TRNG I HC LC HNG

TRUNG TM THNG TIN T LIU

----- -----

BO CO NGHIN CU KHOA HC

TI:

NGHIN CU MT S K THUT

HIU CHNH GC NGHING CA NH

NGUYN TRNG VINH

NG NAI, THNG 06/2011

TRNG I HC LC HNG

TRUNG TM THNG TIN T LIU

----- -----

BO CO NGHIN CU KHOA HC

TI:

NGHIN CU MT S K THUT

HIU CHNH GC NGHING CA NH

Thc hin: NGUYN TRNG VINH

TRN C TON

Ch nhim ti: Hunh Cao Tun

NG NAI, THNG 06/2011

LI CM N

Chng ti xin chn thnh cm n lnh o v cc Thy C Trung tm

Thng tin T liu i hc Lc Hng, ni ti cng tc, to mi iu kin

thun li cho chng ti trong sut thi gian hon thnh bo co.

Bn cnh , chng ti cng gi li cm n n Ban Kho th i

hc Lc Hng to iu kin thun li cho chng ti trong qu trnh thc

hin lun vn cng nh ng dng sn phm nghin cu vo thc t.

Cui cng, chng ti xin cm n gia nh v bn b, nhng ngi

lun ng h v ng vin chng ti yn tm nghin cu v hon thnh bo

co nghin cu khoa hc.

Nguyn Trng Vinh, Trn c Ton

MC LC

Trang LI CM N ......................................................................................................... i MC LC .............................................................................................................. ii DANH MC HNH NH ...................................................................................... iii M U ................................................................................................................ 1 CHNG 1. TNG QUAN V X L NH V BI TON PHT HIN GC NGHING VN BN. ............................... 4

1.1. X l nh v mt s vn c bn trong x l nh. ................................... 4 1.1.1. X l nh l g? ................................................................................... 4 1.1.2. Qu trnh x l nh .............................................................................. 4

1.1.2.1. Thu nhn nh .............................................................................. 5 1.1.2.2. Tin x l .................................................................................... 6 1.1.2.3. Phn on nh ............................................................................. 6 1.1.2.4. H quyt nh .............................................................................. 7 1.1.2.5. Trch chn c im .................................................................... 7 1.1.2.6. Nhn dng ................................................................................... 8

1.1.3. Mt s vn c bn trong x l nh. ................................................. 9 1.1.3.1. nh ............................................................................................. 9 1.1.3.2. im nh .................................................................................... 9 1.1.3.3. Mc xm ...................................................................................... 9 1.1.3.4. Cc im 4 lng ging .................................................................. 9 1.1.3.5. Cc im 8 lng ging .................................................................. 9 1.1.3.6. i tng nh ........................................................................... 10 1.1.3.7. K thut phng to, thu nh nh ................................................. 10

1.1.4. Tng quan v nh vn bn. ................................................................ 11 1.2. Tng quan v bi ton pht hin gc nghing vn bn .............................. 12

1.2.1. Gc nghing v vai tr vic pht hin gc nghing vn bn ............... 12 1.2.2. Phng php phn tch hnh chiu (Profile Projection) ...................... 12

1.2.2.1. Thut ton Postl ........................................................................ 14 1.2.2.2. Thut ton Baird ....................................................................... 14 1.2.2.3. Thut ton Nakano .................................................................... 14 1.2.2.4. Nhn xt .................................................................................... 15

1.2.3. Phng php phn tch da vo trng tm (Center of Gravity) .......... 15 1.2.4. Phng php phn tch lng ging (Nearest Neighbour Clustering) ... 19

1.2.4.1. Thut ton Yue Lu v Chew Lim Tan ....................................... 20

1.2.4.2. Nhn xt..................................................................................... 21 1.2.5. Phng php dng php ton hnh thi (Morphology) ....................... 22

1.2.5.1. Thut ton L. Najman ............................................................... 22 1.2.5.2. Nhn xt..................................................................................... 24

1.2.6. Phng php dng bin i Hough (Hough Transform) ..................... 24 1.2.6.1. ng thng Hough trn ta cc .......................................... 24 1.2.6.2. Nhn xt .................................................................................... 27 CHNG 2. BIN V CC PHNG PHP D BIN ............................... 28

2.1. Bin ca i tng nh ............................................................................. 28 2.1.1. Bin v cc kiu bin c bn trong nh .............................................. 28

2.1.1.1. Bin l tng ............................................................................ 28 2.1.1.2. Bin dc .................................................................................... 29 2.1.1.3. Bin khng trn ........................................................................ 30

2.1.2. Vai tr ca bin trong nhn dng ........................................................ 31 2.2. Cc phng php d bin trc tip ........................................................... 32

2.2.1. Phng php Gradient ....................................................................... 32 2.2.2. Phng php Laplace......................................................................... 34

2.3. Phng php d bin tng qut ................................................................ 34 2.3.1. Khi nim chu tuyn .......................................................................... 34 2.3.2. Phng php d bin tng qut .......................................................... 36

2.4. Mt s phng php d bin nng cao ..................................................... 38 2.4.1. Phng php Canny ........................................................................... 38 2.4.2. Phng php Shen Castan ............................................................... 39

CHNG 3. NG DNG BIN I HOUGH PHT HIN GC NGHING VN BN. .............................................................................. 40

3.1. Tin x l v pht hin gc nghing vn bn t bin ca i tng .......... 40 3.2. Xc nh ng thng Hough trn trang vn bn ...................................... 41 3.3. p dng bin i Hough pht hin gc nghing vn bn .......................... 42 3.4. Thut ton pht hin gc nghing vn bn ................................................ 44 3.5. Chnh sa gc nghing vn bn ................................................................ 51

CHNG 4. XY DNG CHNG TRNH THC NGHIM .................... 53 4.1. S khi. ............................................................................................... 53 4.2. Thit k chng trnh ............................................................................... 54

4.2.1. Module giao din chnh ..................................................................... 54 4.2.2. Module chuyn i nh gc v biu mc xm ............................... 56 4.2.3. Module d bin .................................................................................. 58 4.2.4. Module biu din bin i Hough ...................................................... 60 4.2.5. Module hiu chnh gc nghing vn bn ............................................ 61

4.3. nh gi kt qu ....................................................................................... 61 KT LUN .......................................................................................................... 67 TI LIU THAM KHO ................................................................................... 69

DANH MC HNH NH

Hnh 1.1. S qu trnh x l nh ......................................................................... 5 Hnh 1.2 Ma trn 8 lng ging ............................................................................... 10 Hnh 1.3 Tng quan qu trnh to nh ti liu ........................................................ 12 Hnh 1.4 a gic 6 nh v trng tm c xc nh ............................................. 16 Hnh 1.5 Hnh ch nht ngoi tip nh vn bn thay cho a gic ........................... 16 Hnh 1.6 nh u vo v kt qu sau khi p dng thut ton ................................. 17 Hnh 1.7 Tm cc im xa nht theo cc hng trn nh ........................................ 18 Hnh 1.8 Trng tm c xc nh da vo cc im xa nht ................................ 18 Hnh 1.9 ng c s c ni t trng tm n gc ta ................................. 18 Hnh 1.10 Xc nh gc nghing nh vn bn ........................................................ 18 Hnh 1.11 Phn tch lng ging .............................................................................. 19 Hnh 1.12 Cc K-NN v vector ch phng ng vi K=2,3,4 ................................ 21 trong thut ton Yue Lu-Chew Lim Tan............................................................... 21 Hnh 1.13 ng thng Hough v trc ta ........................................................ 25 Hnh 1.14 Biu din ng thng Hough i qua 3 im......................................... 26 Hnh 2.1 ng bin l tng ............................................................................... 29 Hnh 2.2 ng bin dc ...................................................................................... 29 Hnh 2.3 ng bin khng trn ........................................................................... 30 Hnh 2.4 S phn tch nh ................................................................................. 31 Hnh 2.5 Cc 4- lng ging ca im nh P .......................................................... 35 Hnh 2.6 Cc 8- lng ging ca im nh P .......................................................... 35 Hnh 2.7 V d v cc chu tuyn i ngu.............................................................. 36 Hnh 2.8 Chu tuyn trong v chu tuyn ngoi ca mt i tng ........................... 36 Hnh 3.1 Xc nh hnh ch nht ngoi tip cc i tng ..................................... 40 Hnh 3.2 ng thng trong to cc ................................................................. 41 Hnh 3.3 ng thng Hough trn trc ta ....................................................... 43 Hnh 3.4 V d v mt nh nghing c t k t ch ci .......................................... 45 Hnh 3.5 V d v vn bn nghing c cc i tng bao nhau .............................. 46 Hnh 3.6 S gii thut tng qut ....................................................................... 50 Hnh 3.7 Xoay mt im nh quanh gc ta ..................................................... 51 Hnh 4.1 S tng qut ....................................................................................... 53 Hnh 4.2 Giao din chnh ca chng trnh............................................................ 54 Hnh 4.3 S module x l c bn ...................................................................... 55 Hnh 4.4 Mn hnh giao din chng trnh khi chn chc nng Open .................... 55 Hnh 4.5 S thao tc x l trn nh ................................................................... 56

