T! & & % ) # (2 + B )@ C>- &-#$0%@ B)' + <-$&%' B 0 A #+ ( + $/7#- 0?# & 0 +! 0 < $=8;+ 7-. ( 0 + # ( </ $/7 $/ / )AK =I= 4 2 I - ( &3( > +! @8 7- GB, % +=I=# + 7-4-$/7 GB # 0 -#$0%@ ;)*-3 /$/-# + 7- B) $E $0%! 2 < A % < J AL G; $/=) $/-# + 7- / H!H9< / @8M + 7- A 7 *) #@ <-7@ 3 + $/7#-.! ) *) + 3 + ) #! # / 2 7 #+ # 8, ;) 5* <7' 3 6-3 9) 7 + 7 & ) $/! 3 9 $/7 # 6 = =)!/ +! 7# 7@ 8

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$/7 $/ B O#$&. P + /$/ -& /+ +. $/- 3 + ) $ ( >- + -. ) ; &I= 4 20$/- 8ADB <G ;$/--. C' &Q %'! $F ;77 & 07 2 ( ( )@ %' 7 ( #! I 4 2 $/- * =%' =+ -C'!# 8 7- ;4 Ḧ #$/$/ / 9$/ M+ + # = ) + @8 6+ 7-!! $/9)0 677@ # /) /) #- # 3 4% + # + @8

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

8 O B J J # 8 P ( ( ( ( / ( ( ( / ( ( ( ( ( ( ( @ ( E B S S # 1 01 %1 1 0 %! O 0 O % O! # $ %1, 1 &1 '1 > ) * %, ( & '+, -, ( &.+ / 0 1 1 ( ( H( H @ 1 1 H H 2 3 3 + + 4 5 3 ( 3 ( + ( + 6 7 P 8 9: 6 7 O O 8O 9: O > 6 ; ( < 9 0 ; < 9 @ = > (? @ A >? @ A+ B( G 6 C D= ( G ( 6 C F ) G H I G K ), L Q M N < O $ P 7! M $ Q( ' ; R S+ - ( 0 ( % ( T ) U V W X Y * * E E A Z [4 04 %4 \4 ]^ _ ` T T & & )ba T T & c T U # & #! d % & T ) T '& % & &! T T & ' # & &! %'& T ( T &' # % )

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Ä5!, 8;-. +! <- $

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p c([^bèzeil aez ] [\ Y Èg -<-$/ +&+ #!=! $=G* 3 <9# 67. + # < 7' + 97 -+!8 ) & 0#$&%' );+ + - %@-4'89=7 -+ # 0! ) 3 @:&!=2 + + ## <M! + # GM 9+ # + #7@ =# *&) #!$/ @8 3E+ ) 07 -+ # 0 3 6DB! 8 48! $R 0 + $/7@ 0 3/! : & & - %' 8 2 + ( $/ </#- )@!2 + 8A 2 + %' 0 *+ )B 0+ - %@-4= <$&.

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

START Choose randomly M vectors out of the U training set Set i=1, m=1, min=999 Find d(x, µ ) i m d(x i, µ m ) < min NO Increment i Set m=1, min=999 YES min = d(x µ i, ) m argmin = m i < U NO YES D < Threshold YES YES m < M NO NO Calculate centroids Assign x to µ i argmin STOP R T & $ % ' # & % ( ( & T ) O! 4 5!*G;I<! 5' 8 0 &#/ = $/ %@ 3( M 7' + M3 M3 = + <%' 2 29+. + # @G(3 + #!! 7 -+!/ )B <$0%@ (3 $&%!##(%@# 2 ( =77@ + 8 V< V< + (2VCE07?AR 43OV9 L CE6)C O7QB@ 07T /1/, KI I = -+ +67 -+ 3 # <-!C'. #+ # 89;+ ) 9 -+ M3 M $ ) #+ @8BP /!*7' $/$/ # % G. + 27 7@ 86P 9 + =7@ - ) $/ GB =7 -+ #$/ %'& $/0 0 9% 2! 6%<

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

48B - 7 %% <8A ( B 7 %% <&)*%@!0 48 J 4 L,-8B; B 7 %% <8* A ' ;7 %% < )%@! = A $/ G!0 / / $/ C48 J C4 L 8B0% 2 = <$0%@A7 %% <8; 7 %% < ) % 2-!/ <$0%@ 3 $/- * = ; $/ 8 J L /J L! 7 2 #B $/ ;$/ @G+ $/7 ( 7@ + C. + 0)'&KI IH?# B 7@ + ) <-! 3($/- -7 $/ G N EG % 2 = <-$&%' G )B7 %% </$/ #,0G-O 8B+ $/7+ ( 0 0%' # / 0 ) B ;KI I AJ &L 8 V< V<?B0HU5L CE6)@e0 C):V03L P7CE9 2 KI I 7 2- # < C' @G% 2?-# + J *L;+ %'! =#! (KI9I9G-3 ;! ) =% 2?-# + = + % 2 &) + = /)7' % <-$&%'(% 2 &8 D' 3! / 7 KI9I # /! % 2 =?# + : 484-48; $/ ( C' % 2 @8,-84- + A B J 4 L@% 0 ; ;7 %% < G-3 04 68 84- + 6% 2 6=6 )0 <-$&%' = + +!= <-$&%'(7 %% <6 %#- J L GB3 4 68

$ 8BA ) $N &+ # 0 J L = J 4 L + +! 6 9 M7 %% < G3 K4 68 *-8# + $/ 8 8# )!&%+ 4/ / 7 / 3 7@8 2 0 A) $/ + 7- & )@&KI9IH0 (7 -+ # # 6! =% 2?# + G! %! % 5 # 4 <7 % $/& %' 2 %@ ) 77 <!6 KI IR //. 3 =77 + @: 2 KI I6G *J /L G?# + )0% 2 FJ L G'+ $/7#- $/ + 7 %% < )B % 2 =?# + 0! 2-!0 $/- J 'L 8 2 KI I6G *J /L G?# + )0% 2 NJ *L G@C'9 /7- $/A7 MJ?-# + L J L 8 2 66KI I6GAJ &L GB # 0 7 $/ $/>. $/ 7 %% <)B% 2 =! 2!0 $/- /J @L 8 D' 3!6 = 97 % $/M 97 7@ #- + )A $=8 p bez [\ ^] Y _A` Z [ DaE[Èi[ [ ^Bl ae^] Y _A` ; A3 & 2 # & )@ % 2 &?# +! 2 & KI I68 + $/7#- 7 %% </ % 2?# + 03( 7 -#+ 0%<! 2 $/- 8A * * >- $/ < $/7@ *7 + # < 3 0 + & 0+ - $/!0 2 @+ $/7@!$/- ; ;%@! $/ 8;K + G! ( 0C' $/- ' %@ $/ + % 2 G* 9 3 G* &$/- *3 &! 7 %%. <8 $/7#-! B7 %% < #!/ -#$/! 2 </7@ % (?-# + )'! M * #B0 $/. + #$/! + ; /?# + 03 +?-# J, 4L $&# 7 + 4& 8(3= 2 $/ < %'&# 9 @:

States α (i) t α t+1 (j) S 1 a 1j S 2 a 2j S j S N a Nj t t+1 Time R T $ # %! # $ #!& # & & T!3U ) ) 3( 97 -+ # &9 &%+ 43( 67 -+ # 8&0) 3 97. + # + + # ; ) 3 2 % + = + )A $/ ;) + G' 88 J L G' 0DB! -8,8 & 0 7 7 -+ # : 48) & & N ; ) 3( =7 %% (( 7 %% < )B ; @% 2 8 J L J L 4 J -8 *L,-8) &L & F A+ + # @ ;) 3 07 %% < )' $/ 24;% 0 - *7 %% < )7 2 #*) 3 2. % ) $N A $/ = 0 7 %% ) $H + )A / G'3( * % 2 7 %% < $/ C48 J -L J L J L J -8 L 4 4

$ States β (i) β (j) t t+1 a i1 S 1 S i a i2 S 2 a in S N t t+1 Time R R T # %! # #!& # & $& T![U ) 826 0 &( & R! 2 + + # )J 'L( #$H)A $/ ') 3 =2 % J L 8 J 'L J L J 8 L P >$/!= =+ $/7#- 6 2 2 + + #!= /). 3 2 % = 2 9 + )& $/ G 6 J 4L J 4 L&$0# 7 + 0 J 4L J 4L&-. 8 %+ 43 7 -+ # &) 3 / $//77 + /). 3 7 -+ # 3( 2 77@ + /) $ 3 4G DB! 8 8; & 3/ 7 7 -+ # : 48) & & B 7@G %+ 43( 02 % ;)' + & $/ / 8 J L 4 4 J 8 -L

,-8) &L & + + # &) 3 67 %% < ) $/ % 6 7 %% <= )(%+ 43( 2 % ) $ ( / / $/ 4= 7 %% ) $N + )B 0 / G@3 A % 2 7 %% ()A $/ 48 J L J L J -L J -8 5L 4 C4 $, 4 P >-$/!/ /+ $/7#- 6 2 2 6+ + #!/ %+ 43( &2 % A 2 ; ; ; - + ; )' $/G A, J ;4LB$0# 7 + A J ;4L J ;4 LB 8 p p md] Y c(^bl3me^] f \ [j] \ Y [ Y Èg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

