Bai bao nghien ciiu mot sd loai dac trung co the ap dung cho bai toan nhan dang cbd Viet viet tay rdi rac.. Tir do de xuat mot mo hinb nhan dang chii Viet viet tay rdi rac tren co sd phu
Trang 1Tap ciii' Tin hpc va Bleu khiin hpc, T.25, S.l (2009), 88-97
KET Hgp CAC BO PHAN PHAN iCfP SVM
CHO VIEC NHAN DANG CHU" VIET VIET TAY R6^I RAC
PHAM ANH P H U 0 N G \ NGO QUOC TAO^, LUONG CHI MAI^
^ Khoa Cong nghe Thong tin, Truang Dgi hpc Khoa hgc Hue
^ Viin Cong nghi thong tin, Viin Khoa hgc vd Cong nghi Viet Nam
A b s t r a c t This paper studies some features, which can be applied to Vietnamese handwritten character recognition Base on SVM classification and Haar wavelet features we propose a new model for Vietnamese handwritten recognition Our test results over Vietnamese handwriting with 50,000 character samples show the relatively high accuracy of our recognition model
T d m t a t Bai bao nghien ciiu mot sd loai dac trung co the ap dung cho bai toan nhan dang cbd Viet viet tay rdi rac Tir do de xuat mot mo hinb nhan dang chii Viet viet tay rdi rac tren co sd phuang phap vec t o t u a ket hop vdi lua chon dac trung wave-let Haar Cac ket qua thuc nghiem tren cac tap dii lieu chii viet tay tieng Viet vdi 50000 mau t u thu thap cho thay mo binh nhan dang
de xuat dat do chfnh xac tuong ddi cao
1 G l C r i T H I E U Nhan dang chir viet t a y dang la van de thach t h u c ldn ddi vdi c i e n h a nghien ciiu Cho den nay, bai t o i n nhan dang chur viet tay van chua cd d u g c mgt giii p h a p t o n g t h e Mdt
sd ket q u i chd yeu chi t a p trung tren cac t a p dii lieu chir sd viet tay chuan n h u USPS va MNIST 14, 5, 6], ben canh dd cung cd mdt sd edng trinh nghien ciiu tren c i c he ehfr cii La tinh, Hy Lap, Trung Qudc t u y nhien c i c ket q u i cung chi d u g c gidi ban trong mot p h a m
vi hep 12, 7] D i e biet ddi vdi viec nhan dang chii viet tay tieng Viet lai eang gap nhieu khd khan hon do bo ky t y tieng Viet ed nhieu ky t y vdi hinh dang r a t gidng nhau, chi k h i c nhau chut ft ve phan d a u Do dd r a t ft cdng trinh nghien ciiu ve n h i n dang chii viet tay tieng
Viet Bai toan chiing tdi d a t ra 6 day la xay d y n g mdt md hinh nhan d a n g chii Viet in viet
tay rdi rac Bd ky t y tieng Viet bao gdm t i p ky t y khdng d a u A, B, C, D, D, E, G, H, I, K,
L, M, N, O, P, Q, R, S, T, U, V, X, Y va cac ky t y cd d a u A, A, A, A, A, A, A, A, A, A, A,
A, A, A, A, A, A, E, E, E, E, E, E, E, E, E, E, E, I, I, 1, I, I, 6, O, 6, 6, 6, 6, 0, 6, 6,
6, 6, 0, a, a, o, 6, o, u; u, u, u, u, y, ir, u; u, u, u, Y, Y, Y, Y, Y chung tdi gidi
ban pham vi cda bai t o i n theo mgt sd qui dinh nhu: c i c chir viet p h i i cd mot k h o i n g c i c h
t u o n g ddi, giu'a phan chur va phan dau p h i i tach rdi nhau