Hnh 4.6 S convert nh sang nh phn v a cp xm ...................................... 56 Hnh 4.7 Giao din biu din Histogram ca nh ................................................... 57 Hnh 4.8 Giao din convert nh sang nh phn v nh a cp xm ......................... 57 Hnh 4.9 S chc nng d bin ......................................................................... 58 Hnh 4.10 D bin bng phng php Sobel.......................................................... 58 Hnh 4.11 D bin bng phng php Canny ........................................................ 59 Hnh 4.12 D bin bng phng php Emboss Laplacian ...................................... 59 Hnh 4.13 D bin bng phng php Gradient ..................................................... 60 Hnh 4.14 Biu din bin i Hough ca nh ......................................................... 60 Hnh 4.15 Pht hin gc nghing v xoay nh ....................................................... 61 Hnh 4.16 Mt nh b nghing gc c cc i tng xen ln vn bn, bng biu v nh kt qu sau khi hiu chnh 1 gc 12.9o ........................................ 63 Hnh 4.17 Mt nh b nghing gc ting Nht c xen ln hnh nh, k t v nh kt qu sau khi hiu chnh 1 gc 11.3o ........................................................ 64 Hnh 4.18 Mt bng im b nghing gc khng th nhn dng c ca h thng qun l im v nh kt qu sau khi hiu chnh 1 gc 7.61o .................... 64 Hnh 4.19 Mt mu phiu nh gi cht lng ging dy b nghing gc khng th nhn dng c v nh kt qu sau khi hiu chnh 1 gc 9.72o .............. 65 Hnh 4.20 Mt nh mu ti liu b nghing v nh kt qu sau khi hiu chnh 1 gc 10.82o ...................................................... 65 Hnh 4.21 Mt nh mu ti liu b nghing gm nhiu biu v nh kt qu sau khi hiu chnh 1 gc 17.6o ........................................................ 66

1

M U

Ngy nay vic s dng my tnh lu tr ti liu khng cn l vn

mi m v cn phi chng minh tnh an ton, thun tin ca n. Tuy nhin

vic s dng giy lu tr ti liu trong mt s mc ch vn khng th thay

th c (nh bo, sch, cng vn, hp ng, ). Hn na, lng ti liu

c to ra t nhiu nm trc vn cn rt nhiu m khng th b i c v

tnh quan trng ca chng.

c th c c mt vn phng khng giy khi hng t trang ti

liu s c ct ch trong mt cng kch thc bng mt cun sch nh v

tm kim thng tin trong ngi ta ch cn tn vi giy vi mt ci g

phm Enter th chc chn phi chuyn ton b d liu t cc trang giy vo

my tnh. y cng l cch p ng nhu cu tra cu ti liu in t cng tng

v tr thnh nhu cu cp thit ca mi ngi trong i sng.

Thng thng ngi ta s phi tn rt nhiu thi gian v cng sc mi

c th nhp vo my tnh c ht lng ti liu . Hin nay, chng ta c

cc my Scan vi tc cao, cng ngh x l ca my tnh ngy cng siu

vit vi tc tnh ton vt c tc nh sng, vy ti sao chng ta khng

qut ton b cc trang vn bn giy vo my tnh v chuyn chng thnh ti

liu s?

Bng cch tc v tnh chnh xc s tng hng trm ln trong khi

chi ph li l cc tiu. Vn l khi qut vo my tnh chng ta khng th thu

nhn c ti liu nh mong mun c bi nhiu l do khch quan khin

cho trang ti liu b nghing ng, m nho,. Tt c nhng g thu c ch l

cc tm nh ca cc trang vn bn. My tnh khng c mt nh chng ta

bit u l file nh ngay ngn, ng chun v u l file nh c cht lng

2

thp, nghing cn c hiu chnh cho nn chng i x cng bng nh nhau

vi mi im nh.

Mt gii php c ngh n ngay l xy dng cc h thng hiu

chnh gc nghing vn bn i vi c nh mu v nh trng en thun tu. T

c th bin son thnh nhng ti liu s hon chnh v b qua thao tc lu

tr hng khi giy t chim nhiu khng gian v thi gian nh trc y.

Khi xem xt mt vn bn, kt lun vn bn c b nghing hay khng

cch lm ca chng ta l cn c vo mt s i tng ch o v gc nghing

vn bn c c lng da vo ng ni cc trung im cnh y ca cc

i tng ny. Xut pht t nhn xt trn, ti s trnh by mt phng php

pht hin gc nghing vn bn t k thut xc nh chu tuyn mt i tng

nh v bin i Hough nhng c im khc l s da trn nhng im c

trng c kch thc ch o trong nh. T p dng bin i Hough ln cc

im nh i din cho chng.

* Cu trc ca lun vn gm 4 chng nh sau:

- Chng 1: Tng quan v x l nh v bi ton gc nghing vn

bn: Chng ny cp n cc khi nim c bn v x l nh s, qu trnh

x l nh. Bn cnh l s phn tch, nh gi i vi mt s phng php

pht hin gc nghing vn bn.

- Chng 2: Bin v cc phng php d bin: Chng ny gm cc

khi nim c bn v bin ca i tng nh v vai tr ca vic d bin trong

xc nh gc nghing vn bn . Ton b chng tp trung vo vic lm r cc

khi nim c bn cng nh i su vo phn tch cc phng php d bin

nh: phng php trc tip (Gradient, Laplace), phng php d bin tng

qut da vo chu tuyn, phng php d bin nng cao (Canny, Shen

Castan).

3

- Chng 3: ng dng bin i Hough pht hin gc nghing vn

bn: Trn c s cc thut ton tm hiu, ton b chng ny nu r tng

bc thc hin vic p dng bin i Hough vo xc nh gc nghing v tin

hnh hiu chnh gc nghing vn bn.

- Chng 4: Xy dng chng trnh thc nghim: Tin hnh xy

dng chng trnh thc nghim pht hin v hiu chnh gc nghing vn

bn da trn c s l thuyt tm hiu c v vic p dng bin i

Hough.

- Kt lun.

4

CHNG 1. TNG QUAN V X L NH

V BI TON PHT HIN GC NGHING VN BN.

1.1. X l nh v mt s vn c bn trong x l nh.

1.1.1. X l nh l g?

Con ngi thu nhn thng tin qua cc gic quan trong th gic ng

vai tr quan trng nht v 80% thng tin c thu nhn bng mt tc l

dng nh. Mc khc vi s pht trin mnh m ca phn cng my tnh, x l

nh, ho ngy cng c nhiu ng dng thc tin phc v cuc sng. Nh

vy, x l nh ng mt vai tr rt quan trng trong s tng tc gia ngi

v my.

Cng nh x l d liu bng ho, x l nh s l mt lnh vc ca

tin hc ng dng. X l d liu bng ho cp n nhng nh nhn to,

cc nh ny c xem xt nh l mt cu trc d liu v c to ra bi cc

chng trnh. X l nh s [20] bao gm cc phng php v k thut bin

i, truyn ti hoc m ho cc nh t nhin.

1.1.2. Qu trnh x l nh

Qu trnh x l nh l mt qu trnh thao tc nhm bin i mt nh

u vo cho ra mt nh kt qu nh mong mun. Kt qu u ra ca mt

qu trnh x l nh c th l mt nh "tt hn" hoc mt kt lun.

Mc ch ca x l nh gm:

Bin i nh, lm tng cht lng nh.

T ng nhn dng nh, on nhn nh, nh gi cc ni dung ca nh.

5

Camera

Sensor

Thu nhn nh

S ho Phn tch nh

Nhn dng

H quyt nh

Lu tr Lu tr

Hnh 1.1. S qu trnh x l nh

Nhn bit v nh gi cc ni dung ca nh l s phn tch mt hnh

nh thnh nhng phn c ngha, phn bit i tng ny vi i tng

khc. Da vo ta c th m t cu trc ca hnh nh ban u. C th lit k

mt s phng php nhn dng c bn nh nhn dng cnh ca cc i tng

trn nh, tch cnh, phn on hnh nh v.v.. K thut ny c dng nhiu

trong y hc (x l t bo, nhim sc th), nhn dng ch trong vn bn.

1.1.2.1. Thu nhn nh:

y l bc u tin trong qu trnh x l nh. thc hin iu ny,

ta cn c b thu nh v kh nng s ho nhng tn hiu lin tc c sinh ra

bi b thu nh . B thu nh y c th l my chp nh n sc hay mu,

my qut nh, ... Trong trng hp b thu nh cung cp cha phi l dng s

ho ta cn phi chuyn i hay s ho nh.

Qu trnh chuyn i ADC [17] (Analog to Digital Converter) thu

nhn dng s ho ca nh. Cc thng s quan trng bc ny l phn

gii, cht lng mu, dung lng b nh v tc thu nhn nh ca cc thit

b. Mc d y ch l cng on u tin song kt qu ca n c nh hng

rt nhiu n cng on k tip.

6

1.1.2.2. Tin x l:

bc ny, nh s c ci thin v tng phn, kh nhiu, kh

bng, kh lch,v.v vi mc ch lm cho cht lng nh tr ln tt hn

na, chun b cho cc bc x l phc tp hn v sau trong qu trnh x l

nh. Qu trnh ny thng c thc hin bi cc b lc.