,-8) & & 8)O L & 826 0 &( & J L!J J L L J L J -8, H-L J L H J -8,!4L 4 J L!'J J L L $/> J -L J L;J -8,,L J L!$/> J -L J -8, -L *-8)M% N9A 3 3 & p 4, $/> AJ -L J -8, -L!$/ > BJ -L J -8,*L J L J -8, -L C4 $, 4 _JXE[lHmE^B\ ^Bc([j] [\e[z ] Y c(^] Y _A` +!&!3 0= $/7- $/ /7-. $/ $/- @7 $/ G 1 G /( /%' + %@ 3 /% 2?-# + -+ + # 8/7- $/ <9+ 9$/>- $/ % 2 =?# + 07 %% <G J 'L G! 2 $/- G AJ L 8( 0 / <- + @77 + ) ( G' 3 2 =. 2&7 -+ # & #+ 6 0O#$&. P + 9$/ -@G*4 3 6 = 9B>7' + -. I=>- $/ =J 9(I9L G- (77 & 0 -+ <0$/>- $/ ( 4 --J 'L( )A + AJ L 8 $/ &7 -+ # ;! <& 7@ 0 C' ) + M$/- 7 $/ 8M# G6 /) % = $/

$ States α (i) t β (j) t+1 S1 a 1i a j1 S 1 S2 a 2i Si S j a j2 S 2 SN a Ni a jn SN t-1 t t+1 t+2 Time R - # % $ & % $ #! & T # & & % & T 3U $ % # & % ) S %! ' % # & % ) ) ) $0# ;) 4 J -8,%L J -8, -L J L! # J -8, 5-L A + %'= =7 2- #&!9) $&# &$/ $/ + <G; J -L%' 07 %% <= );%@!/ ( $/ G@ / $/ C4! 2 = $/- *= % 2 =?-# + J -L J @L J -8 H-L A-4-!& /DB!8 = 0 C' )B ) 3( %+ 43 2 % G 9;?8-8 H/$/ <%@3 = J -L J L J L J -L /J @L J L J L J -L $ $ J L J L J -L J -8 4L 4-#$/$/! J -L; 2 A4 4 # ( / >7' + =-#$0%@ )A ;) $ B 8

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

$ 4 5 3 1 2 1 2 3 4 % R! d % && c ' ) $ $ $ $ $ $ $ $ $ $ 4-$/B77 + @ #+ 0* 7@ + 0 +! + + * +!.?# + + = 6 6 $/ >@8 $/7 $/- ) <-!/ 0+ 2 B!- +0! 3 0 + ' @ @ O% KI I J!. KI I9L GB DB! 8 *. %@8 &$/- <= $/7' & $/7@ @ 0 KI I + 3 #$&. %@ /+ + #/) &% 2 /-+ + #!97 0 )! -#$0%@ = 8( $/ + 77 = : 48B?-# + 0$0# 048 4 4 H 4 J -8 %-L,-8+ / 3( /3 9 + 3 = + # $/ 3?# 8 CH J -8 5-L

%' 2 =$/ >/3 @%@ $ H $ H H $ $ $ $ H H H H H H H 84-$/ 77 + ; + (!+! ( + (%< $/7'!6 + M 97' $/ #$&%' ) #$/7 H J -8 H-L, #$/,G 3 @%@ $ H H H $ H H H $ $ $ $ H H H H H H H V< V<. -L K ID4EQAK 03O e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

K I= 4 2$/- ; 2%' = 077 / &, % + + +. >- +! @8, 5!* G' 0+ # )B 3 9 $/! 3B!$/ & ) *% ( $/ @8A A # 0 0?# + )- %' G B * )-3 + 3*+ C' %<C'!( ;KI IF3 +! 20 &! 7 %% <8A= #+ 0 &+ $/7#- $/0 + / / +! 6 GB!$/ 030&+ $/7 9 = 3 )B$/- 3( + $/7 // +! #7 +. +!6 6 97' M) =!$/ 3 3 @8!!& + %< I 4-#A I<! 5%G@I<4 AO/5'-G'O4I=55 8 ; <- $ 7@ (& $/ &)*+ + ;$/- G- >-. + @G'=! $/$/B) $1!& $/7 8;!07 4 + ; )* >-+ #7 /3 /! #/ #- @G- >?# 2-. & ) / >-& $/!GB0 7#- 86 @G( + / 0 2 3 2 77!2 + 3 3 ;) $F3 + /) # 2 + ( > + @8 + + $/-!9+ $/7' / 4 / =) # 2 + (& + 7'!! #/ #- / $/ B +. + A$/- 8A( +! 7 ;) 3 @ ( $/( 70 >- + ) # 2 + 3 + = # 3 = 5@ 4 3! # + $/!&7 &C' + +?# + 3! 4 -- /J @L 8 % # 9+ 7-2 + # E 3 $/7' - 3 + E # #!#-( @:BQ; + # K I 4 2I=- 8 2/! 2 0)( /-2! 0 -. 2! A) B77 <! Q 3( & +! @8A 2 7 </ )*KI I 8;) -+ #B3(/7<- + @ >7 ; )@ % +$/ $/ + 2 2 @8 ( 2 &% <= 2 3 = $/7. $/ 9 )(KI I + + 3( 9 +! )(-#$0%@ )!#! + #!&, % + 8

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( - $ # % #( ( ) H ( ( 7 & + (( ;# #.# $ G #( # #. ( # ( # $ 8 # #( #( $ A % ( ( @ #(.# + $ % #( #( ( % # ( ( #. + (( 7 + -( 8 8 #( $( )#( ) #( AC/ N> ( ] B @ / ]? / 3A? B? / /# %1K#L 8 24)# + :4# G & ( C G 0 8* ]( / K 1 # #? \4 ; $# & ) #( # & %1 # ) H %4# # # G ) + '# /# G %1 # #, * IB AN/ N> ( ] ]> B C I N / @ ( T :4)#( H# ( K & #(.# T 04 /# 8 %478 /# W7 /# P ) 24 O # 2 F %4# 7 R W &'& &. 8, # 1 #, * ] 6 # ) \4# ; $# & C/ @ CAC / @ @ > 24 O # 8 #( T '# 1 + )( H # ( K#L 8* J #( H # (,# %4#; $# & - & & ( & &! & T % # & T ) ) S %!& T & % & &!& & ) < ] (? > / B < A? [ = N> ( < / > %1 + 4 ( /# K %478.#%1 /# %K 4 /# 1 ;!G 8* 78 1 /# % M 7 78 K! ( ( G, 8 ( / T ' C ' 1 # ( /# T > 018 ( [ AC ( # > [ [B @ > [3CAC * 9 ; 8O 78 C! @ 2, %4' H# 4 # $ O ' %1 78 24 F $# %4( ) 6 ; K1L 8 Q E 04 + &1 G 78 C ' 7 :' ( T ' 24 F $# 4 ( > C / B ] 1 3 7 :' 2 8 J + %04 O -( 8 + G 78 ( 4 K 2 $ #, 6 ; /# K1L 8 & %78 - & & ( & &!' & T & % & & T $ % # & T ) ) S %! & T & % & &!& & )

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& & &..# $ ) & &, &.# 8 ( & $ + # $ $ # ) & # G #( * $ # & - $ # - 0O & #. $ $ # ( #. $/# + 7-8 @N A?@] = A < _ < N = [ A?A N> ( C / CAC A?C /# V E 01 & 8* # %, $( & ( / 8 B # 8 %1 *# ( 0 # Q # 8 78 #%4! # /# 04+# Q 3 #( ( /# * # Q 8$ 78 /# ; #4! G# 1 *& 8 1 T ] = &( 018 ( > /# > > < N 04+# Q 3 #( + # $O%1) M 04+#:1 # 1 & 78 M P #.#/( 3 ) ( /# /# ' T&( 018 - + 8# G# - & & ( & &! & T % # & $ ) S %! & T & % & &!& & ) 5< V< N -< *$/# + 7-* * % $ /0& * 12 & ) 7 &8 7 0 + % $ 0& 5& 7. * 7 & 1 / 2 7 0 + L &;! ' @ > L & 8; ( ( + + # )!! 7<) 9;! <7-M 0 ( 2- &!6) * & &8 7 1 & 5& &7 3; @ ' 8= 30+ $/7 6%< 0) * & & * / 3 & & ) 0 &K &9%< #- 3 $/ - (77@ G %', K1J 4 * H 9(L 8 ($/-# + 7-3 /!--N 4@8/ $/ (/ ; 3 /! @G-! @G = @8;DB! 8 4 H& 3 / + 7- > + =) $ $/# + 7-8 5< V< N -< '+ /%@-4= = 37 8O( =2 #$/ %@! % #7- <=3 #- /7 ) + 8; )A 3(7 ) 3 : 48 0 &* &* & ) + '! >0,-8 ) 7 :& 7 $ 0 & 0 &* & ) + &* '! / &

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% # %! c! & ' ( % T & ( S '& T T & % & # S & T & % S! & T c ( % & % S & T T %! & & % ( & T!$ & T& T %! $ U % ( %& T $! & % S %! & T T %! '! ) % V & Z ^ 3Z & ^ )#%! (* [Z ( Y[Z & ^ 3 $/!$/ <=%'0+ N, F 7'G@ + $/!7 > & = 7 M + %' 9) $ # % /) ) # ;+ $/7#- ;7 -+!-8;(3(&! #7; )*! $/B # /) 7# 7@ :B %@# <= + 7- G@! = + 7-8 H< H< + 03G-OV9-4?AR, CD@BID?AK HQB03?B@ 2 2C' +!! ()@ + + 3 $/!8 ;!( @ B = B3 ; +!B) $ B)! # / 0%+ 4! #@G*2 + 2 -G*-+ + # 8,F+ 9+ # 2&%@# < 7 =6+ # G3 =M7' M+ # 2 %@# <M 7 4 @8;D' 3! $/( +?# ; ( + %@( %@# < )A 7@ 8