P h u a n g p h a p vec t o t y a (SVM Support Vector Machines) la mdt p h u a n g p h a p m i y hoc tien tien d a cd nhieu t h a n h cdng khdng chi trong eae linh vyc khai p h i dtr lieu m a cdn trong linh vyc nhan dang Trong nhurng t h i p nien gan day, SVM d a d u g c i p dung rgng rai v i o
Trang 2nhieu bai t o i n t h y c te va cho nhieu ket q u i rat k h i quan | 1 , 3] Vi vay, ehdng tdi sU dung
phuang p h i p vec t o t y a cho mo hinh nhan dang ma chung tdi de xuat TVong mdt he thdng
nhan dang thi viec trfch chgn d i e trung l i mot b u d c quan trgng, nd cd i n h hudng rat ldn
den do chfnh xac cda he thdng n h i n dang Cd rat nhieu p h u a n g p h i p trich chgn d i e trung
hieu q u i ed t h e i p dung cho chur viet tay nhu: ma tran trgng sd, t o i n td' Kirsch, cac bieu dd
chieu 14, 5, 7], trong bai b i o nay chung tdi da sdr dung v i cii dat t h d nghiem tren mgt sd
cic loai dac t r u n g dd va quyet dinh sd dung y t u d n g cda p h u a n g p h i p trfch chgn dac trung
wavelet Haar l8] cho mo hinh n h i n dang chii Viet viet tay rdi rac
Tiep theo, Mue 2 se tdm t a t nhung y t u d n g ca b i n cda p h u o n g phap vec t o tua Mue
3 trinh bay cac ket q u i t h y c nghiem tren dii lieu chu' viet tay tieng Viet vdi mdt sd p h u a n g
p h i p trfch chgn dac t r u n g thdng dung Mue 4 p h i t hga kien true cda md hinh nhan dang
chir Viet viet tay rdi rac va c i c ket q u i t h y c nghiem theo mo hinh nay Cudi cung la phan
ket luan va h u d n g phat trien
2 P H U O N G P H A P V E C T O TU*A
Cho t i p mau huan luyen xi £ R^, i = 1, , N vk cac nhan t u a n g ung yi e { - 1 , +1},
mue tieu cda SVM la tim mgt sieu phang phan each (dugc xac dinh bdi w) sao cho khoing
each (margin) giiia hai Idp d a t cyc dai (Hinh 1)
Hinh 1 Sieu phang tach vdi khoing cich cyc dai
Ham mue tieu cda mgt m i y phan ldp SVM nhi p h i n cd the dugc phat bieu nhu sau:
gix) = w.^ix)-\-b, (1)
trong do, vec t a dau vao x G R^, w la vec t o chuan cda sieu phang phan cich trong khdng
gian dac t r u n g d u g e sinh ra tur i n h xa cda bam $(a;) : R^ -^ P ^ ( M > TV, $(a;) cd the
tuyen tfnh hoac phi tuyen) va b Ii do lech so vdi gdc tga do ll], SVM gdc dugc thiet ke cho
bai toan p h i n Idp nhi p h i n , vi vay dau cda gix) cho biet vec t o x thugc ldp +1 hay ldp —1
Viec tim sieu p h a n g phan eich chi'nh l i viec giii bai t o i n qui hoach toan phuang
(QP-Quadratic programming):
1 7,
m a x ( a i — -a Ha) (2)
a 2
Trang 390
thda man 0 < Oi <C, ii vk ^ j ^ i Qiyi = 0, ' trong dd a = ]ai, ,a/v]-^ va H la ma tran kfeh thude N x N dugc ggi la ma trin nhan
(kernel matrix) vdi mdi phan tir Hii,j) = yiyj^ixi).^ixj)
Giii bai toin QP (3) ta thu dugc:
"^aiVi^ixi) (3)
Mdi mau huan luyen Xi tuong iing vdi mdt he sd Lagrange cnj Cic miu cd cii > 0 dugc
ggi la vec to hd trg
The (3) vao (1), ta cd:
9ix) = Y2aiyi^ixi).^ix) -b 6 (4)