+ Kh nhiu: Nhiu c chia thnh hai loi: nhiu h thng v nhiu

ngu nhin. c trng ca nhiu h thng l tnh tun hon. Do vy, c th

kh nhiu ny bng vic s dng php bin i Fourier v loi b cc nh

im. i vi nhiu ngu nhin, trng hp n gin l cc vt bn tng

ng vi cc im sng hay ti, c th kh bng phng php ni suy, lc

trung v v trung bnh.

+ Chnh mc xm: y l k thut nhm chnh sa tnh khng ng

u ca thit b thu nhn hoc tng phn gia cc vng nh.

+ Chnh tn x: nh thu nhn c t cc thit b quang hc hay in

t c th b m, nho. Phng php bin i Fourier da trn tch chp ca

nh vi hm tn x cho php gii quyt vic hiu chnh ny.

1.1.2.3. Phn on nh:

Phn on nh c ngha l chia mt nh u vo thnh nhiu phn khc

nhau hay cn gi l cc i tng biu din phn tch, nhn dng nh. V

d: nhn dng ch (hoc m vch) trn phong b th cho mc ch phn

loi bu phm, cn chia cc cu, ch v a ch hoc tn ngi thnh cc t,

cc ch, cc s (hoc cc vch) ring bit nhn dng.

y l phn phc tp kh khn nht trong x l nh v cng d gy li,

lm mt chnh xc ca nh. Kt qu nhn dng nh ph thuc rt nhiu

vo cng on ny.

Mc ch ca phn on nh l c mt miu t tng hp v nhiu

phn t khc nhau cu to ln nh th. V lng thng tin cha trong nh rt

7

ln, trong khi a s cc ng dng chng ta ch cn trch mt vi c trng no

, do vy cn c mt qu trnh gim lng thng tin khng l . Qu

trnh ny bao gm phn vng nh v trch chn c tnh ch yu.

1.1.2.4. H quyt nh:

nh l mt i tng kh phc tp v ng nt, sng ti, dung

lng im nh, mi trng thu nh phong ph ko theo nhiu.

Trong nhiu khu x l v phn tch nh ngoi vic n gin ha cc

phng php ton hc m bo tin li cho x l, ngi ta mong mun bt

chc quy trnh tip nhn v x l nh theo cch ca con ngi. Trong cc

bc x l , nhiu khu hin nay x l theo cc phng php tr tu con

ngi. V vy, y cc c s tri thc c pht huy.

1.1.2.5. Trch chn c im:

Vic gii quyt bi ton nhn dng trong nhng ng dng mi ny sinh

trong cuc sng khng ch to ra nhng thch thc v gii thut, m cn t

ra nhng yu cu v tc tnh ton.

c im chung ca tt c ng dng l nhng c im c trng

cn thit thng l nhiu, khng th do chuyn gia xut, m phi c

trch chn da trn cc th tc phn tch d liu.

Vic trch chn hiu qu cc c im gip cho vic nhn dng cc i

tng nh chnh xc, vi tc tnh ton cao v dung lng nh lu tr gim

xung.

Cc c im ca i tng c trch chn tu theo mc ch nhn

dng trong qu trnh x l nh. C th nu ra mt s c im ca nh sau

y:

- c im khng gian: phn b mc xm, phn b xc sut, bin ,

im un v.v..

8

- c im bin i: cc c im loi ny c trch chn bng vic

thc hin lc vng (zonal filtering). Cc b vng c gi l mt n c

im (feature mask) thng l cc khe hp vi hnh dng khc nhau (ch

nht, tam gic, cung trn v.v..)

- c im bin v ng bin: c trng cho ng bin ca i

tng v do vy rt hu ch trong vic trch chn cc thuc tnh bt bin c

dng khi nhn dng i tng. Cc c im ny c th c trch chn nh

ton t Gradient, ton t la bn, ton t Laplace, ton t cho khng (zero

crossing) ..

1.1.2.6. Nhn dng:

Nhn dng nh l qu trnh xc nh ni dung nh.

Qu trnh ny thng thu c bng cch so snh vi mu chun

c lc (hoc lu) t trc.

y l bc cui cng trong qu trnh x l nh.

Nhn dng nh c th c nhn nhn mt cch n gin l vic gn

nhn cho cc i tng trong nh. V d nh khi nhn dng ch vit, cc i

tng trong nh cn nhn dng l cc mu ch, ta cn tch ring cc mu ch

ra v tm cch gn ng cc k t ca bng ch ci tng ng cho cc mu

ch thu c trong nh. Gii thch l cng on gn ngha cho mt tp cc

i tng c nhn bit.

Chng ta cng c th thy rng, khng phi bt k mt ng dng x l

nh no cng bt buc phi tun theo tt c cc bc x l nu trn, v

d nh cc ng dng chnh sa nh ngh thut ch dng li bc tin x l.

Mt cch tng qut th nhng chc nng x l bao gm c nhn dng

v gii thch thng ch c mt trong h thng phn tch nh t ng hoc bn

t ng, c dng rt trch ra nhng thng tin quan trng t nh, v d

nh cc ng dng nhn dng k t quang hc, nhn dng ch vit tay v.v

9

1.1.3. Mt s vn c bn trong x l nh.

1.1.3.1. nh :

nh l mt mng s thc hai chiu (Ii j) c kch thc (m*n), trong

mi phn t Ii j (i=1..m, j=1..n) biu th mc xm ca nh ti v tr (i, j) tng

ng.

1.1.3.2. im nh:

Gc ca nh l nh lin tc v khng gian v sng. x l bng

my tnh, nh cn phi c s ho.

S ho nh l s bin i gn ng mt nh lin tc thnh mt tp im

ph hp vi nh tht v v tr (khng gian) v sng (mc xm). Khong

cch gia cc im nh c thit lp sao cho mt ngi khng phn bit

c ranh gii gia chng.

Mi mt im nh vy gi l im nh (PEL: Picture Element [20])

hay gi tt l Pixel. Trong khun kh nh hai chiu, mi pixel ng vi cp ta

(x,y).

im nh (Pixel) l mt phn t ca nh s ti to (x, y) vi xm

hoc mu nht nh. Kch thc v khong cch gia cc im nh c

chn thch hp sao cho mt ngi cm nhn s lin tc v khng gian v mc

xm (hoc mu) ca nh s gn nh nh tht. Mi phn t trong ma trn c

gi l mt phn t nh.

1.1.3.3. Mc xm: l s cc gi tr c th nhn ca cc im nh.

1.1.3.4. Cc im 4 lng ging:

Gi s (i,j) l mt im nh, khi cc im 4 - lng ging l:

N4 = {(i-1, j); (i+1, j); (i, j-1); (i, j+1)}

1.1.3.5. Cc im 8 lng ging: N8 = N4 {(i-1,j-1); (j-1, j+1); (i+1, j-1); (i+1, j+1)}

10

1.1.3.6. i tng nh:

Ta ch xt ti nh nh phn v mi nh u c th a v dng nh phn

bng k thut phn ngng. K hiu F l tp cc im vng, F l tp cc im

nn.

F: l im en

F : l im trng

Quan h K lin thng (K = 4, 8) l mt quan h phn x, i xng, bc

cu, l quan h tng ng. Mi lp tng ng ca n biu din mt

thnh phn K lin thng ca nh. V sau ta gi mi thnh phn K lin thng

ca nh l mt i tng nh.

1.1.3.7. K thut phng to, thu nh nh:

Khi nh qu ln chng ta mun nhn ton b nh th chng ta phi thu

nh nh li v ngc khi ta mun xem chi tit mt b phn no ca nh th

ta phi phng to n ln.

+ K thut phng to nh:

Khi phng to nh vi mt t l k no ta thu c nh mi to gp k

ln nh c (k l phng ca nh) nh th nh mi s c kch thc l :

Height=Height*k

Width=Widht*k

P3 P2 P1

P4 P P0

P5 P6 P7

Hnh 1.2 Ma trn 8 lng ging

11

Vic tnh cc im nh tng ng ca nh mi s c tnh theo cng

thc:

xp=x/k

yp=y/k

+ K thut thu nh nh:

Tng t nh phng to nh, khi thu nh nh ta thu c nh mi ging

nh c nhng c kch thc nh hn nh c. Kch thc ca nh mi l :

Height=Height/k

Width=Width/k

Vic tnh cc im nh tng ng ca nh mi s c tnh theo cng

thc:

xp=x*k

yp=y*k

1.1.4. Tng quan v nh vn bn.

Trang nh vn bn hay nh ti liu c cp y l cc file nh s

ho thu c bng cch qut cc trang ti liu dng my scanner, my nh s,

hay nhn t mt my fax, file nh ny c lu gi trong my tnh. nh ti

liu c nhiu loi: nh en trng, nh mu, nh a cp xm vi cc phn m

rng nh JPG, TIF, BMP, PCX,

12

1.2. Tng quan v bi ton pht hin gc nghing vn bn

1.2.1. Gc nghing v vai tr vic pht hin gc nghing vn bn

Gc nghing vn bn l mt bi ton kinh in trong x nh vn bn.