! p fe^by ` i_dxe[z 6 + %@ 6%@# <7 > G 6+ #= 6 4 7 > G@ );/ 7'0#!/D' $/ + - D' 4 8 0 7 % =.(. + + 2- <=)A 0!$/ 8 0 + )A + =!$/ + - %<#!&&#$&%'!0 + $/ G' DB!0*-8 48 *+ $/7+ A 7 0 2 B! A$/#A)-!;$/ $/ <8 0$/ -6 3 3 %+ 4- :/ 0 2/ GA6 0 2 ( / = @8! p p k5_al ndga_aè^bl3^bmeme\ _ Y c(^] Y _A` + %@ 0+ # ( 0 4 97 >- (2 //!?# + G; DB!=*-8 48=$/ -6+ 2 09! + $/7 ;7 2 #A77 + @G 3 2 A A 7' * ; $/; 3. %+ 4 ( + + - 8! p Y gaè^] ae\ [ * #+ * ; $/ < )- ;7 % $) $ ( 3. $/ 7'( 7. $/ ) #+ 7 @8 + $/$//77 + B 0+ + # ( + /)*0+ %'#-. <G@ 9+ $/7#- 0 & + 0) $H &+ &%'# < 7 > 8! &$/ - ) &+ + 2 % + G( 4/ &) #M <-7@ 9 + 7- -3 9 + 7- G@ () +!/)B 3/% + : )( + / + + # 9) + 7 C' 62 #/ ) /! 3 A! /9$0%!## + &$/ # 8&P ); + ; $/7 /!0+ (+ # 2! & + $/. # A,. 7' - + + 0 /2 8! p _AaE\ Y [\exe[z i\ Y md] _A\ Z ($/ - >7 + 7 >- AJ LB & + #(;0+ $/7 > -#$0%@ 8/0 '. / 6 / B>-. & = $/! < >- 8 #+ / 7 % $ $/ </) $, E =4 08@I 2 77 <-!/ 0 + ) D'# ) $ # &) #+ 7 -#+ & + $/7 > + - + &3 + M =+ =D'# & + 7-8 D'#

A ) $ & $/7' 0) # 3 + M 0 /!-. )?# + < + $/7@ 0+ + #0) C' ; 3. )?# + < + $/7@ $/ % + 7'8 &$/ - &%' #+ + ) # <77 6, % ++ + +! 9 %-GI= 5% 81K 3( 2 G0 = #$/ %!$/ )* 3( = (%- % G3 + 7 + + ( + 8D'# $/ G'3 0D# 0 # % ) 0 $/7 0+ # 2 ) + + G(D#0+ &%'77 + <9 &3 %'. + # )' (+ $/7 >- <) + # 2( B+ + ; (+ + 8! p! \ ^BÈZ d _A\ c ($/ -/ + %@ (0, 7'3 + ;+ $/7@ /)*7 $/ + + # 2! 4 B5!,G! # 5' 8;$/ - 4-0 $/. %<= )!0 + = )A % + 0! )A 7' + - 0 <- $=80K 3( 2 A MA ) $R?-# % + + $/7' =)A&C' )B $/- =7 $/ ++ # 2 $/ '!$/ 8 + + 3( +! & + # 2 %- #! 77 <-!//!& 4! $=8 A$/ * A *$/ - A 2; <0 B B$/ <5@ + #- 7#- )A!&! $=8 H< H< CDMHK 0HO, CD@BID?AK HQB03?B@ 7 7@ )B (! @8;,E $/7 77 + + %!= /! 6 # & & 3( + 7- :0 & 7@ $/ 8; & ( -#$0%@ )A7 > + 3 =%'# <)9! @G; =7' $/ & 0 =! )! %@# <86 &77 + 077 6 % + 03 2 = 8(3$/ 7 + $/ - :($/$/!. 7' ; ) $=8! p p _Ac([À] Z &3( 0C' 0 -#+ 6%<6K # K#!, 8&,1 7 2/77. + 6 )$/$/ = +! /, % +/+ + 0+ 6%@&) # 9! B5HG 9;,A5HG', O%5%G 9;, B5'-G-4-5% 8

, D',. 7@ $/! $/$/ )B J L C' AJ L J *8 4 L + A$/$/ + %' >7 9 J *L J L BJ L J *8,L 3 $/ + *$/$/ G C' 3 C4, J *8 L P 5, G )& 2 & &2N N & /3 6 2 ) $ + =$/$/ 8; $/$/ ( +! @G- @G 7 + $/ 8! p p p _Ag m _Al ^B\ \ ^BÈZ d _A\ c B77 + / A% /&7 2- #A3( 4%< 4-+ 3 = 4-+ ' 3 + &( < 0 ; 7@! <) (-#$/02- #- <- $=8#9;+ 7 > B);, 7@& 9=+ $/7 > -#$0%@ 8 /77 + 6 % 69 &7 7' <6)( &! $N) + $/7 >-#$0%@ J L J L $, G-3 =! -#$0%@ 8+ $/ < B7 + 77 A )- ;! $ *# /J HL J *8 L J *8 *L J L J *8 L $/ &) # )@ ; ) $1 B (%@ +!/. = )B 2, F 7'0 ) $/ = && = 7

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

( & T T & )T % &! T (!$ & T ') H< V< /14 -K 6G-6, K @QB47O5IDC F 036 -GHQB4 QAK 0HO,, 7'/$/ <6 2 $/ / %# & 7 #!;! $/ 8 & 0+ + # = 2 & 0 7'0+ @8, 7 > (J L 7 6% 9= &+ 9! 0L &> ( )B @ 7'7 > () $ + @8 0$/ > $0#$ 9;#+ + %@ 3( 9 0+ @G /G= @7 > $/> J L J L 0+ - ; ) $=G%9G) A + &7 > - >- A3 + &$/7*,. 7@&) $R 6 = 7@ + - / <- $ 3! /8 6J L J L J L J L H 4 97@ / $/! & $/ 6 9 = 68 M + =%@%GA = /7@ $/!& % ' 7 > 8

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

# % T # # & T # & ( % &! % & )$T! $ + :4%1 #Q < @ % ( S 3! ' ( ' % #! $ & & % /#( %04 1#! ' ( ' % #! $ & & % %! & % # & ( % &! % & ) T! ' T M %4$!7 8 % ( T & S 1 3!

! $ ( % # '! $ & & % %%! # $ # & ( % &! % & )'T! ' P E & + ' [ a ( c & % #%(* Y %]Y P 3 T & S 6 & + D'# ) $ &77 6 = = $/ 7@ B $/!3 + # / / 7 2 #( + @8B% + 2 /7 -#+ /D'# + - /+ 3 + 2 &+! = G' 7 + $/ G= @8 D'# AA ) $ #B 5 ' B )' $/ B $/7@ A - )!B7 -+!-8/&77 + 9 ); /D'# A ) $N = $/! @J L;+ %' 7 J L @J L J *-8 -L H =D' &D'# 0A ) $ 097 + + ;3 <6 9+ $/7#- D'# A ) $H)B&) #+ P 5, 8 7 /! C'+ 2!= 9+ $/7#- 9+ $/7 > <9%<9 #+! /?-# 67'. () $ 3 = 68 =7 2- #& + @G( &3/ 3 /< 3 $/!0 6 9 / $/ 97@ $/! 8

-! ( & T '! ( /# ; %G O = ' & & % %! d % & T %! ' & & % %! # & ( % &! % & ) 7 7@ < ) =D'# &A ) $ 3 + M & 7. @J L J L J *8 5L B 3 B ; ) ; 0 (! 0 )' () #+ *J L* # 6$0# 7 <! J L%<9 / + 6 >7' B $=8/A4 $/! # J L J L + ; J L + J L J *8 4 H-L ) B ) * @J L'- * A5@ + * ;$/! #B ) *D'# A ) $=8; # D'# ( 7@ + #$)* $/ /7@

#( # #! ( ' & T '! 24 1%7 8 T & $ & & % %! d % & T %! ' & & % %! # & ( % &! % & ) T $/!( B 2 B <&+! ; & = G- 7 + $/ G-/! 3 $/! 8 4- + 9 $/ 7@ = $/!9 M! D'# A ) $H)A $/! > % 2 & L!! A 0N P 5, J L J L J *8 44L 3 J LA * + $/7 >0+ #! () J L 8B A /&$/!& J L J L J *8 4,L

A$/ @ A )- ;D'# * 7@ + #$ A # /+ A + #+ $/!+ $/7 <8 DB!# *8 5-G*8 4 HG 2*-8 4!4; 36 @ ;$/ A + $/ @D'# + - + 6 -+ = 6! @86! )0 = 7-. %< % +!! <M) 7 @G /J H HL 8 $/! #= / ) M 6& < + - + =%@ + # 96 $/!. <&7 ; ; + # @8 J H H-LA B7 7' 2!(2 # ) $/! @J L 8B, $/ /7 -+ 0 D'# ( 7@ + #$ 7' ) $/ %< 2!& *D'# 7@ + #$N$/! #2 # %< + - /+ J H H-L 8 4- + J H H-L( 0! 2 #G $/ 07 -+ ( + ; D'# ; 7' + #$$/! # B 2 H 4 8 % #,M$/ -0 )@ >- +!D'# *) # A) $E 3( & $/!;B%@ 7 @8$/ - ) 3( $/! // $/ 7@ ( $/! / 7 8(DB <G + $/7#- ( $/!+ @8 @G B+ + # A ($/ > $0#$E + (%' 3 & 7 > A + @8BDB <G A$/7* + 0 $/!A7 > ;7' @+ - #!& + == $/ > $0#$ + 2 # 8 A %- ;D'# ') # G ;$/ -77 ' B 3. $/ D'# A ) $1 & 7' $/! 8B # D'# 7' +. #$ $/! # 3 + 2 0 9+! 0 9 7 + $/ G = G' @8 ) 3!0 3(+ 7- # ) # /! 3( <- $/=# +! 9, % +=3 8F 9 < $/= % = $/7 $/ +!&= I 4 2 $/- 8