Gii sir ^ixi).^ixj) = Kixi,Xj) Nghia la, tfch vd hudng trong khdng gian die trung
tuong duong vdi mgt him nhin K cda khdng gian dau via Vi viy, ta khdng can phii tfnh
tryc tiep cac gia tri $(xi),$(xj) ma chi can tfnh tfch vd hudng < $(a;j).$(a;^) > giin tiep
thdng qua ham nhan Kixi, Xj) Nhu vay, ta ed ham myc tieu cho bai toan phan ldp SVM ed
gix) = ^ atyiKixi, x) -\- b (5)
3 N H A N D A N G C H U V I E T TAY VOTI C A C D A C T R U N G T H O N G D U N G
TVong phan nay, ehung tdi gidi thieu mgt sd die trung da dugc sii dung rat hieu qui trong
cic bai toin nhan dang chir viet tay 14, 5, 7]
3.1 Trong so viing (Zoning)
m
Hinh 2: Trfch chgn die trung trgng sd viing
Anh ky ty dugc chia thanh N x N vung (zones) Tong sd diem den cda moi vimg se duoc
chgn de tao thanh vec to die trung
TVong thye nghiem, vdi inh kich thudc 16 x 16, chung tdi chon N = 8, nhu vav cd
8 X 8 = 64 die trung
Trang 43.2 B i ^ u d o c h i e u ( P r o j e c t i o n h i s t o g r a m s )
S'^' %
Hinh 3 Trfch chgn c i c bieu dd chieu ngang, dge va 2 d u d n g cheo
Y t u d n g ca b i n cda p h u a n g p h i p trfch chgn dac t r u n g nay l i chieu c i c diem den tren
inh 2 chieu theo c i c h u d n g ngang, dge v i hai d u d n g cheo thanh mgt day c i c tin hieu 1 chieu
U'u diem cda c i c dac t r u n g nay l i khdng phu thugc vao nhieu, tuy nhien no van phu thudc
vao do nghieng cda chur
TVong t h y c nghiem, vdi i n h kfeh thudc 16 x 16, chung tdi chgn 16 ngang -bl6 dge -1-2 x 16
cheo = 64 d i e t r u n g
3.3 TVich c h o n c h u t u y e n ( C o n t o u r profiles)
rAJ
Hinh 4 TVi'ch chgn cac khdi ben ngoii cda chii
Phan d u g c trich chgn l i khoing cich tii bien cda khung chiia i n h tdi diem den dau tien
cda chii tren cung 1 ddng quet P h u a n g p h i p trfch chgn n i y md t i tdt cac khdi ben ngoii
cda chir va cho phep phan biet mdt sd lugng ldn c i c ky t y
TVong t h y c nghiem, vdi i n h ki'ch thudc 16 x 16, cd 16 t r i i -|-16 phii -1-16 tren -|-16 dudi
= 64 dac trung
3.4 Trfch c h g n d a c t r u t i g wavelet Haar
Chung tdi sd dung y t u d n g cda p h u a n g p h i p trfch chon dac trung wavelet Haar |8] de
chgn t i p d i e t r u n g cho mdi i n h ky t y dau vao
Tu i n h nhi phan kich t h u d c 2n(2n (Hinh 5), q u i trinh tn'ch chon d i e trung dugc md t i
theo thuat t o i n sau:
Procedure HaarFeature
Input Ma tran vudng (A, n) cap 2"
Output T a p c i e d i e trirng { F i , F2, P2"x2'' }•
Trang 592
0 0 0
O D D
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
O OD
O 0 0
0 0 1
O 0 1
o i l
1 1 1
1 1 0
o o o o
0 0 DO oooo
0 0 0 1
0 0 1 1
0 1 1 1
1 1 1 1
1 1 O Q
1 1 0 0
1 0 0 0 oooo oooo
0 0 1 1
D i l i
1 1 1 1
1 1 0 1
1 1 0 0
1 0 0 0
1 1 1 1 oooo oooo oooo
1 0 0 0 0
1 O O D 0
1 0 0 0 0
1 0 0 0 0
1 1 0 0 0
1 1 O D 0
1 1 1 0 0
1 1 1 0 0
1 1 1 1 0
0 0 1 1 1
0 0 0 1 1
0 0 0 1 1
0 0 0 1 1
0 0 0 0 0 0 0 0