Gii quyt bi ton gc nghing l nhim v tin quyt v cng khng th

trnh khi ca bt k mt h thng x l nh vn bn no. V l , cng vi

s pht trin ca x l nh ni chung v x l nh vn bn ni ring, bi ton

gc nghing vn bn cng c quan tm ngy cng nhiu v di nhiu gc

khc nhau. Gii quyt c vn gc nghing vn bn s lm cho hiu

qu khu nhn dng vn bn tng ln ng k. C rt nhiu hng tip cn

cho bi ton gc nghing vn bn t trc ti nay. Cc thut ton pht hin

gc nghing thng c xy dng cho cc h thng phn tch nh vn bn

khc nhau nn ch gii quyt cho nhng loi nh vn bn c th.

Sau y l mt s hng tip cn ph bin cho bi ton gc nghing

vn bn.

1.2.2. Phng php phn tch hnh chiu (Profile Projection)

y l mt trong nhng phng php ph bin nht trong pht hin gc

nghing vn bn. tng chnh ca phng php ny l tnh histogram cho

tt c cc gc lch. Histogram ca mt gc l s im nh en trong nh sao

cho cc im ny nm trn nhng ng thng c cng mt hng tng ng

Ti liu Thit b thu nhn nh nh s

Hnh 1.3 Tng quan qu trnh to nh ti liu

13

vi gc . Sau , dng mt hm tnh chi ph p dng cho cc gi tr

histogram ny. Gc nghing ca vn bn tng ng vi gc c gi tr hm chi

ph l ln nht.

Theo hng tip cn ny, cc thut ton pht hin gc nghing c

xut bi cc tc gi: Akiyama v Hagita, Bard, Bloomberg, Nakano, Kanai v

Bagdanov, Komukai v Saiwai, Lam v Zandy, Messelodi v Modena, Shutao

Li, Qinghua Shen [13], Pavidis v Zhou, Postl, D X Le [12] v Spitz.

Cc thut ton pht hin gc nghing da vo hnh chiu thng bao

gm cc bc chnh sau:

+ Dng mt hm rt gn F chuyn nh u vo thnh mt tp cc b

ba (x,y,w) trong (x,y) l ta ca mt im nh i din cho mt i

tng v w l trng s ca im . y, im i din c hiu theo

ngha l im biu din cc k t trong cc i tng ca nh. Trng s w

thng ph thuc vo tng thut ton.

+ Mt hm P dng chiu cc im tm c trn vo mt mng m

A[] theo cc gc chiu khc nhau. ng vi mi gc c mt mng A[]

dng lu s im i din. Mng A[] l mng mt chiu, phn t A[r] s

cho bit s im i din nm trn ng thng to vi trc OX gc v

khong cch t gc ta ti ng thng l r.

+ Sau khi tnh c mng A[], p dng mt hm ti u ha cho cc

gi tr ca mng ny theo mt tiu chun no . Cui cng gc lch ca vn

bn l gc tng ng c gi tr hm ti u ha cc i.

S khc nhau ch yu ca cc thut ton theo phng php ny chnh

l vic xy dng cc hm rt gn F v hm ti u ha .

14

1.2.2.1 . Thut ton Postl

Postl [18] dng cc tn s ly mu theo chiu ngang v chiu dc

ly cc im en trong nh lm cc im c s. Hm rt gn v hm ti u

ha nh sau:

FP(I) ={ (x.,y.,1)| 0 < x < w/ , 0< y

15

FP(I)={( x,y,w) | (x,y) l ta gc tri di ca hnh ch nht bao

quanh mt i tng, w l chiu rng ca hnh ch nht }

P(A[p])=(1-U(A[p]))

Vi U(A[p])=1 nu A[p]=0, ngc li U(A[p])=0.

Pht hin gc lch vn bn bng cch chiu cc gc l mt phng

php n gin v d hiu. Tuy nhin, nhng thut ton da trn phng php

ny cn hn ch nhiu v chnh xc vi cc gc lch ln. Baird cho rng

thut ton cho kt qu c chnh xc cao th gc lch vn bn phi gii

hn trong khong 150. Hn na, nu vn bn c nhiu nhiu v cc i

tng phi vn bn nh bng biu, hnh nh th chnh xc ca thut ton

cn gim i ng k.

1.2.2.4 . Nhn xt

Gn y, ngi ta kt hp phng php hnh chiu v phng php

cc i tng vi mc tiu gii quyt vn v gii hn gc lch. Tuy vy,

phng php ny li ph thuc nhiu vo khong cch gia cc dng vn bn

v quan trng l ch x l c vi nhng nh c cha nhiu dng vn bn v

kch thc b c 512 * 512 pixels.

1.2.3. Phng php phn tch da vo trng tm (Center of Gravity)

y l hng tip cn tng i mi cho bi ton pht hin gc

nghing vn bn. tng chnh ca phng php ny l i xy dng mt a

gic t cc im cc bin ca vn bn. Mt ng thng c xy dng t

ta trng tm ca a gic n gc ta . Nh vy, gc lch ca ng

thng ny so vi trc honh chnh l gc nghing ca vn bn.

Theo hng tip cn ny, vic xc nh ng c s ni chung l bc

quan trng nht ca ton b qu trnh. Mt phng php mi c s dng

(3)

16

trong thut ton ny ln tt c cc t ni tip trong a gic. Trng tm ca a

gic vi gc ta s to thnh 1

ng thng lch mt gc no

vi trc ngang. Gc c xc nh

cng chnh l gc nghing ca t,

on vn v c nh vn bn.

Hnh 1.4, mt a gic c 6

nh c tm thy v trng tm ca

a gic c xc nh bng cng

thc [15]:

cx= (xi + xi+1)(xiyi+1 xi+1yi)

cy = (yi + yi+1)(xiyi+1 xi+1yi)

Nh vy ty theo a gic tm c qua bc xc nh im xa nht

theo cc hng m ta p dng thut ton cho tng trng hp c th. Hnh

ch nht c thay th cho a gic nh trong hnh 1.5 cng c m t nh l

mt cch xy dng ng c s gip xc nh gc nghing vn bn.

Hnh 1.4 a gic 6 nh v trng tm c xc nh

Hnh 1.5 Hnh ch nht ngoi tip nh vn bn thay cho a gic

(4)

17

* Thut ton gm cc bc:

+ u vo: nh vn bn b nghing ging nh hnh 1.6

+ u ra: nh c hiu chnh gc nghing.

+ Bc 1: Xc nh nhng im xa nht trong tt c bn hng. Hnh

1.7 cho thy hnh nh qut im xa nht

+ Bc 2: Tm trng tm bng cch s dng bn im va xc nh

c bc 1, bn im trc i din cc gc a gic v trung tm a gic

(COG) c th c tnh bng cch s dng cc phng trnh (4).

+ Bc 3: c c ng c s, tin hnh k ng thng ni trng

tm n gc ta . Hnh 1.9 cho thy ng c bn c tm thy.

+ Bc 4: Tm gc ca ng c s so vi trc ngang pht hin gc

nghing. Hnh 1.10 cho thy vic pht hin gc nghing trn nh vn bn.

+ Bc 5: Xoay nh vi gc nghing tm c theo chiu ngc chiu

kim ng h c nh vn bn ngay ngn, d nhn.

Hnh 1.6 nh u vo v kt qu sau khi p dng thut ton

18

* Nhn xt:

Phng php ny t ra hiu qu khi pht hin v hiu chnh gc

nghing ca nh vn bn c scan vo t tp ch, sch gio khoa, bo ch v

ti liu vit tay, vi phn gii khc nhau, phng ch khc nhau v t l

chnh xc kh cao. Bn cnh , phng php ny kh n gin v phc

tp thp dn n thi gian thc hin qu trnh x l nhanh. N khng b nh

hng bi nhiu v ng thi cn ph hp lm vic vi vn bn c phng

ch khc nhau v c cc vn bn c phn gii khc nhau.

Hnh 1.7 Tm cc im xa nht theo cc hng trn nh

Hnh 1.8 Trng tm c xc nh da vo cc im xa nht

Hnh 1.9 ng c s c ni t trng tm n gc ta

Hnh 1.10 Xc nh gc nghing nh vn bn

19

1.2.4. Phng php phn tch lng ging (Nearest Neighbour Clustering)

Mt hng tip cn khc cho bi ton pht hin gc nghing vn bn l

phng php phn tch lng ging ln

cn hay lng ging gn nht. Cc thut

ton lin quan n phng php ny

c xut bi cc tc gi:

Hashizume, O' Gorman, Jiang, Loibios,

nhm Yue Lu v Chew Lim Tan [14],

nhm Pal v Chaudhuri, nhm

Shivakumara, Kumar, X, Jaing, H, Bunke [10], Guru v Nagabhushan.

Theo hng tip cn ny, cc thut ton trc ht dng cc k thut

xc nh bin cho cc i tng ring l. Sau , ng vi mi mt i tng,

tin hnh xc nh mt s lng ging gn n nht, dng mt vector nh

hng vi hai u l hai im c chn t hai trong s cc i tng ny

xc nh gc nghing. Hai i tng l cc lng ging thn cn ca nhau nu

kch thc ca chng phi thuc mt khong no v khong cch gia

chng cng tha mn b hn mt ngng no c nh ngha trc. Hai

im i din cho hai i tng c th l cc ta gia cnh y ca chng

hoc c th l cc ta di tri nhng cng c th l tm ca cc hnh ch

nht ngoi tip cc i tng ty theo tng thut ton c th.