K L M # $ 6 7 M. 20 3 4 6 8 < >= / B 3 B 5 # L $6 # $6 # N $6 O P M O N # $6 # 7 $6 # $6 #E $6 7OQ R S! # $&% *')( +-, /01 5 # 7 $&% 9;: 3?5 6 # $&% 8 @A, 0 C D 5 6 #E $&% +*')( H A GF., IJC /01 20 3

J B. < G. >, ; 7 /. %& $ $A $!? & 3 $ 3 %! $ % $ K 01 H I * D E F C %& $ 021!B @A? % 1 $ < = % 1 $ 3 8:9 * % 1 4 5 6 %& $ 3 021, - + #! ) * ' ( S T B R % 1 $ K A Q B / Q B! % 1 % 1 % 1 $P 0 1. O<N H 7 ' M L

' B P 3 O 6 # $ 7 M,, 0/ I M 6 3 K L 5, G :, 7OQ R S J C C / 3 O 5 6 #E $ % H,. /0 R 5 # L $6 # $6 # N $6 O P M O N # $6 # 7 $6 # $6 #E $6! # $ % H + C 3 5 # 7 $ % 9., H. I C /2C 6 # $ %, 9

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

- 7@!= & +! <- $R 7@ + C'+ G*7 + $/7. /+ /%' + $/7 & /3 (2 <&)'3 <- 8(+ $/$/0) + %@ 3( $/ &7 + $/7 9 +?-# & 7 + %@ $/. # $/ 0) $/ < %' 3 6 3(=) # / 8= $/ #. $/ )A $/ <0+ %@ /$/ $/ + <0 )* 7 2 # = =0) # 7+ 8 $/ + $/$/ </# +?# ; )A + $/ # 3 + &+ + # * + (%@ 3( & 7#-A) # ;& + ) ) + =) # / 6 = % = =-. $/ ) # 7+ 8 V< H< + GVIEL K 9-CD43O 9-K @QB43OVIDC)6)CD47@BG5?BC B @ ( $/7 B + ;$/ # 8B A!A ( 7#-A) # + ) + ) # 0 8! 9;#+ + $/ ;+ B #+ A ;7 % $E )' +! + $/7#-! + $/ # 8 9;#+ + ;%' 3 3 7' '. $/ 7+ 0 h J L J 8 4L 9;#+ = + 7' ) $/(3 @3 2 + = + ) # 77 > $/ < $// + / 0!0?#B3!0 + $/ = / ) # 7+ 8 V< H< :3QB4 QAK @QAK ID43Le9-K @QB43OVIDC6)CE4 @AGV?AC + 0 &(! : &> 8 $/ < %'&! 9 9 # 9;#+ 9 + &$/ # 80& + & %- %<M $/!9 9 $/7 =2 + 8. $/ ) # =2 + /3 + $/ # %' 3 M 3(

- 7@ ;! 2 =%< J -8,L $/ <=%@ > 0 '. $/ ') # 7+ Dh Dh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

4 ωy ωy N 4 N 4 N 8 N 8 ω x ω x N - 8 N 2 N - 8 N 2 - N 4 - N 4 T # & #! & % % & # % c %! S S ) T # & # & T # & & % ) G J, FGA3 >- + = 8< 6 >7' $/ + %@ %' 3G 4!*-8 V< V< / G5L QAK -L C 50HO7Q F 47@C 9;+ /3( & > + / ; 7 =%<07 <-7@) $/ &) $ 2!+ - /+ 2 # )B/ $/7 )A!03( 8 4 4, J 8 -L 3 =#$&%' 0)3( $/! 0 7! 3 0# + + # & $/7 8= 0 0 # /+ 0) 9;#+ + $/ # 8;D'; 4 + $/ # G- B &(! &/ + + # & $/ + 8 J L 4, J 8 *L

Image Word Normalisation Polar Transform 2D-FFT Template Creattion Template Matching Templates Decision Making $! ( % U % & % & &! & & % ( % & % c & ) Recognised Word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

F F 6 $ 6 $ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ] ^ _ ` ( % & % & & T & & $ % & )+a T $ % &$#! % ( % && #!& T & &! & ) S+ * $ Y 0 6 0 0 6 0 0 6 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ]^ _ ` ( % & % & & c $ & & %! ) + $/7 = >- + <) # ) $H () 8, + = )A >-7@ $/ (3(7' ) $/ /3 /3( / $/7 + + # %< 2!!() #* $/ 3( D'# * 7' + #$E$/!. #2 # 8& +! ); 7#- 3 3% 9= 3( + $/ # :B 9;#+ 6J 9L( 4 6J 4 0L;. + =$/ # 8M= $/ D'# & 7' + #$ $/! # &) ( 7#-B3( 03( (+ $/7 &! B $/7 A % G & 3( &3;! / 3 / $/7 (3 & $/ -. $&#$F + 8BA% 8, 3 ; +! / # ;)*$/ 4 HH <-7@ 3 93 $/7 3 $/7 + + # 6%< 2!! )?# + <%& >- + ) $ $/ =D'# 7' + #$N$/! # 8(0 +! = + % $/ $0#$ 9;#+ = + $/ # 8

DB!-8 #$/$/ / 3 9 9;#+ 9 4 + 6$/ # 6# M+ $/7 6 7#-=3( $/7 3 9 2 < $/7 8D'#+ # 2 & 3 @: 3(= 3 + *3B# 0 + #+ B B $/7 G ; A 3 3 3(# @8(3( 3( #$/ = &%@# +! 3 &- & &77' &$/!= / 76 7@ % 2 0 ) 3 @8// GA + GA &-#$0%@ )# +! 63( 2 =%< @-#$0%@ )B 7#-3 8 25% Band8 & ED Band8 & SD Band16 & ED Band16 & SD Error rate 15% 5% 0 0 50 100 150 Words in the lexicon R a & ( % &' % & c $ & & % % & ) DB!-8 3 % 9 4 9 + 0$/ # $/7 /) $/ #! + - /+ = 3 3( 7' ). $/+ ; 0 () $/ 0#! B+ - + 8; A% 2 + + # 03! >7' + / $/=+ C'+ 6) #+ $ $&#+ $/ / 2& = /) # / $/ < 6 -. 8# ( # / %@ / (%' + # $/7 B ) $/ 0) $ $/7 &3 M $&# 7 /) G( = <- =2 0M+.?-# <! 8B ;;0$/ ( 5* + (& $/ # 8

F F * * * * * * F * * * * * * F * * * * * * F * * * * * * ] ^ _ ` R ( % & % & ' & T # # & ( % &! % & '! % ) & ' $ ) P 5 Y 0 6 0 0 6 0 0 6 0 * * * * * * * * * * * * * * * * * * ] ^ _ ` ( % & % & $ & T # & ( % &! % & %! ) & $ ) A# E 5@ + 7@ ) $/+ 93 E#! 9;#-. + <4 + 6$/ # G0 + + $/7#-.! ) 30 2! 7 <9 6A% 8 #! / $/&3 $/7 # 9 = 7' & # )(A% 8,-80A% -8 3 ; C' ( ) - 7' ) $1%@ ;3 =#! 9;#+ = + 0$/ # 3 ) /! +! ( &3 /#! 4 & + $/ # (3 + / + # = M 2 =+ + # 8 & + 0 C' ; ) ; 2 $/ A 7' #+ # 8;A0+ + 4& 2. <=); + $=G@ >-7@ $/ 3(7@ ) $/ 3 & + 3 $/7 ;) $/ %< 2!!&D'# ( 7' + #$H$/!. #0 ) $N + 9 )B ) @ 8A% -8 / 3 0 +! ) 5* 2-+ %# <= = 8 D'=4 *. 3( >- + + ) = +!!& 0 >+ 3 + 2 3 +!0) E8

100% 100% 150 100 100 150 150 100 100 150 Words in the lexicon 50 50 Words in the lexicon Words in the lexicon 50 50 Words in the lexicon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

25% 15% 5% 0 Source A Source B Source C Source D Source E Source F Source G Source H Source I 0 50 100 150 Words in the lexicon Error rate a ' & ( % & % T %! $ & & % % & ) & )

25% 15% 5% 0 Source A Source B Source C Source D Source E Source F Source G Source H Source I 0 50 100 150 Words in the lexicon Error rate a ' & ( % & % T %! $ & & % % & ) & $ )

$ * * * * * * ] ^ _ ` ( % & % & ' & T # &! % & %!! % )+a #! %! & % $#! $! & c$ # ) + & >7' $/ B $/7 B) A + 03( 0 ( >- + 3(B + $/ <9) $R3 $/! 0-3 $/# + 7-8 $/7 3( 0 9# 9 +! 03 6 $/! ) $H & $/ ) 8,+ +! C'!# -8 * -8 ( B) B+ 0%@( 2-0 C2! #7; 2( +! & ; 7@ +! 8(D' 3 %' 7' ) $/+ $/!0 3 + = + ( /$/ 0+ 03!= < /$/! 0 A /-3 ) 8D' R) 3GB ) B + $// @G = /) # 7 + + $/ ) F 68;DB <G- C) =7 + 3 0 /) $/ /,!* GA) 7 0 $/ + 3!& < $/!& @ $/-# + 7-8 V< 5< 503G5? 503O3Q CD?JK 6)C O7QB@ (3= >7' $/ 3 /7' ) $/ 9 ) # + 9) : 3() 3-3 G& 3M3 M+ $/7#-.! &) = 8;D' E3( + %' + # < 2 %' (+ ;3! <- $/! ; -3 ) 7 2 # <= # @8 3( $/7 (3( ) $/ =%<=+ + #! 2!2. # & ) =D'# 7@ + #$ $/! # 0) $/ < + 3 / $/7 () $F + / + &) 8BA% -8 * # A +!. ) / >7' $/ 8&& % & 3 9 + &), 0 +! 3 6#! 9) 8A% -8 = 3 / 6 +! 9 &) + 9) 7 <8