D D O D D O O D
O O D O ' l O D I
O D D l^-^O 1 1
0 0 0 0 0 0 1 1
0 O D O O 1 1 1
0 0 0 0 1 1 1 1
0 0 0 1 1 1 1 1
0 0 1 1 1 0 0 0
D O I CJ^i:! D 0
o i l ^^3 0 0
1 1 1 0 0 0 0 0
1 1 1 0 0 0 0 0
0 1 1 1 0 0 0 c
1 1 1 1 O D O C
1 1 1 1 O D O C
1 1 1 c-ioo
1 0 1 l ? A o 0
1 0 D 1 1 0 0 C
0 0 0 1 1 1 D C
0 0 0 0 1 1 0 c 1 1 1 1 1 1 0 c
0 D 0 D 0 1 1 C
o 0 0 0 4 1 1 1
G 0 O'-'^O 1 1
0 0 0 0 0 0 1 1
0 0 0 0 0 0 1 1
Hinh 5 Ttn'ch chgn die trung wavelet Haar
Method
1 Khdi tao: Queue = $; z = 1;
2 - Tfnh Fi bang tdng eie diem den trong toin bd ma tran (A, n);
- PUSH{iA,n),Queue);
3 While Queue ^ # Do
{
- POPiQueue,iA,n));
- if (n > 1)
{
Chia inh thanh 4 phan: Ai, A2, A3, A4;
for (i = l;i = 4;i-b-b)
PUSHi(Aj,ndiv2), Queue);
}
- Ggi 5 1 , 52, 53, 54 la tdng cic diem den tuang urng vdi Ai, A2, A3, A4;
- Tfnh Fi+i = S1 + 52;
Pi+2 = 5 2 - b 5 3 ; F; + 3 = 54;
-i = i-\-3;
}
Trong thyc nghiem, vdi phan chii chung tdi chgn n = 4, nhu viy ta cd: 1 -b 3 4- 4 x 3 -t
4 x 4 x 3 - b 4 x 4 x 4 x 3 = 256 die trung, edn vdi phan dau chung tdi chon n = 3, nhu viy
cd tat c i 64 dac trung
Phuang phap trich chgn die trung nay se tao ra mgt day sd cic dac trung giim dan, Vdi ciing mdt chur thi cic gii tri ldn d dau day tuong ddi on dinh, cd the dai dien cho hinh dang
khii quit cua chu; cdn cac gia tri 6 cudi day nhd dan va khdng dn dinh, the hien sy da dang
trong tung chi tiet cda chii
3.5 K e t qud thu'c nghiem
Dii lieu chii viet tay tieng Viet cda chung tdi dugc thu thap tir 655 ngtrdi viet khic nhau ddi tugng chd yeu la sinh vien Mdi ngudi viet khoing 200 chu' in hoa, cac ky ty duac viet
Trang 6KET HOP CAC Bp PHAN PHAN LOP SVM 9 3 rdi rac Chung tdi chgn Igc ra 50000 mau de tien h i n h t h y c nghiem, trong dd sd dung 30000 mau dilng de huan luyen va 20000 man phuc vu cho viec nhan dang
Cdng cu phan ldp d u g c x i y dyng t u cac SVM nhi phan Chung tdi chgn thuat t o i n SMO ]1] de huan luyen c i c m i y phan Idp nhi p h i n theo chien luge mot chdng mgt (OVO- One verus One) vdi c i c t h a m sd C = 100 va sdr dung ham nhan la ham Gaussian vdi c = 0, 5
Bdng 1 Ket q u i n h i n dang theo c i c loai d i e t r u n g k h i c nhau
T a p d i e trung Zoning Projection histograms Contour profiles wavelet Haar
Do chi'nh x i c 75.37%
73.82%
73.14%
77.28%
Cac ket q u i t h y c nghiem d b i n g 1 cho t h a y ddi vdi b i i t o i n nhan dang chir viet tay tieng Viet, i p dung d i e t r u n g Haar cho do chfnh xac cao han so vdi sii dung c i c d i e trung khac Tuy nhien, do bg ky t y tieng Viet qua da dang nen viec i p dung c i c d i e trung nay len t a p dii lieu viet tay tieng Viet van chua dat hieu q u i cao Vi v i y can p h i i cd mgt md hinh hieu
q u i cho bai t o i n nhan dang chii viet tay tieng Viet TVong phan sau chung tdi se de xuat mgt mo hinh hieu q u i cho viec nhan dang chir viet tay tieng Viet