Vector ca mi mt nhm lng ging ln cn s cho mt gc lch

tng ng cho nhm . Thng thng, cc thut ton theo phng php ny

dng mt mng tch ly lu histogram cho cc gc lch ny. Ngha l, gi

tr ca mt phn t mng tch ly s cho bit s nhm lng ging m vector

nh hng cho gc bng vi ch s ca phn t mng . Gc lch ca vn

bn l gc tng ng vi phn t histogram ln nht.

Hnh 1.11 Phn tch lng ging

20

Vic gom cc i tng thnh cc cp lng ging gn nht mc ch

gom cc cp k t k nhau trong cc dng vn bn v vector gia cc i

tng ny cho bit gc ca ng thng i qua y ca nhm k t . Tuy

nhin, trong trng hp nh c nhiu nhiu hoc vi nh c phn gii thp,

cc k t ch ci c chia thnh nhiu phn ring bit th cc vector nh

hng s khng phn nh c ng hng lch ca vn bn na.

1.2.4.1. Thut ton Yue Lu v Chew Lim Tan.

Trc ht, dng thut ton phn tch thnh phn lin thng thu c

cc i tng nh ring bit. Mi mt i tng Ci ni tip trong mt hnh

ch nht c cc cp ta trn tri v di phi tng ng l (xli,yti) v

(xri,ybi), trng tm ca hnh ch nht k hiu l (hci, wci), k hiu hci v wci

l cc chiu cao v rng ca hnh ch nht. Ta c cc nh ngha sau [14]:

a. nh ngha 1: Khong cch t tm ti tm ca hai i tng C1 v

C2 c nh ngha:

dc(C1, C2)= x + y

Vi x = |xc1-xc2| v y = |yc1-yc2|

b. nh ngha 2: Khong ht ca hai i tng C1 v C2 c nh

ngha:

dg(C1, C2) =max (xl2 - xr1, xl1 - xr2) nu x > y

dg(C1, C2) =max (yt2 - xb1, yt1 - yb2) nu x < y

c. nh ngha 3: nh ngha lng ging ln cn

C2 c gi l lng ging ln cn ca C1 nu tha mn cc iu

kin sau:

hc1 hc2 nu x > y hoc wc1 wc2 nu x < y

Cx2 > Cx1 vi x > y hoc Cx1 > Cx2 vi x < y

(5)

(6)

21

dg(C1,C2) = min dc(C1,Cm) vi mi m

dg(C1,C2) < .max (hc1,hc2)

Vi l mt hng s c nh ngha trc trong thut ton.

d. nh ngha 4: nh ngha K- lng ging (K-Nearest-Neighbour chain

K-NN)

K-NN c nh ngha l mt dy cha K i tng trong hai

i tng k nhau l cc lng ging ca nhau theo nh ngha 2.

e. nh ngha 5: nh ngha gc lch ca mt dy K-NN

Gi s c dy K-NN: S=[C1, C1, C1,..., Ck,]. Gc nghing ca

dy cc lng ging ny c nh ngha nh sau:

Nu xck-xc1 < yck-yc1 th slopeK = (xck-xc1)/(yck-yc1)

Nu xck-xc1 > yck-yc1 th slopeK = (yck-yc1)/ (xck-xc1)

Hnh 1.12 Cc K-NN v vector ch phng ng vi K=2,3,4 trong thut ton Yue Lu-Chew Lim Tan

K=2

K=3 K=4

22

1.2.4.2. Nhn xt:

im ci tin ln nht ca thut ton ny l vic quyt nh hai i

tng c l lng ging ca nhau hay khng da vo cc tiu ch v kch thc

ca mi mt i tng v khong cch gia chng. Chnh cc tiu ch ny s

loi b c nhng trng hp ngoi l v em li kt qu chnh xc hn cho

thut ton.

Trong nh ngha 4, K l s cc lng ging trong mt cm lng ging,

K cng ln th vector nh hng ca cm lng ging c hng cng gn vi

gc lch thc s ca vn bn. Trong thut ton, K c gim dn cho n khi

s cc cm lng ging xc nh c gc lch cho vn bn. Hnh 1.12

trn minh ha mt nh vn bn nghing, cc cm lng ging v cc vector ch

phng tng ng thu c khi p dng thut ton tm K-NN vi cc gi tr

ca K=2,3,4.

1.2.5. Phng php dng php ton hnh thi (Morphology)

1.2.5.1. Thut ton L. Najman

Mt s thut ton xc nh gc nghing s dng cc php ton hnh

thi. tng ch o ca phng php ny xut pht t mt c im ca

php ng nh l c kh nng gn cc i tng cnh nhau. Cc thut ton

ny thng dng php ng nhiu ln vi mc ch ni cc dng vn bn vi

nhau. Giai on tip theo s dng cc vector ch phng ca cc dng xc

nh gc nghing cho vn bn tng t nh trong phng php phn tch lng

ging.

Theo hng tip cn ny gm cc thut ton ca cc tc gi: L. Najman

[16], nhm S. Chen v R.M. Haralick v nhm A.K. Das v B.Chada. Thut

ton ca L. Najman c th c xem l ci tin nht trong s cc thut ton

23

dng php ton hnh thi xc nh gc nghing vn bn. Chng ta s la chn

thut ton ca L. Najman trnh by i din cho phng php ny.

Trc ht, ta nh ngha cc php ton hnh thi c bn phc v cho

thut ton L. Najman.

* nh ngha 1: Php gin n (Dilation)

Gi s c nh I v mt mu B. Ta nh ngha php gin ca I theo cu

trc B l tp tt c cc im x I sao cho Bx chm ti I. Vi Bx l dch

chuyn ca B ti v tr x ca nh I.

I B={ x | Bx I }

* nh ngha 2: Php co (Erossion)

Php co ca nh I theo cu trc B l tp tt c cc im x I sao cho Bx

nm trong I. Vi Bx l dch chuyn ca B ti v tr x ca nh I.

I B={ x | Bx I }

* nh ngha 3: Ton t ng m. Gi s c nh I v mu T. Khi

Ton t m c nh ngha: OPEN(I,T)=(IT)T

Ton t ng c nh ngha: CLOSE(I,T)=(IT)T

Cc php ton hnh thi c mt s c im th v sau: Php gin n

cho php ni cc nt t trong cc i tng. Php co c th xa nhiu trong

nh, vi nh vn bn c th dng php co tch ch. c bit, php ng c

kh nng gn cc i tng cnh nhau trong nh. Nu nh l vn bn gm cc

k t th dng php ng s trn c cc k t thnh mt t v trn cc t

thnh dng vn bn trong trng hp vn bn khng b lch gc.

Da vo c im trn y ca php ng, tng chnh ca thut ton

ny l s dng php ton ng gn cc dng vn bn pht hin gc

(7)

(8)

(9)

(10)

24

nghing cho vn bn. Tuy nhin cng thc php ng trn y ch c th gn

cc dng trong vn bn khng nghing.

V vy, trong thut ton ny, L. Najman dng php ng vi cc mu

nghing cc gc khc nhau theo cng thc: RLC(I)= I T T

Vi cu trc mu by gi l T. Trong , l gi tr cho bit di

ca mu, tc l mu c phn t theo chiu ngang v l gc nghing ca

mu T.

Gc nghing ca vn bn c xc nh bng cch cho thay i cc gi

tr trong php ng, ng vi mi gc , tnh s histogram tc s im nh

en trong nh kt qu, gc ng vi trng hp histogram cc i s tng

ng l gc lch ca vn bn.

1.2.5.2. Nhn xt

Do phi p dng cc php ton hnh thi nhiu ln mi c th a ra kt

lun v gc nghing, nn nhn xt u tin v thut ton l vn chi ph tnh

ton. Trong trng hp nh c kch thc ln, ch mt ln duyt ht tt c cc

im nh c th mt rt nhiu thi gian cha ni phi thc hin nhiu ln

duyt v ng thi thc hin php ng nh trong cch lm ca L. Najman.

1.2.6. Phng php dng bin i Hough (Hough Transform)

1.2.6.1. ng thng Hough trn ta cc.

Mt hng tip cn ph bin khc cho bi ton pht hin gc nghing

vn bn l phng php dng bin i Hough [4,12]. Nhng thut ton dng

bin i Hough thng xc nh mt s im en v dng bin i Hough tc

ng ln cc im .

(11)

25

Hnh 1.13 ng thng Hough v trc ta

Bin i Hough nh x mt

ng thng trong mt phng thnh

cc cp (r, ) trong khng gian

Hough vi r l khong cch t gc

ta ti ng thng v l

gc nghing ca ng thng so

vi trc ngang. S dng cc tham s

ny th phng trnh ng thng

c th c vit l:

V c th c phn phi li l: r = x cos + ysin. Do vi mi

ng thng c xc nh trong khng gian Hough s c duy nht

mt cp (r, ). Nh vy mi mi im bt k trn mt phng nh vi

trc ta (gi s l (x0, y0)) th cc ng i qua n c dng: r () =

x0*cos + y0*sin vi r (l khong cch gia cc ng thng vo gc

to ) c xc nh bi .