F F * * * * * * F * * * * * * F * * * * * * F * * * * * * ]^ _ `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

50% Error rate 30% 10% Band8 & ED Band8 & SD Band16 & ED Band16 & SD 0 0 50 100 150 Words in the lexicon a & ( % &' % )! & & $ $! % & $$ % & %! %?T & ) 3 =) $/ ) $ ) ) G;3 6 $/ -#$0%@ / )) G 3 = ' 2 % ) 8! _AÀ] m [\ d _A\ c(^bèi[ (+ ; 5@ (+ 8 + + /3( & $/7 3) $/ 6%<6 $/ <6 +! / $/7 &) $R / $/7 7! 03 @8 0! 2 0#06 + 9)( +. + < )A 3!& < G@7 2- # <= + # @8 + 3&) # ) (3 0 + # = /) $/!3 = $/7 G 303 0-3. M 3 3( 9+ $/7#-.! @89;+ M3 $/7 =3( + + # 9%<9 2!!/) # 3 6 $/7 3( & $/ <. + ) $1 $/7 7!& 3 @G' $/7 ) $ + 9) 8 6+ & & *) 7 2- # <9$/ 9 7- G-3 0 + # = =+ + #!3 = $/7 8 DB! 8 0 # B +! )*3( $/7 ;) $F) M 9+ 8 = %2 # =+ 69 7 =

100% 90% Case one Case two Case three Recognition rate 80% 70% 60% 50% 0 50 100 150 Words in the lexicon % & ( % & % & ( % &' % )! = $/!6 9 + 3( M $/7 &3 6 &%<&<0 A) A3 + &$/!B 2( 5* B3( & 7@ 8 / 3 + / 7 & $//+ + 7-/ 93 + 6 3 $/7 * A 7 B<0 )- (7 + 7!() 8A < 3 0 7 2 @G' 0 2!G@ ); *)A $=8 5* + ()' ; B+ ; &+ + $/ () ;7 + 7 =+ + #!0 2!2 # 8! p _A`J] m7[\ d _A\ c(^bèi[ + ) # 5@ + 8 =+ 0 + =3 = $/7 3) $/ 6%<6 $/ <6 +! / $/7 &) $R / $/7 7! 03( @8 0! 2 0#0 + 9)( +. + </)' 3! < G;7 2- # <& + # @8 /+ 3 + $/7#-.! &) ;3 + # &) $/!3 / $/7 : - 89;+ /3 / $/7 3(+ + # /%</ 2!! 3 $/7 ( 3 0 $/ < + =) $ 0 $/7 7-.!9 /3( @G $/7 ) $ + M) 8 = =3(

100% Case one Case two Case three Case four Case five Recognition rate % 90% 80% 0 50 100 150 Words in the lexicon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

( # #( # # $ %!$& & %!$ S # 04+! # T S S #( % P # c S (ST # U + :1G# % S S + 9 6 01 # - $ S S % + Q #( 1 S %! S 8H # V $! ) ) ( S S! # 78& H G %1G ' S S T )!& & &

# # $ # - $ # #( V %!$& & %!$ S M %4# T S S $! ) /#( G!&( KL 8 T T S %! (ST M #!7 8 T '% ( T & S S! 8H # ' )!& &!& & %! S #( )!& & ' $! ) % # /# S %! S! 1 & 297 $/7. % M < $ ) +!! + # 2, % +03( 8 9;+ 93 6 9 & >- + 3 7 %<6= -. /# %Q#

# (# ( $ # % R! & & %! S H ; # K& # T! S S! 24 3 # #! S S # U H # 8# * - % ( S %! (ST F 6#7 8 T % )!& & ' $! ) 24 # 01 - % ' )!& & $ $! )!& & %! S /# %4( 0 H& # 7 8 T $ S %! S!! / $/7 8 0 $/7 3(&) $/ %<M%! =!=) =D'# &+ - + G + %' M =7 2 #/+ 7- G( 6 3

)?# + 8 B $/7. % +! *7@ ) $/ 3( +!!( <7'. 3 ) GM 2- #-3 ) &3 + 3! <- 8 + G (7' ) $/ /7@- <&3 $/7 3( ) $/ 9) $ $&# 7 0-3 6) 8 3(0#/ = / 2-.!!97 -+ ) 5@ /3( M $/7 8M 7 -+ 7 -#+ 6D'# 7@ + #$ $/! # ) 0 + 6 2 # ) + + @8A/ $/ -< /!&$/ -) >- +! D'# ) # 0) $ +! &) / # %' $/7 $/ @8 ) 3!0+ 7-9I= 4 2=$/- (7 < 8

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

ω y ω x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

G ω y o 60 o 30 o 0 ω x o -30 o -60 T # & #! & % % &! % & & ) #$=8!==! 2 +?-# ) A + ); &D'# 7@ + #$ - / /7 2=?# + + + &) + 8 + 9%'& $/ 9%<!& 0D'# 7@ + #$R + + )( / + 0 + )(3 + 7 %<6 7 QE+ - %'-48( 77 + = ) /N N & < G= (3 <= $/7 $/ = = 7' + +!! 5% 8, 0! 2 + (?-# + = ) #+ + 2+ - %'-4 <$0%@ 0 7 /+ G -89= + $/ 0 + ) + *?# @ ; 2!B2 #B )- ; + B$/ # *%- ) $ / #+ + 2/2 + 0?-# 8=, #$/&3( 2 3( 6 $/7 =!= GB + $/7 / D'# 7' + #$ + G 4, (8 F+ - %'-4 G + M=) $ 2 + G G 4, 4, (8A 2! + $/ # 9)!!63 $/7 = 9+ ) 1 #+ + 2

4 4 Training Word Images Normalsied Polar Transform 2D Fourier Transform FFT Spectrum Decomposition Vector Quantisation Testing Word Images Normalsied Polar Transform 2D Fourier Transform FFT Spectrum Decomposition Cluster Centroids Classification Observations Reestimation For HMMs Model Parameters Multiple HMMs Probability Computations Recognised Word R T ' '! ( U & # % & %!! ( % ) <$0%@ 4 J 8 4 L $/ $/ @J L J 8,L L* * 9;#+ 0 + ($/ # ;%@ 3( & (+ -. 3 'J %@-4/2 + = 7#-2 + 8 B + B (+ $/7 >- <0 )' + - %'-4!(%<& ) + ) (8 P / 07 2 & $/+ $/7#- ;+ $/7 >- <6&! + - %'-4% 2 +?# 8 < H< CE@BG-L QB@ & ;+ 7- G Q! $E ;77 0 5* (+ 8 6 + 6+ G* &2 +?-# 6#!= 0)D'# 7@ + #$H$/! # 2 + 8 48 ^BZ [!02 + & 0%- #! @3( $/7 7!= 5* 0+ $/7#-.! 9) 8&0! + A4 H 'H02 + 8

3 2.5 Case-I Case-II Case-III Average distortion 2 1.5 1 0.5 0 64 128 256 Log(M) & & T U (! & & % U # '! ),-8 ^BZ [!&2 + 0 0 >- + ) $N @3 $/7 7!6) ; 8 =!9 + H'%&2 + 8 8 ^BZ [!02 + 0 0%- #!/ @3( $/7 7!M ) 7- -89! +,H,!, H02 + 8,77 <-! %. $/ B+ #!! $=G B + %' &&7! *%-G >= #+ + 22 +?# (3! = + 3 =& 7-. + - %'-48 #!9 =+ # ) #!9! $ 2!9 M7' ) $/+ 9+ @G ) ; 9;?'8-8,-GB3&$/ @86DB! -8 6 3 0 =7 & ) *2 # EG M6!6 + G() ' 4, BC,!* 8 =+ + =! + 0 2! &3 / -#$0%@ ( )*+ # + + - %@-46 + ) $ %= 4,%-89 0!. C'+ 5@ + # C' & + 6+ $/7#- 3!/! + - %'-48=P / 0 $/ ; 5* + 9 2!

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fe[c(_dxe[l3z ] \ aeij] ae\ [ 5@ (KI IN <-7@ 2 3 = 4- +8 8 8B,$/! <-7@ ; B ; 2 ' @ @ @$/- 8B ($/- '7 -+ (?# -. <& #!!0) $ #$&%' = +

1 2 3 4 5 T $ & T % & % & S % c % $! ) %@! / + #< #$&%' )B G' #!==+ + # $/ & )@ $/- 7 $/ ;+ /%@ /+ # ; )@ #$&%' ;) ;7@ ;$/- -%@ + $/ B -! 8# & ;+ 7- G A ' @ @ <-7@0 + ) 3 9$/- (3 -#$0%@ );?# -G' 0DB! -8 *-8; + = *$/- @ 3 ( < 9) $ & 0 #+ + 8< &+ 6%@/$/ $/ + < 7 CH ) C4 p fe[[z ] Y c(^] Y _A` _Ad3] fe[ c(_jxe[l3me^b\ ^Bc([j] [\ Z 0 )..!KI9I #+ #?# #!& < 7. $/ 8; '7 %% </7 $/ /% <2 # 4 4 H, 0O#$&. P +!&7 -+ # 0$/ = 4- + -8-8,8 /!# 0 + & -+ -$/ > $0#$=8AK 3 2 G-& 2( );$/- A7 $/ 2 # + # =< $/- (3 9! 3 2 # &) /86D' =+ # >7' $/ G; $/ &) R3 =! 5* / $/ <6 + 2 # GB) 3( %< $/ 7 -+ & ) </ + 4 4, J -8 -L J L 4 4, J -8 -L 6