4 M O H I N H N H A N D A N G CHLT V I E T V I E T T A Y RClI R A C
[ ^ ( ( 3 ^ ) ^ Trich ch^ti
dac tnrng ^^
Anh
16x16
y
Ket qua n h ^ d ^ s
Hinh 6 Kien true cda he nhan dang chu viet tay tieng Viet
TVong phan nay, chung tdi se trinh bay chi tiet kien true cda md hinh n h i n dang chu Viet viet tay rdi rac Tren c a sd c i c t h i n h phan lien thdng cda i n h , chung tdi phan t i p ky t y tieng Viet thanh 3 nhdm va t i c h c i c ky t y cd dau thanh c i c phan rdi nhau Sau dd chung toi
Trang 794
xiy dyng cac may phan ldp SVM de nhan dang eho ttrng phan chir va dau, cudi cung ghep ndi cic ket qui phan ldp cda cic phan chir va phan dau de cd dugc ket q u i nhin dang cuoi cung
4.1 Tien xiV ly
Myc dfch cda giai doan tien xii ly nham ting do chfnh xac cda he thdng nhan dang Khi quet inh thudng gap cic Ioai nhieu, vi vay chung toi sdr dung mdt sd ky thuat lgc nhieu de khdr cic nhieu ddm va nhieu vet dai Ddi vdi nhieu ddm, sdr dung cic bd Igc trung binh va Igc trung vi, cdn vdi cic nhieu vet dai thi chung tdi sd dung phuang phip khii cic vimg lien thdng nhd (Hinh 7)
De thuin tien cho viec xii Iy sau, nay, chiing tdi bien doi inh dau vao tir inh da cap xim thanh inh nhi phan
O /
A A I
(a) Nhieu ddm (b) Nhieu vet dai
Hinh 7 Mdt sd nhieu thudng gap khi quet inh
Chuan hda inh theo vung lien thdng Chuan hda inh nham myc dich tao dieu kien thuin tien cho cdng doan tich inh thinh ti^rng phan chir va dau
Bu"6"c 1: Xic dinh eie vung lien thdng tren inh (Hinh 8)
" -1 -2
0-(a) (b)
Hinh 8 Chuan hda inh
(a) Anh gdc
(b) Xae dinh cic viing lien thdng va dinh thu ty cic vung lien thdng
Du'o'c 2: Sip xep cic vung lien thdng theo thii ty tir tren xudng (Hinh 8b)
Btfo-c 3:
0
m
(a) ^ (b) (e)
Hinh 9 Chuan hda eie vung lien thdng
Trang 8- Neu i n h chi cd 1 vimg lien thong: Chuan hda i n h ve ki'ch thudc chuan 16 x 16 (Hinh
9a)
- Neu i n h cd 2 vung lien thdng: Ggi 5(z) la dien tfch vung lien thdng t h d i
Neu 5(1) > 5 ( 2 ) thi dau cda phan lien thdng 2 la dau nang (.) va chl can chuan hda
vdng lien thdng 1 ve kich t h u d c chuan 16 x 16
Ngugc lai: T i c h i n h t h i n h 2 phan: phan chu va phan dau Chuan hda phan chu ve kich
thudc chuan 16 x 16 va phan dau ve ki'ch t h u d c chuan 8 x 8 (Hinh 9b),
- Neu i n h cd 3 vung lien thdng:
Neu 5(3) = m l n { 5 ( i ) } thi dau cda phan lien thong nay la dau nang (.) Do dd chi can
chuan hda thanh phan lien thdng 1 ve kfeh t h u d c chuan 8 x 8 v i thanh phan lien thdng 2 ve
kich thudc chuan 16 x 16,
Ngugc Iai: T i c h i n h thanh 3 phan t u cic vung lien thdng Chuan hda cac viing lien thong
1 va 2 ve kich t h u d c chuan 8 x 8 va chuan hda vung lien thong 3 ve kich thudc chuan 16 x 16
(Hinh 9c)
4.2 P h a n n h o m so" b o
Dya vao sd t h a n h phan lien thdng chung tdi t i c h bg ky t y tieng Viet thanh 3 nhom:
Nhdm 1: Nhdm cd 1 vung lien thdng A, B, C, D, D, E, G, H, 1, K, L, M, N, O, P, Q R, S, T,
U, V, X, Y, O, U'
Nhdm 2: Nhdm cd 2 vimg lien thong A, A, A, A, A, A, A, E, E, E, E, E, E, I, t, I, I, I, 6 , 6 ,
6,0,6, o, 6, 6, 6,6, o, u, u, u, u, u, u; u, u', u, y, Y, Y, Y, Y, Y,
Nhom 3: Nhdm cd 3 vung lien thdng A, A, A, A, A, A, A, A, A, A, E, E, E, E, E, 6, 6 , 6 ,
4.3 Trich c h g n d a c t r u t i g
Chung tdi sii dung d i e t r u n g wavelet Haar, Vdi phan chd, chung tdi chgn kich thudc i n h
16 x 16, nhu v i y t a c d : l - t - 3 - b 4 x 3 i - 4 x 4 x 3 - | - 4 x 4 x 4 x 3 = 256 d i e trung, cdn vdi
phan dau kfeh t h u d c i n h 8 x 8 thi cd t a t c i 64 d i e trung
4.4 X a y drfng c a c m a y p h a n l d p S V M
TVong phan niy, chung tdi se xay dyng 3 may p h i n ldp SVM, sd dung t a p d i e trung
wavelet Haar de huan luyen phan Idp va nhan dang,
SVMl: p h i n Idp ddi vdi nhdm ky t y cd 1 vilng lien thdng {A, B, C, D, D, E, G, H, I K L,
M, N, O, P, Q, R, S, T, U, V, X, Y, O, U'}
SVM2: ddi vdi c i c ky t y cd dau thi phan chir deu la cic nguyen am vi vay may nay chi phan
ldp cac nguyen am {A, E, I, O, U, Y}
SVM3: phan Idp cac dau {/, \ , ?, ~ , A, V} (sac, huyen, hdi, nga, dau 5, dau a)
Cac m i y p h i n ldp S V M l , SVM2, SVM3 dugc x i y dyng t u cic SVM nhi p h i n Chung
tdi chgn t h u a t t o i n SMO |1] de huan luyen cic m i y p h i n Idp nhi p h i n theo chien luge mgt
chdng mdt (OVO One verus One) vdi c i c tham sd C = 100 va su dung ham nhan la ham
Gaussian vdi CT = 0, 5
Trang 996
4.5 Ket qud thu'c nghiem
Vdi 50000 mau ma chiing tdi thu thap de tien hanh thyc nghiem, trong dd 13782 mau chu khdng dau dung de huan luyen, phan cdn lai phuc vu cho viec nhan dang
Ba tap dii lieu dugc xay dyng phuc vu cho viee huan luyen:
• TrainDatal: Tap cic dau tieng Viet {/, \ , ?, ~, A, V}, vdi 2485 mau
• TrainData2: Tap cic chir cii nguyen im tieng Viet {A, E, I, O, U, Y}, vdi 4128 mau
• TVainDataS: Tap cac chir cii tieng Viet khdng dau {A, B, C, D, D, E, G, H, 1, K, L, M, N,
O, P, Q, R, S, T, U, V, X, Y, O, U'}, vdi 13782 mau
f
A
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i
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1
A
£
E
6
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E
0
0
A
X
E
6
6
A
A
£
5
L)
I
d
A
£
C
i(
A-A
E
0
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A
/T
E
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E
6
i
Hinh 10 Cic mau trfch tir tap ky ty viet tay tieng Viet
Bdn tap dii lieu dugc xay dyng phuc vu cho viec nhan dang, ket q u i thyc nghiem the hien d Bing 1:
• TestData 1
• TestData 2
• TestData 3
• TestData 4
Tap cac ky ty tieng Viet cd 1 vung lien thdng, vdi 7143 mau
Tap eac ky t y tieng Viet cd 2 vung lien thdng, vdi 16856 mau
Tap cac ky ty tieng Viet cd 3 vimg lien thdng, vdi 12219 mau
= TestData 1 U TestData 2 U TestData 3