Gc nghing ca vn bn tng ng l gc c tng s im nm trn

nhng ng thng cng lch gc l ln nht. S cc im en c p dng

bin i Hough ty thuc vo tng thut ton, c th l tt c cc im en

hoc c th ch nhng im tha mn mt s rng buc no hoc ch l

y ca cc i tng nh.

Lin quan n hng tip cn ny l nhng thut ton ca cc tc gi:

Hinds, Jiang, Dianel Le, Sugwara, Nakano, nhm Srihari v Govindaraju,

nhm Yu v Jain, nhm Amin, Fischer, Parkison v Riscky.

(12)

26

Hnh 1.14 Biu din ng thng Hough i qua 3 im

Trong s , phng

php ca Srihari v

Govindaraju l p dng

bin i Hough cho tt c

cc im en ca nh. Tt

nhin, vic p dng khng

c loi tr mt im no

dn n chi ph tnh ton rt

ln v nh hng n chnh xc ca thut ton. gim thi gian chy v

tng mt phn chnh xc, Hinds ch p dng bin i Hough cho mt s t

im hn bng phn tch chy di theo chiu dc. Mc ch ca nn chy di

theo chiu dc trong thut ton ny l ly ra cc im y ca cc dng

vn bn, loi b i nhng im en khc k c chng thuc vo mt k t v

dng bin i Hough ln im en . Tuy nhin, chi ph tnh ton ca thut

ton ny vn cn ln v vic p dng bin i Hough cho tt c cc im en

y c th dn n nhng kt qu sai trong trng hp nh u vo c

nhiu i tng phi k t nh nhiu, bng biu hay picure.

V l thuyt, c th ni theo hng tip cn ny, thut ton ca Dianel

Le l mt trong nhng thut ton c nhiu ci tin nht c v thi gian chy

ln chnh xc. Dianel Le dng phng php phn tch cc thnh phn lin

thng v rt ra nhng im y ca cc i tng. Bin i Hough ch c

p dng cho nhng im y ny nu i tng c kch thc trong mt

khong no . y, Dianel Le dng hai ngng kch thc c nh

ngha trc l chiu rng v chiu cao loi bt i nhng i tng qu ln

nh picture hoc qu b nh nhiu. V vy, thut ton ny cho chnh xc

cao hn v gim ng k chi ph tnh ton.

27

1.2.6.2. Nhn xt

Thut ton ca Dianel Le s gp kh khn nu cc i tng trong nh

cha nhau. Chng hn, cc k t nm hu ht trong cc i tng c kch

thc ln m y ca chng khng phi l nhng ng thng. Khi , c th

nhng k t khng c xt n, thay vo li p dng bin i Hough cho

im y ca cc i tng phi k t dn n kt qu a ra gc lch sai cho

vn bn. Hn na do cc ngng kch thc c c nh trc nn thut

ton ny ph thuc nhiu vo kch thc cc con ch v s lng k t trong

vn bn.

28

CHNG 2. BIN V CC PHNG PHP D BIN

2.1. Bin ca i tng nh

2.1.1. Bin v cc kiu bin c bn trong nh

Cc c trng ca nh thng bao gm cc thnh phn nh: mt

xm, phn b xc sut, phn b khng gian, bin nh [2]. Bin l mt vn

ch yu v c bit quan trng trong phn tch nh v cc k thut phn on

nh ch yu da vo bin.

Hin nay c nhiu nh ngha v bin nh [1] v mi nh ngha c

s dng trong mt s trng hp nht nh. Song nhn chung, ta c th hiu

l: mt im nh c th coi l bin nu c s thay i t ngt v mc

xm.

V d: i vi nh en trng, mt im c gi l im bin nu n l

im en c t nht mt im trng bn cnh.

Tp hp cc im bin to thnh bin, hay cn gi l ng bao ca

nh (boundary). Chng hn, trong mt nh nh phn, mt im c th c

gi l bin nu y l mt im en v c t nht mt im trng nm trong

ln cn im .

Mi mt bin l mt thuc tnh gn lin vi mt im ring bit v

c tnh ton t nhng im ln cn n. l mt bin Vector bao gm hai

thnh phn:

- ln ca Gadient.

- Hng c xoay i vi hng Gradient .

2.1.1.1. Bin l tng:

29

Vic pht hin bin mt cch l tng l vic xc nh c tt c cc

ng bao trong i tng. Bin l s thay i t ngt v mc xm nn s

thay i cp xm gia cc vng trong nh cng ln th cng d dng nhn ra

bin.

Hnh sau y minh ho im nh c s bin i mc xm u(x) mt

cch t ngt:

Mt bin c coi l bin l tng khi m c s thay i cp xm

ln gia cc vng trong nh. Bin ny thng ch xut hin khi c s thay i

cp xm qua mt im nh.

2.1.1.2. Bin dc:

Bin dc xut hin khi s thay i cp xm tri rng qua nhiu im

nh. V tr ca cnh c xem nh v tr chnh gia ca ng dc ni gia

cp xm thp v cp xm cao. Tuy

nhin y ch l ng dc trong

ton hc, t khi nh c k thut

s ho th ng dc khng cn l

ng thng m thnh nhng

ng lm chm, khng trn.

Hnh 2.1 ng bin l tng

Hnh 2.2 ng bin dc

30

Hnh 2.3 ng bin khng trn

2.1.1.3. Bin khng trn:

Trn thc t, nh thng c bin khng l tng, cc im nh trn nh

thng c s thay i mc xm t ngt v khng ng nht, c bit l nh

nhiu. Trong trng hp khng nhiu (bin l tng), bt c mt s thay i

cp xm no cng thng bo s tn ti ca mt bin. Trng hp kh c

kh nng xy ra, nh thng l khng l tng, c th l do cc nguyn nhn

sau:

- Hnh dng khng sc nt.

- Nhiu: do mt lot cc yu t nh: kiu thit b nhp nh, cng

nh sng, nhit , hiu ng p sut, chuyn ng, bi, cha chc rng hai

im nh c cng gi tr cp xm khi c nhp li c cng cp xm trong

nh. Kt qu ca nhiu trn nh gy ra mt s bin thin ngu nhin gia cc

im nh. S xut hin ngu nhin ca cc im nh c mc xm chnh lch

cao lm cho cc ng bin dc tr ln khng trn tru m tr thnh cc

ng bin g gh, mp m, khng nhn, y chnh l ng bin trn thc

t.

31

2.1.2. Vai tr ca bin trong nhn dng Mt cch tng quan c th ni rng bt k mt h thng x l nh no

cng tun theo mt s giai on sau:

Con ngi thng nhn nhn s vt theo hai cch hoc l da vo bin

hoc l da vo xng ca chng. Chng hn, ta da vo bin khi quan st

cc i tng nh ao, h hoc mt ci xe t. Nhng nu phn bit mt

khc sng vi nhng i tng khc trn bn a hnh th ta li da vo

xng ca n. V vy, cng vi xng th bin c mt tm quan trng c

bit trong phn tch v nhn dng hnh nh.

Bin l mt vn ch yu trong phn tch nh v cc k thut phn

on nh ch yu da vo bin. C th thy tm quan trng ca bin khi ta

theo di mt kin trc s lm vic. Gi s anh ta mun thit k mt phng

khch sang trng, nt u tin c phc ha chnh l ng bin hay tng

ca cn phng sau mi n cc chi tit ni tht bn trong. Nh vy, mi

ch nhn bin ca s vt ta cng hnh dung t nhiu v n v c th phn

bit c n vi cc s vt khc.

Nhn chung v mt ton hc, c th xem im bin ca nh l mt im

m c s thay i t ngt v sng. Xut pht t c s , ngi ta

thng s dng hai phng php pht hin bin sau:

Hnh 2.4 S phn tch nh

Phn on nh

Phn loi nh u vo cho

qu trnh tin x l Phn loi

Phn tch c trng

32

Phng php pht hin bin trc tip l lm ni bin da vo s bin

thin v sng ca nh. K thut ch yu c dng l da vo o hm.

Nu ly o hm bc nht ca nh ta c phng php Gradient, nu ly o

hm bc hai ta c phng php Laplace.

Phng php pht hin bin gin tip. Nu bng mt cch no ta

phn bit c nh bng cc vng th ng phn ranh gii gia cc vng

chnh l bin. Hai k thut d bin v phn vng cc i tng l hai bi ton

i ngu nhau. Tht vy, d bin phn lp mt i tng nh, nhng nu

phn lp xong th th c ngha l phn vng c cc i tng nh v

ngc li, khi phn vng c cc i tng nh th cng phn lp c

cc i tng nh v ta c th pht hin bin.

Phng php pht hin bin trc tip t ra kh hiu qu v t chu nh

hng ca nhiu, song nu s vt c s bin i sng khng t ngt

phng php ny t ra rt km hiu qu.

Phng php d bin gin tip tuy kh ci t nhng li p dng tt

cho nhng nh c s bin thin sng t.