+ 9;?-# 8-8 ' (# 0 $/ $/ + 8 K 3( 2 ) &C'!&?# + 0)B! 0G J L($/ <=?-# = 8/ 0+ + # J L = ) <6&2 # 8 4-3?#!/ 7 % $=8A/ $/ -< G'7'. $/ + J L, # ) 3 J L 4, 4, J 8 *L 3 *7 C' 2 #8A,) @ B 7 + $/ J L, $/! @8 ael ] Y mel [_AbEZ [\ ^] Y _A` Z [ DaE[Èi[Z P / $/7 ; 4 /) $1 5@ ;) G <-7@ 3 //-. 3 @8&% + 2& ); & +! <- $R %- ). 7' B$/- 8A% 2 0?-# + G G+ # <+ )A 2 * 7'?# + G 4, G-3!?# + ) ;) 'G ; @#$&%' ()*) # /) ;! 3 $/- 8B, + $/7 ()* 5* () # = / ;3( 4/ ( 3 = 7-8B 4 --/7 %% < );$0# 7 % 2?# + / 3(= 797 -+ 8! 9;?8-8 G- C' 7 + + # /J 'L;) + =?-# + G 4!/ /+ 07 -+ ) $N 48 + = 7 $/ > $/ ( 7 -#+ )A 7 %% /J 'L J 8 L

λ1 Probability Computation P(O λ ) 1 λ 2 Probability Computation P(O λ ) 2 Observations Maximum Selection Recognised Word λ V Probability Computation P(O λ ) V! ( # & & % ( ' & & % % ( % % (& T % # & U & % # % & & T $ % % % ( $! ) $/ ) $&# -8 ' 8 G) #&&7! *G # + +! < J L $ $ J -L $ $ J L $ $ J L J $ $ $ $ J -L $ $ J -L $ $ J -L J -L $ $ J -L J -L L J -L J L J L J -8 L J -8 -L

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

100% Recognition rate 90% HMM-I1/128 HMM-I2/128 HMM-I3/256 HMM-I4/256 Band16 80% 0 50 100 150 Words in the lexicon ( % & % & ' & c $ & & %! ) )* <$0%@ (7' ;+ - %@-4'G% )@ 0 ( & 3( $/- 8 >7' $/ ), 4, 8 = 9 >7' $/ + 9+ - %'-437 :,*% <-$&%' 8 A 4 C' >7' $/ ' )A 0 / 3 # = & 3 $/- 8 & >7' $/ & 0 ) 4,*%-8 ) # = >7' $/ $/ B 0 7 2- # >7' $/ >-+ 7- % )B & 3# 9 / = 03 9$/- 8 >-7@ $/ ) = &,,*%-8 DB! -8 0 # B +! # )* ) #( >7' $/! (3 / 7@ ) $/+ )* $/7. % +!. + %' 0 0 (7 2- #B+ 7-8B( $/7. % & +! B#. = =3( $/7 / <9;#+ M + $/ # 8 = $/ 4-&+ M%' + + # ) $ 0C'!# :=C' G -.

100% Recognition rate 95% 128 Clusters 256 Clusters 90% 33% 66% 100% Size of training data set T d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

2 F F 6 5 $ $ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * F F $ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ]^ _ ` ( % & % & & c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

O O N 7 M N O O 7 E 3 N 7 E 3 O O E S O O S? # L $ # $!! N! M N O O E 6! # 7 $ # N $ # # N! M N 3 O O O 7O N 7 M 6 M L 7 0 0 0 0 0 0 Words in the lexicon 50 50 Words in the lexicon Words in the lexicon 50 50 Words in the lexicon Words in the lexicon 50 50 Words in the lexicon 150 100 150 100 150 100 150 100 150 100 150 100 100% 100% 100% 0 0 0 0 0 0 Words in the lexicon 50 50 Words in the lexicon Words in the lexicon 50 50 Words in the lexicon Words in the lexicon 50 50 Words in the lexicon 150 100 150 100 150 100 150 100 150 100 150 100 100% 100% 100%

100% Recognition rate 90% Band16 128 Clusters 256 Clusters 80% 0 50 100 150 Words in the lexicon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

100% 100% 150 100 100 150 150 100 100 150 Words in the lexicon 50 50 Words in the lexicon Words in the lexicon 50 50 Words in the lexicon 0 0 0 0 -. -. 100% 100% 150 100 100 150 150 100 100 150 Words in the lexicon 50 50 Words in the lexicon Words in the lexicon 50 50 Words in the lexicon 0 0 0 0 (!(, (!(, T! $ % % '! & % % # % & & ( % & % c & $ S # &! & ( % & % & & ) % #!! % & %! ) % %!! & T! & & $#! & % % ( & T! $! )

F 2 2 Y 6 5 $ $ * * * ) * * * ) * * * $ * * * ) * * * ) * * * $ * * * ) * * * ) * * * $ * * * ) * * * ) * * * ]^ _ `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

100% 90% Band16 HMM-III1/128 HMM-III2/128 HMM-III1/256 HMM-III2/256 Recognition rate 80% 70% 60% 50% 0 50 100 150 Words in the lexicon ( % & % &! ' U % & %! )' T ( %!!! & T & & % ) $/ 0 ) 6 = 4,!* 8&&) # 6 >7' $/ 0 $/ 6 97 2 #= >7' $/ = >+ 7- ' ) 3( # 6)! &3( 6$/- 8 >-7@ $/ & ) 6,,!* 8 DB!8 4,/ A% 8 # 0 +!. # ); ) # >-7@ $/! 3 07@ ) $/+ 0 ); $/7. % 6 +! GA + %@ &7 2- #+ 7-8/ $/7. % / +! ;#. = (3 & $/7 B& 9;#+ + /$/ # 89A% -8 3 & +! 2 Y * * * S S S * * * S S S * * * S S S * * * S S S * * * ] ^ _ ` R ( % & % & ' & T # $ % & $ %!& T & &! ( % )

!!! #!! $!!!!!!!!!! %! &! '!!!!!!!!!! (! )! *!!!!!!!!!! +!,! -!!!!!!!..!.!!! / 0 12 3 4 5 3 K B B 6$ % A 7 3 A R B P A 1 B K 89:. 7 B 3 T

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

P. P. S 3 3 A.!? 6 3Q 3 3 P Q T Q A Q 6 % $A % B! 1 100% 100% 100% 150 150 150 150 150 150 100 100 100 100 100 100 Words in the lexicon 50 Words in the lexicon 50 Words in the lexicon 50 50 Words in the lexicon 50 Words in the lexicon 50 Words in the lexicon 0 0 0 0 0 0 100% 100% 100% 150 150 150 150 150 150 100 100 100 100 100 100 Words in the lexicon 50 Words in the lexicon 50 Words in the lexicon 50 50 Words in the lexicon 50 Words in the lexicon 50 Words in the lexicon 0 0 0 0 0 0 B B K 1 A B 3 B A Q B B 3 B B 3! A % $ % $P! A!B! B?! T B B K : 9 $ 3 B T!B! K B B A Q

# $ # $ #.# %!& & %! S & ( %G ' # &T S S (! T 04 H$# 7 8 @ @ T ( % S S 2 F G '% S (ST F P *# A c # % S S /# 7 %1# G ' S %! S + :4'# 8 % )! & & $ $! )?-# + 8(A 2 + $/ 2 & )@ + ; = G?-# QF3 $/7 $/ @8?-# &# & )( > + - %'-4 G* ) + = +! #7@8 #B 6)& 939# ) =!M 63( E$/- G 3 /3# M) &! = +! < $ 7'.

O$ # + :4 #( /! % S %! Q / #! & T & #! % & ( % & c 8 7 8 > > -T ) ) $/+ 8; <- $H+ 2 =&! +! + $/7 & $/7. % = +! G' + %@ 7-8

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

% V % & & % ) a T %! $ & T & ( T &' % ) ( & ' 3Z ^ $/! )* 3( / 0%@ +! = ( -#+ / 0 <- $ $/ >6 )% + 497 >- /J &)! #'L93 /7 > J %+ 4! #'L 8 / ( + @G0-#$0%@ ()A 7# / &7 7 3 / $/!B) *) # > + 0 ( + # @8; 7; + # % $/ @G!-G= 4 =$/- C'+ @8AO#-C' G # %' ;7 -+!) B (3 $/!( $/-!7 -+ G ) 4- +2,8-8,8 4G' 77 3 + = #+ $/! 8 V< H< + 4 @BC ek OVC @QAK 6)4 QAK 0HO ( (& = ' #; #!/ + + =7 $/ 2 ) >- 8# 0 % < $/!B G (% B3 2; ;$/ > $0#$ -#$0%@ ( )*% + 4&7 >- 8BD';-3 / + 7- G # / $/7 + < +!& 0% 0 3 =7 + @8 # $/ 2 $/ / ) 7@ %@ 2 %@ 3 0 89K 3 2 G + # $/ )A % # /+ ) ( $/ -= &C> ) + 07@ # 9 ( + 207' )B + + G 7' + < G'%' 20%@ 3 8

$ V< H< (25K O5O-K O5M! #+! 4 ( & 3! 3 - )* 7 >- 3 C. <& $/7 ) < 2! $ 84- +A,-8 8,-8 * 2 3 0#$&%' )!9! $/ 8 K 0$ $/7 $/!= @!. 4-#! $ 4' 8/ =7 A$/ -93 0 /7 >-, 3 2 # 7' / < 2 # /4 3 M) $ =7 2- #&. @8 9 = 3( #%-. &3 M + @8 M C' ( #%-. @G7 >- B$/ 4 &) ; & )' ) 3! ) # + ( ) # C' @: N 4 N 3 N 2 N 5 P N 1 N 6 N 7 N 8 ) ) ) ) % ) '% # & & % & T % % & U & c% # ) % & T ' T & 48# + + 2- <9#$&%' 80&+ + 2- <9#$&%' $/ # )* 3 $/</% + (07 + # ;7 >- $/!(+ + 8