Bdng 2 Ket qui nhan dang tren cic t i p dii lieu tieng Viet viet tay rdi rac
T i p mau TestData 1 TestData 2 TestData 3 TestData 4
Sd miu
7143
16856
12219
36218
Do chi'nh xac 82.24%
90.69%
87.78%
88.04%
Cac ket qui thuc nghiem d Bing 2 cho thay md hinh nhan dang chfi Viet viet tay rdi rac
ma chung toi de xuat dat do ehinh xic cao ban rat nhieu so vdi cic ket qui thuc nghiem d Bing 1
5 KET L U A N
Bai bio da sii dung mgt sd phuang phip trfch chgn dac trung de ap dung vao bai toan nhan dang chii viet tay rdi rac Cie ket qui thyc nghiem tren dii lieu chii viet tay tieno- Viet
cho thay i p dung 6.ac trung wavelet Haar cho do chfnh xac cao nhat trong sd cic die trung
dugc lya chgn Vi viy chung tdi da de xuat md hinh nhan dang chtr Viet viet tay rdi rac dya tren co sd phuang phap vec t a tya ket hgp vdi trfch chgn dac trung wavelet Haar Cic
Trang 10ket q u i t h y c nghiem cda chung tdi tren md hmh nhan dang chii Viet viet tay rdi rac dat do
chi'nh rat k h i quan TVong t u a n g lai, ehung toi tiep tuc nghien cuu phan hau xU ly, i p dung
md hinh ngon ngii N-Gram de c i i thien do chfnh xac cda md hinh nhan dang
T A I L I E U T H A M K H A O
II] J Piatt, Fast training of support vector machines using sequential minimal optimiza-tion,
Ad-vences in Kernel Methods - Support Vector Learning, Cam-bridge, M.A, MIT Press, 1999
(185-208)
12] Le Hoai Bac, Le Hoang Thai, Neural network & genetic algorithm in application to handwritten
character recognition, Tgp chi Tin hpc vd Di'iu khien hpc 1 7 (4) (2001) 57-65
13] Chih-Cbung Chang and Chil-Jen Lin, "LIBSVM: a Library for Support Vector Ma-chines",
National Taiwan University, 2004
14] D Gorgevik, D Cakmakov, An efficient three-stage classifier for handwritten digit recognition
Proceedings of 17^^ Int Conference on Pattern Recognition, 1CPR2004, Vol 4, IEEE
Com-puter Society, Cambridge, UK, 23-26 August 2004 (507-510)
15] D Cakmakov, D Gorgevik, Handwritten digit recognition using classifier coopera-tion schemes
Proceedings of the ^ ' ^ Balkan Conference in Informatics, BCI 2005; Ohrid, November
17-19, 2005 (23-30)
16] Pham Anh Phuang, Nhan dang chii viet tay ban che voi mo binh SVM, Tgp chi khoa hpc Dgi
hpc Hue (42) (2007) 157-165
|7] G Vamvakas, B Gates, 1 Pratikakis, N Stamatopoulos, A, Roniotis, and S, 1, Perantonis,
Hybrid off-line OCR for isolated handwritten greek characters The Fourth lASTED
Interna-tional Conference on Signal Processing, Pattern Recognition, and Applications (SPPRA
2007) ISBN: 978-0-88986-646-1, Innsbruck, Austria, February 2007 (197-202)
18] P Viola, M Jones, Rapid object detection using a boosted cascade of simple features, Proc
Intl Conf on Computer Vision and Pattern Recognition (CVPR) 1, Kauai, HI, USA, 2001
(511-518)
Nhgn bdi ngdy 3 - 3 - 2008 Nhdn lai sau siia ngdy 6 - 2 - 2009