2.2. Cc phng php d bin trc tip

2.2.1. Phng php Gradient

Phng php Gradient l phng php d bin cc b da vo cc i

ca o hm. Theo nh ngha, Gradient l mt vector biu th tc thay i

gi tr ca im nh theo 2 hng x v y. Cc thnh phn ca Gradient c

tnh bi:

dx

yxfydxxfx

yxffx ),(),(),(

dyyxfdyyxf

yyxffy ),(),(),(

(13)

33

Vi dx, dy l khong cch gia cc im theo hng x v y (c tnh

bng s im nh). Trong h to cc ta c:

f(x,y) = f(r.cos, r.sin)

x = r.cos, y = r.sin.

ry

yf

rx

xf

rf fxcos + fysin

v

y

yfx

xff r.fx.sin + r.fy.cos.

Trong thc t, khi ta ni ly o hm ca nh thc ra ch l m phng

v xp x o hm bng cc k thut nhn chp hay php cun. Do nh s l

tn hiu ri rc nn o hm khng tn ti.

* K thut PreWitt: K thut ny s dng 2 mt n theo hai hng x v

y nh sau:

Qu trnh tnh ton c thc hin qua 2 bc:

* Bc 1: Tnh I Hx v I Hy

* Bc 2: Tnh (I Hx ) + (I Hy)

* K thut Sobel: Tng t nh k thut PreWitt, k thut Sobel s

dng 2 ma trn mt n nhn chp l:

-1 0 1 Hx = -2 0 2

-1 0 1

-1 -2 -1 Hy = 0 0 0

1 2 1

-1 0 1 Hx = -1 0 1

-1 0 1

-1 -1 -1 Hy = 0 0 0

1 1 1

dx = dy = 2

(14)

(15)

34

2.2.2. Phng php Laplace Cc phng php nh gi Gradient trn lm vic rt tt khi sng

thay i r nt. Tuy nhin, khi mc xm thay i chm, min chuyn tip tri

rng, phng php Gradient li km hiu qu so vi phng php o hm

bc 2 Laplace [11]. Theo nh ngha, ton t Laplace nh sau:

2f = 22

2

2

yf

xf

Ta c: x

yxfyxfxf

xxf

)),(),1(()(

2

2

[f(x+1,y) - f(x,y)] - [f(x,y) - f(x-1,y)]

= f(x+1,y) 2f(x,y) + f(x-1,y).

Tng t:

2

2

yf f(x,y+1) - 2f(x,y) + f(x,y-1).

Mt n nhn chp:

Trong thc t, ngi ta thng s dng mt s bin dng khc ca ton

t Laplace bng cch s dng mt s mt n sau:

2.3. Phng php d bin tng qut

2.3.1. Khi nim chu tuyn

Chu tuyn ca i tng nh E c nh ngha l dy cc im nh

P0,P1,P2,...Pn ca E tho mn: Vi i=1,2,...,n Q E vi Q l 4-lng ging

0 1 0 H = 1 -4 1

0 1 0

0 -1 0 H1 = -1 4 -1

0 -1 0

-1 -1 -1 H2 = -1 8 -1

-1 -1 -1

1 -2 1 H3 = -2 4 -2

1 -2 1

(16)

(17)

35

ca Pi v Pi-1,Pi-1 l 8-lng ging ca Pi. Trong P0=Pn. Khi , ta cng gi n

l di hay chu vi ca chu tuyn.

Trong , 4-lng ging c nh ngha l cc im trc tip bn trn,

di, tri, phi ca mt im. V 8-lng ging l nhng im 4-lng ging

hoc cc im trn tri, trn phi, di tri, di phi trc tip ca mt im.

* Chu tuyn i ngu

Hai chu tuyn C = v C = c gi l hai chu

tuyn i ngu ca nhau nu v ch nu:

i j sao cho pi v qj l 8 lng ging ca nhau.

Cc im pi l nh th qj l nn v ngc li.

* Chu tuyn trong

Chu tuyn C c gi l chu tuyn trong nu v ch nu:

Chu tuyn i ngu C ca n l chu tuyn ca cc im nn.

di ca chu tuyn C nh hn di ca chu tuyn C.

* Chu tuyn ngoi

Chu tuyn C c gi l chu tuyn ngoi (hnh 2.7) nu v ch nu:

Chu tuyn i ngu C ca C l chu tuyn cc im nn.

di ca chu tuyn C ln hn di chu tuyn C.

T nh ngha, ta thy chu tuyn ngoi ca mt i tng l mt a

gic c dy bng mt bao quanh i tng.

P

Hnh 2.5 Cc 4- lng ging ca im nh P

P

Hnh 2.6 Cc 8- lng ging ca im nh P

36

2.3.2. Phng php d bin tng qut

Gi s nh c phn vng. V c bn thut ton d bin trong mt

vng bao gm cc bc c bn sau:

+ Bc 1: Xc nh im bin xut pht.

+ Bc 2: D bo im bin tip theo:

bn+1 = T(bn)

+ Bc 3: Lp li bc hai cho n khi no gp im xut pht

Do xut pht t mt tiu chun v nh ngha khc nhau v im bin,

quan h lin thng [3], nn cc ton t d bin cho ta nhng ng bin vi

sc thi khc nhau.

Kt qu tc ng ca ton t d bin ln mt im bin (bn) l mt

im bin (bn+1), l im 8-lng ging ca bn. Thng thng cc ton t ny

c xy dng nh mt hm i s bool trn cc 8-lng ging ca bn. Mi

cch xy dng ton t u ph thuc vo nh ngha quan h lin thng v

Hnh 2.8 Chu tuyn trong v chu tuyn ngoi ca mt i tng

Chu tuyn trong

Chu tuyn ngoi

Chu tuyn C Chu tuyn C

Hnh 2.7 V d v cc chu tuyn i ngu

Chu tuyn C Chu tuyn C

37

im bin, v s gy kh khn cho vic kho st cc tnh cht ca ng bin.

Ngoi ra v mi bc d bin u phi kim tra tt c 8 - lng ging ca mi

im nn ton t thng km hiu qu. khc phc hn ch trn ta s phn

tch ton t d bin thnh hai bc:

+ Xc nh cp nn vng tip theo.

+ La chn im bin.

* Bi vy thut ton tng qut s tr thnh:

+ Bc 1: Xc nh cp nn vng xut pht.

+ Bc 2: Xc nh cp nn vng tip theo.

+ Bc 3: Lp li bc hai cho n khi gp cp nn vng xut pht.

Khi nim cp vng nn c nh ngha gm mt im vng v mt

im nn, trong nu im vng i c mt vng chu tuyn th im nn

cng i c mt vng chu tuyn i ngu.

Cc bc c m t c th nh sau:

- Bc 1: Vic xc nh cp nn vng xut pht c xc nh bng

cch duyt nh ln lt t trn xung di, t tri qua phi, ri kim tra iu

kin theo nh ngha nh x cp nn vng (ch mang tnh quy c). y ta

chn im vng xut pht l im vng u tin duyt n. im nn xut

pht l im ngay sau im vng xut pht (theo chiu ngang).

- Bc 2: Ta gi nh x cp nn vng tip theo l ton t d bin. Cch

tm cp nn vng tip theo nh sau: ly tm l im vng hin ti, ta xoay

theo chiu kim ng h bt u t im nn hin ti, cho n khi gp mt

im vng l 8-lng ging ca im vng hin ti th dng li, im chnh

l im vng tip theo. Vn ly tm l im vng hin ti, im nn tip theo

l im 8-lng ging ca im vng hin ti ngay sau im vng tip theo

xoay ngc chiu kim ng h.

38

- Bc 3: Cp nn vng tip theo tm c trong bc hai c coi l

cp nn vng hin ti. Sau lp li bc hai. Bc 3 c lp li cho n

khi gp li cp nn vng xut pht.

2.4. Mt s phng php d bin nng cao

2.4.1. Phng php Canny

Phng php ny do John Canny [6] phng th nghim MIT khi

xng vo nm 1986. Canny a mt tp hp cc rng buc m mt

phng php pht hin bin phi t c. ng trnh by mt phng

php ti u nht thc hin c cc rng buc . V phng php ny

c gi l phng php Canny.

* tng ca phng php ny l nh v ng v tr bng cch cc

tiu ho phng sai 2 ca v tr cc im ct "Zero" hoc hn ch s im

cc tr cc b ch to ra mt ng bao.

Cc rng buc m phng php pht hin bin Canny thc hin

c l: mc li, nh v v hiu sut. Trong :

+ Mc li: c ngha l mt phng php pht hin bin ch v phi

tm tt c cc bin, khng bin no c tm b li.

+ nh v: iu ny ni n chnh lch cp xm gia cc im trn

cng mt bin phi cng nh cng tt.

+ Hiu sut: l lm sao cho khi tch bin khng c nhn ra nhiu

bin trong khi ch c mt bin tn ti.

Rng buc mc li v nh v c dng nh gi cc phng php

pht hin bin. Cn rng buc v hiu sut th tng ng vi mc li

dng.

Canny gi thit rng nhiu trong nh tun theo phn b Gauss v

ng thi ng cng cho rng mt phng php pht hin bin thc cht l

39

mt b lc nhn xon c kh nng lm mn nhiu v nh v c cnh. Vn

l tm mt b lc sao cho tho mn ti u nht cc rng buc trn.