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

! R # & & T % % % ( ( & T $ ) - & % $! & % & T! & %! %& T! % & # S '$ ( % (! % & & # % & %! # & % ( % ( # % & S %! $ % & # & % ( & T! & % )

;) # G 7 > * ( ) = &=I/&(AE & +9 &( 2E & G 0?+ %E & G' 7@ + 2 <8 -+ ;) # / ) = 4 M = 5* + M%<!! $=8(D' >-$/7 G' 0+ 7@ 2 9 & 3(!-. %@#! % + 07@ 8A-# G B * $/7@ * # (%' ;! / /3 = $/! ; 0+ + # 4 @8; 77 +?# ( A07-0) B# & *KA5H -3 0$/>- $&#$H+ + +?-#3# $/- ) <!/. # 8;0! $ =() 3 : 48B, -+ ') # 7@ = $/! 08,-8BD'B + 0) # (7@ @G$/ # ; # )' (! + + ()@% + 407 >- A3 0! - $/! 9 ; ;+ *8; # /$/ $&#$F2 #)B8 8BD' + 67 )() # &7' 0+ + # 9;#-. + + 8 )0 = + 6 = ==?# M$/ 4 = 3(6) # =7@ &) /$/!! /! #7@8 8# ) 0$/ 4 %'&$/! 9 $ $/ 4 0 %'($/! @G $ ( $/ 4 ) $/! + 0 /!! #7@8 *-8BD'B + /! #70C'& ;2 #()' 3+ ;%</ 2!! ) # /7' 07' 8/,! #76)(/$/ $&%' + + ' /! ) # 7' 8 8BD'B + /! #7& (;$/ ( /$/ $0%@ B -% + 4 7 >- * 6) 3 + 0+ + B) @) # ;7' A$/ $&%' 8-8#! + + + 43 77 7! #7=+ 8 8 $/7#- + + 2 <=-#$0%@ )B +! #7 + (). 3 : G d _A\! K &= B L E _AÈÈ[ij] Y Y ] n 2@%G

% 58#! $/ 2=<! #7 3 6+ + 2- <#$&%' 03 +?# / 8 / + & / =3(/6 7# #/% + M3 + + # & > + )@% + &7@ ;&& /7' 8AP 6 3) # 97@ 3( 6$/! @G 6 7@ 7-. 7' = % + =7@ %' + $/& $/@7 > 8 %]Y Y Y3Z &_^ 4! 7 ) =3( $/!&+ 0) -#$0%@ 0) 4 3 + 4 + $/$/ + M $/ &3 M6) # 7' 8 ;! >- + B 4 G- ; & ) $/B 3( / 4?# + )') # (2 + 8; ( 3 5@ ; #+ # ) # & # 9 @8O( > + -7) $ 4 =! 7=%@ ) >- +!0 $/!0) # 8 V< V< + ek O HQB?A4 IJQAK 03O + & 4 6! 799 > + 4 80 %< 2! + 4!9) $ ) # 7@ 7 -+! ) $ 7 > ( 9 0 + /# ( +!9 ) # 7@ 8#!/ 7 -+ 07 -+ # &$/ 4- <97 >- * %@ 2 2 M 2!! @8 =3 $/! /# = 2M 9 + E9J #;O I L(C' '/% + 47 >-?# A G 3 (7 > -?# #= -G0 2 &% + 47 > -?# 3(8,M $/7@?-# $/ = & # = 4/.! 9=+ + A / &% 2 9?-# + &) 0KI I 3 A C' @8& 4 > + 7 -+ # &# 9 B!# /%<& () 3! # :B ) B ; ( 3() # 7' & $/ #%-. 3( ; -+ &!() G- 4-3 + % + ) $ # 9%'0 > + 9%' ) 0<9 )B 4-(% +!&) $ 8

) & $ - %! & T & % $ % % $[T %! $ & & % & & ) V< V< 0V0 HQB?A4 IJQAK 03O #!0 4 +!G- 4 (+ + 4 ) -7;3 + = 7 6%<9+ 97 );7 > 8,1#$&%' );, % +0 26-7-. 4 7@ G ) A%,-8 481 6 + %@ 2 & +! :A $/7 ( -7@G+ $/7 >0-7@G&#% -7@8 p Y c(mel [l _D_Am + )=! & 4= 0%@! ) $R) # /7' 0 # / 0 $/7@! @89B>-$/7 )B +! < + %@ % $ @ G % @ -G 0@ G$ G + $ @ G * ' G + * ' @ G G * : BG' @ 8;, & G G' $/ <) $H/ $/7-73 & <& -3 &B &3( * ;.*P,- 3 =DB! 8 *-8 p p _Ac(mEl [ l _J_Am G (+ ( )A B 3(&($/ 4;3 + /+ + 30B ) # 7@ 89B>-$/7 )B0 3(. 4/ -7+ %' = ' @ 0@ G @ @ G * + 6%'& 6 @ -7 :0 3.(I?-#, 8 @ @ G ( @ G* ( * @ 8 9B>$/7 )(. 4-7 * @ @ 80DB!-8 */ 3 3( 3(. 4 93 & /. #!-,B /

p h _AaEbEl [l _J_Am 0+ 0)( 3(9+ + $/7 / + $/7 >6-7 8<9B>. $/7 )A +! <=+ =%@ J @%@ @ L 8 V< V< 5CD4 QAGV?AC):HCDQ K 2-! >- + 0 4-* -7@) $ ; 4 0! 7)- B3( $/!G* + 6 4 3F ) $/ 6 =. $/ *) # 2 + 89;+ =) # ) 3!0 + 7- @: 48+ $/! 9) # =J >4L : ) # &! 2 &! )( 4= 2 4! 0 $/3( @8 + + # =() 3 : - - J -8 L - $/ $&#$1/ $/ > $0#$ 4! ) 3( @G* 7@ + 2 <8 + 2. # 0 = 2 H 4 89 ) # / ) & = @8,-8 # 2 # ) # J >,L :B A) # $/ # B + # 2 # ) 484- $/7 < 2-9;#+ 9 + 0%@ 3( 9 3( ) # 7@ 0 ) / 49%< 0+ #(! @86 ) #?-# = 03 4& ;0 $/7-7@G=4 3 4! 8O;<9 C' (,/?# 3(3 0 + $/7 >= -7@G 3 = /#% -7@8, #!0 *) # - B;$/ # ; + # 2 # 7 + <G 3+ # 2 M 2( $/ (, 2 #G <& ( # ) #*3 + $0% 3 = ) # 8 8#9;7' ) # J -L :( ) # C' 3( 7@ )A 4'8 )A ) 3!2 # :

d c b a & # # & % % T & # T U # ' # S T % T ' & # T 3U # # ) Q; # + 7- H &2E & &BE & 4 &2E & &( 0E &, &2E & %E & &( 0E & &2E & &( 0E & &( 0E & * &( 0E & %E & %E & &(BE & %E & &> 0E & %E & %E & ;) # +!# /%@ 3( = $/ ; 4(%'!! 5@ &+ + 86DB! -8 # 39 4 /. * &, /, 8; 3(/ 4-2 $/ + @) # 2 # ( >-+ 7-) $(3 + =?-# = &/ G' 7@ + 2 <8 T & % $!! % (& T! & & % ' & U $& & T % ) T &! & ' & T &$ & & & T % S & T & T! C %4 1 #04 # c S %! U & T % S & T & T! C %4 1 # 0 -T # c ) 8#! 2= -+ 6) # J L : % < ) # +

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# v u 17 16 15 m 11 12l 14 13 n 10 k c 2 6 h 7 8 i j 9 3 d 4 e 5 f a 1 b g T! ( % % ( '& T ( % & %( T & T! 6 ; K1L 8 ( >! c S %! & T & % & $ % (& % $! % & # % % $ ( $ % & T!' & T% # )!$ & T & & ) & # % & XEgA[ Y ` Y Èg 4!) $1) # 7' G + 7 > ' / 4& (7 #$/ / %@!& //!!$/ G@ / + 7 >- // # * $/ <+ (2- @89;+ ( 7 %<M & 3 7@ GM = ), /7 > @8 = $/3 <G' ) 3!& () $ 4/ > + =# ' >-) # 7' + @8(DB! -8 5& # = >$/7 )B 7 -+ 3 + = %@ 3: 48BD' + = )B7 >- ;3 + = 7 & 4/%' 3 = 30). # 7' 8,-8BA ) &7 > ; ==?-# + /)( &!$/ ). 3 : J L 4 ) $ C' 7 >- * / 8 J %'L0, >7 > * &/ 3 @%' )B7 >- %'!!0 0 > 4'8 J + L + 4& 7@ 7@ + # ( + %@ 3( '7 > ( / ;0 (!; ;%@ 3( & (C' ;0 ;7 >-

8 J 'L ) * + ; @ @ 7 C'! J,%'L G 7 -+ = 0 > 7@8 J L 4 7/!07 >- B + # G- + / 7 > * 8 J ) L,!/ C' (& 3 (7 > ;B!$/ 7' 8 J!L ) ( ( $/ ;7 > A ( A! 0J -L G (7 -+ @8 J 'L A & >/7 > ( &%'/ = 3H!97' 8 =J,L 8 84- #A8 p [ÈgB] f ^BÈX _A\ Y [À] ^] Y _A` 9;+ & 40 B 3M ) $/ /?-# + )@ $/ (!$/ 8 9;+ /!$/ & 3(9 7' 4 2,-GA3 + 2/ + - J LMJ L GB 7' + 2 <8 A9+ + &!$/ ( 3(0) # ( >- +!$/! 9! 816!$/! @G G $/7 < 9;#+ = + %' 3 = 3/ 7' J L J L J -8 L &! G -G* &! & 0!$/ 0$/4 3 '. >- 8 M J -8 *L *7 -#+ A 3(. $/ ) # B2 + *) * + 0 B!$/ %@!!0 &/ 4'8 ae\ ÈY Èg(m _AY `J] Z = = &) # =7' G; < & $/(% + 467 > 3 9 4 +! = $/ + < ) $ 9 + M -. 8 07@! 22 #% -) $/ =%@#- 0%@ 2 #

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

0 0+ 6 $ $ $ 0+ $ ] ^ _ `! $ & # & ) 0 0+ 6 $ $ $ 0+ O O Y + 0+ Y + $ ] ^ _ `! & # & ) V< 5< + F 0V95C U-0V0 /+ - %@-4 + # <-$&%' 8 <$0%@ M A% -8 48 C' C2& <-$&%' 0 2 ) G@% + 47 > 3 <= + + 2 <=2 # G@ -73 + 3( ) $/ =3 >. +!& 4-8;0 )A <-$&%' 7 9%<= + + 3 + =. $/ '2 + 8 V< 5< F 0V95C U-0V0 9+ - %@-4M + # H <-$&%' 8F 9 <$0%@ = 9 A% 8,-86/C' & 3 2= <-$&%' 0 2 ) 0 GB) # 7@ G' -7 G'= #!/7@ 8& )B 0 <-$&%' 0 7-. %< + + 3 + = 3. $/ '2 + 8

10 5 30 31 29 28 27 26 25 24 23 22 21 20 13 16 15 12 14 17 19 18 11 9 4 3 2 8 6 7 1 '% # & & % & % % ( & c $ & & %! ( % & # % & # 3U & V< 5< OVID0V9-K OVM V436 5L CD@ + # ( 07 -+ / > + ) $N! 2 93( 6 $/! G* 9 ) $/!0 ==?-# + /) <$0%@ 8 ] \ ^Bij] Y Èg 4!/) $R9! *3( 9 $/!G' &$/- C' 4 9! 7 C' &% 2 @GB &3( 6) # &2 + & & >- + @G; C' <& + - %'-4/ & (# 0) $1 % 2 =?-# + 8 D' 3!0 7 &7@ ) $ ( 4': 48B, 77 <!6! $=G;/ 4- +8,-8,-G;) 3 %< 4 &$/- C'+ @GA 4- + 8,-8 8A B # A 0 $/- C' 4 @G@ 3 =DB!# -8 44. %= -8 4,. %@8

27 23 19 25 18 20 13 24 17 14 10 22 21 16 9 15 12 11 8 3 4 5 6 7 2 1 '% # & & % & % % ( T %! ' & & %! ( % & # % & # 3U &,-8#9B> + ; 4-A& -7*) $ ($/- C' 0 4 &A >-7 4- + 8 8 4-8 -8,8B;3( 0 $/!; 3 & 0DB!-8 44. + 7 -#+ )4,() # ;2 + GA,. 4 + $/7 > -7@G $/7-7@80P 0 03 6 $/!& 3 6 9DB!-8 4,. +&7 -#+ 04, ) # 2 + 3(/ $/7-7 8 8B,!= + -7 & 7 7@ + - %@-4 <$0%@ 8 8BD' + -. -7= 4: C' (2 # $/ = <4- +-8-8 -8! + =) # 2 + /0 )B 0 2 <9+ -. %@-49 <$0%@ 0% 6 $/ $0#$ 9;#+ 6 + $/ # G' A% -8 48 p ] \ ^Bij] Y Èg A 4( 0 7 2 #B + @G 7 -+ ; B3 0&! 3( $/! &7 -#+ 0$/- C' 4 @G = >- + (3( /) #

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

0C' +?-#0 ) $/ 9 + 9 4=. $/ ) # (2 + G3 ( + & +?-#( ) & + / 4?# + / )( $/ A 0!$/ 89;+ 9 +?-#&# 6 7 + - %@-4& 0 + - ) # 2 + ( 0 + <$0%@ # % ) (!& +! =7# 7' #!/KI9I= 8

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

) + Zero-order Probability First-order Probability Words of the dictionary Training State Assignment Probability Computation State Transition Probability Initial State Probability Training Samples Link & Loop Extraction Feature Extraction feature vectors Clustering (VQ) symbol prob. Modified Viterbi Algo. Recognition classes centroids Test Samples Link & Loop Extraction Feature Extraction feature vectors Classification symbols Result! ( '& T! %! U % ( % & % c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) ) ) *) ) ) ) * / ) $ ) %< <6) # 7' 0 #& & 0 $/7' % & + $/7' / /$/ 4( $/ ; & 48B( &+ $0% A+ $/7, G, G, G, G, G *, G, G, G, G &, G# 0, G#, G $, G#, G# * &, G# 0, G#, G 3, G' 3, 8 2 3 1 8 7 6 4 5 2 3 1 3 2 1 1 2 S1 S2 S3, % S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 %, % T & & & R T %!' $ & & 1 %! 7 O > ) % & % %!! 24 a $ % & c# % & % & % ( & & 1 %!! O 7 > ) 9;+ $/ <=# 7 0 #+. # 9 )..!KI9I98*&-#$0%@ )( $/- 2 0 #$&%' )B 4( (; 3(. + $0%. = 8(D' >$/7,'$/ <=%@ + $/7' : 3(0 4-B3 ( ; & @G G;$/ () $/ G-B 4-3 9 = & ) $=8 $/7 & $/ < # 7!&,-(( ; (3 + +?# <&7 2 $/>- $&#$F#$&%' B)@ 4-A) B, 8,-$/ <%' + $/7' 0!( 4-(;) 3( 8;

) + $/7 * B $/ <&# ( 7!,+ $/7! 8;DB!05-8 & 3 ( /) $ )B,<, 8 & 3 + $0%, 0, 8 p p nec b7_al3me\ _AbE^BbEY l Y ] Y [Z &QF +?#/ $/ ) 6# 6)!!= <-$&%' 9 + ;KI9I177 + @8B). $/ *+ #!! $=G 4- + 8,-8 8 4G 77 7 = 0!/ $/7 9;#+ 9 7+ #$&%' * ) <$0%@ + 8B * 73(* + # 0 4- + 8 8 8 48 <$0%@*7 %% (+ =%@+ + # =) 3 J L # J 58 4L & <-$&%'A7 %% + $/7#- = + $/7 =!!8# & +! /! + /) # 2 + ( B! & + - %@-4= <-$&%'*+ % = 9;#+ + $/ # 8 p p p ] ^] [me\ _AbE^BbEY l Y ] Y [Z, $/7@ ( 7 07#-! KI I 07 + + ; 0 $/ $/-, 7 $/ 8 /C' & 7 2& + < + ) $R! 2 92-+ %# <93 + + # =. C'. ( 7 %% 8! J L # J 58,L J AL J 58 -L P! J LA B 7 %% < B - B &! 2 &3 G' J AL ( 07 %% </ 0 6) 3 ( =&! 2 =3( @8 ' 7 %% <&+ =%'+ $/7#- % = -+. )A 3 ( $/ <# <-7@ )B $/ -. <# (3 7 &! (; #+!& 8 ) / &C' 03 6 # 03 + 6 7 &! /

H H ; 7 %% < *?-# )- A 8 )- ; $/ -. </# ( 7 ( 3(0 #+!0 ; / 7 %% < )A C'?# ( 7 -#+ ) )A C' ; /7 %% <&) $F C' ; + J AL 8;0 @ 7 %% </?# = / 3 8! J L! J L J AL H /7 %% <03 & $/ $/ <&# + + # () 3 J L # J 24 A L J 5-8 L ( ; 7 %% <%@ 3( /< 3 B ($/- + + # + +! < J L J BL p p _JXEY [X Y ] [\ bey7wl ga_a\ Y ] fec 9;+ 03 / 0 >- + & B 7 /%<&; ;7 0 #! &KI I68* / & 2 B7@ % 03( <)( -+!/ &7- $/ =?# + 9 -+ 3! 2 M% 2 M?# + 8 # /=$/- C' ) $R); &Q %B! $=G 4- +-8-8,8,GA 9 &C' 7- $/@7 = $/. 7- $/@7 8 D' 0 40)B3( 9 +! 77 + @G'+ % 0 $&. 7 2 $/ (+ %' $/ )@$/ ( / (C' 7- $/-7 / ; + 2. @8 77 + / > = / $/ 3 + 6 7 /+ + F8&, #$/! /$/- B 6 + / 97@ % J L/ 9+ M %' /7 & + M J L GB3 07 %% 0 J L;3 4, F8

( + < H< P 47L GV4 QAK 0HO CE@BG-L QB@ &3 $/! %'!! /#-0)( & 9) 7. 6 7- /3 : 4- $/7 C', % +G*-# #- @G*9, % + A *) 8 9;+ $/!C' 07 6 0C2/ 7 7 -+!?# + /$/ 9 7- :!G@ 4 6$/- C'+ @G 4-7= >- + @G) # 0 >- + @G'Q08' # 6?# + 9 )% 2 0 &3 -#+ KI9I98 A% A58 40 3 +! )A $/7 $/ < $=8 F + 5 2 @ * * * * @ * * ]^ _ ` T ( % & % & & T % ( %! U % c & ) 6 5 $ M %4 ) B M %4( ) M %1 ) B M %1) M %4 ) B ] ^ _ ` T c & # & # & & T! M %4 ) B! % & ) $ % % &$ %& T % S %! $ % % &'3U! $! ) A/ ( 7@ ) $/+ )A ( + $/G KI IR3(( #! H!H. 3( > + @8 #B ) =+ 7#&3(/# ) 0! 7# 7@ 81A% :5-8,MG%5-8 G 5-8 3R 9 <- $ #- 7#- ) =3( $/7 /=) $ + ) G 8 P < $1#- 7#-; 3 ; $/(3( /$/ ( /+ G B$/ B $/;3 &3(; +! /%<& 5* ;7 0 #!0 KI I68,(