2.4.2. Phng php Shen Castan

Shen v Castan [7] c cng quan im vi Canny v mt mu chung

trong vic tch cc ng bin. l: nhn xon nh vi mt mt n lm

mn, sau tm ra im bin. Tuy nhin trong nhng phn tch ca h li to

ra mt hm khc ti u, l vic xut cc tiu ho hm sau trong

khng gian mt chiu:

Ni mt cch khc l hm m lm cc tiu trn l b lc mn ti u

cho vic tch bin. Tuy nhin, Shen v Castan li khng cp n vic thut

ton s nhn ra c nhiu cnh trong khi ch c mt cnh tn ti.

(18)

40

Hnh 3.1 Xc nh hnh ch nht ngoi tip cc i tng

CHNG 3. NG DNG BIN I HOUGH PHT HIN

GC NGHING VN BN.

3.1. Tin x l v pht hin gc nghing vn bn t bin ca i tng

Qua nghin cu bi ton gc nghing vn bn v mt s phng php gii quyt, ti nhn thy rng hu ht cc thut ton ch lm vic tt cho mt s trng hp c th. C nhng thut ton ch lm vic tt vi cc nh c gc lch b hoc c kch nh thc b, c thut ton khng chnh xc vi nhng nh c t k t ch ci hoc nhiu nhiu, c thut ton ph thuc vo font ch, kch c ch v nhn chung rt nhiu thut ton c chi ph tnh ton ln. C nhng thut ton vt qua c gii hn ca gc lch nhng li gp vn phc tp hoc yu cu s lng k t trong vn bn ln. V tt c cc thut ton u mi ch lm vic vi cc nh vn bn hai mu, trong mt mu l nn v mt mu l vng, cha cp n pht hin gc nghing vn bn trong nh nhiu mu.

T tng pht hin gc nghing ca thut ton khng khc nhiu so vi nhng thut ton dng bin i Hough. Trc ht, ta dng k thut d bin xc nh chu tuyn cho cc i tng nh. Cc hnh ch nht cha cc i tng ny c lu li cho cc qu trnh x l tip theo. La chn mt s i tng c kch thc ch o trong nh ri dng bin i Hough p dng cho cc im i din l trung im cnh y ca hnh ch nht ngoi tip cc i tng ny. Cui cng, gc nghing vn bn s c c lng t mng tch lu ca bin i Hough.

41

3.2. Xc nh ng thng Hough trn trang vn bn Mi ng thng trong to cc c xc nh bi cp (r, ) nh

hnh v:

Gi s (x,y) l mt im thuc ng thng th ta tm cng thc rng

buc gia x, y, r v .

Ta c:

r = (m + y) . sin

Mt khc ta c:

tg = x/m

sin / cos = x/m

m.sin = x.cos

Do ta c mi lin h gia ( x, y ) v (r, ) nh sau :

r = x.cos + y.sin

x

y

m

Hnh 3.2 ng thng trong to cc

r

(19)

42

Nh vy, nu n im (xi, yi) nm trn mt ng thng th ta c

phng trnh :

r = xi.cos + yi.sin , vi mi i = 0.. n

Bin i Hough nh x n im ny thnh n ng sin trong to cc

m cc ng ny u i qua (r, ). Giao im (r, ) ca n ng sin s xc

nh mt ng thng trong mt phng. Nh vy, mi ng thng i qua

im (x, y) s cho duy nht mt cp (r, ) v c bao nhiu ng qua (x, y)

th c by nhiu cp gi tr (r, ).

3.3. p dng bin i Hough pht hin gc nghing vn bn

tng ca vic p dng bin i Hough trong pht hin gc nghing

vn bn l dng mt mng tch lu m s im nh nm trn mt ng

thng trong khng gian nh. Mng tch lu l mt mng hai chiu vi ch s

hng ca mng cho bit gc lch ca mt ng thng v ch s ct chnh

l gi tr r khong cch t gc to ti ng thng . Sau tnh tng s

im nh nm trn nhng ng thng song song nhau theo cc gc lch thay

i. Gc nghing vn bn tng ng vi gc c tng gi tr mng tch lu cc

i.

Theo bin i Hough, mi mt ng thng trong mt phng tng

ng s c biu din bi mt cp (r, ). Gi s ta c mt im nh (x, y)

trong mt phng, v qua im nh ny c th xc nh c v s ng

thng m mi ng thng li cho mt cp (r, ) nn vi mi im nh ta s

xc nh c mt s cp (r, ) tho mn phng trnh Hough.

43

Hnh v trn minh ho cch dng bin i Hough pht hin gc

nghing vn bn. Gi s ta c mt s im nh, y l nhng im gia y

cc hnh ch nht ngoi tip cc i tng c la chn t cc bc

trc (cc i tng c chn l nhng i tng tiu biu c xc nh t

thao tc d bin v xy dng hnh ch nht ngoi tip). y, ta thy trn

mt phng c hai ng thng song song nhau cng tho mn phng trnh

Hough. ng thng th nht c ba im nh nn gi tr mng tch lu bng

3, ng thng th hai i qua 4 im nh nn c gi tr mng tch lu bng 4.

Do , tng gi tr mng tch lu cho cng gc trng hp ny bng 7.

Gi Hough[360][Max] l mng tch ly, gi s M v N tng ng l

chiu rng v chiu cao ca nh, ta c cc bc chnh trong qu trnh p dng

bin i Hough pht hin gc nghing vn bn nh sau:

Bc 1: Khai bo mng tch ly Hough[][r] vi 0 3600 v 0 r

NNMM ** (vi M v N l chiu rng v chiu cao ca nh).

Bc 2: Gn gi tr khi to bng 0 cho cc phn t ca mng.

Bc 3: Vi mi cp (x,y) l im gia y ca hnh ch nht ngoi

tip mt i tng.

Hnh 3.3 ng thng Hough trn trc ta

y

x.cos+y.sin=r1

Hough[][r1]=3

x

0

x.cos+y.sin=r2

Hough[][r2]=4

44

- Vi mi i t 0 n 360 tnh gi tr ri theo cng thc:

ri = x * cos i + y * sin i

- Lm trn gi tr ri thnh s nguyn gn nht l r0

- Tng gi tr ca phn t mng Hough[i][r0] ln mt n v.

Bc 4: Trong mng Hough[][r] tnh tng gi tr cc phn t theo

tng dng v xc nh dng c tng gi tr l ln nht.

Do s gi tr ca mt phn t mng Hough[0][r0] chnh l s im

nh thuc ng thng r0 = x * cos 0 + y * sin 0 v vy tng s phn t ca

mt hng chnh l tng s im nh thuc cc ng thng tng ng c

biu din bi gc ca hng . Do , gc nghing ca trang vn bn chnh

l gc ca hng trong mng tch lu c gi tr ln nht.

T c s l thuyt tm hiu c, tin hnh xy dng mt thut ton

xc nh gc nghing nh vn bn da vo bin i Hough.

3.4. Thut ton pht hin gc nghing vn bn

* X l i tng nh ngoi l

Sau giai on tin x l nh ta thu c nh trung gian. Thut ton pht

hin gc nghing s lm vic vi nh trung gian ny tm ra gc nghing

cho vn bn v sau dng thut ton xoay nh xoay nh ban u vi gc

nghing va tm c.

Tuy nhin, do nh tin hnh x l c thu nhn t nhiu ngun khc

nn cht lng nh cng nh cc i tng trn nh cng khc nhau. Nn mt

im cn c xt n trong thut ton pht hin gc nghing l x l nhng

nh vn bn phc tp hoc cc trng ngoi l. Ta s ln lt a ra cc

phng n x l cho cc trng hp ny.

45

+ nh c qu t k t.

Trng hp th nht l trong nh c qu t k t ch ci cha xc

nh c gc nghing. Cc i tng trong nh ch yu l hnh hoc nhiu,

c bit cc k t nghing cc gc khc nhau do c th ring ca nh. Hnh

v di y minh ho mt nh vn bn nghing vi s k t rt t.

Nh vy, sau khi loi b cc i tng t hm xc nh chu tuyn v

dng ngng kch thc th s i tng c la chn p dng bin i

Hough s cn li rt t. Nu chng ta vn tip tc cc bc tip theo v a ra

kt lun v gc nghing cho vn bn th r rng chnh xc khng c

m bo. L do n gin v nhng i tng c la chn cha chc l

nhng k t. Chng c th l nhng i tng phi k t nhng c la chn

v kch thc ca chng tho mn ngng. Vic xc nh nhng i tng

ch o lun mang tnh tng i v cng chnh xc khi s i tng k t

trong nh cng nhiu. Khi trong nh c t k t th cng khng th chc chn

c rng cc i tng c chn l k t.

V vy, ta ch a ra kt lun v gc nghing cho vn bn trong trng

hp s lng cc i tng ny phi ln hn mt ngng no .

Hnh 3.4 V d v mt nh nghing c t k t

46

+ Cc i tng bao nhau.

Mt trng hp ngoi l khc l cc i tng bao nhau. y l mt

cn tr i vi nhng thut ton xc nh gc nghing khc c bit l nhng

thut ton theo phng php phn tch lng ging ln cn nh c cp

trn. V vi nhng i tng ny rt d dn n s nhm ln khi xc nh

i tng ch o trong nh.

Mc d s k t trong vn bn c th rt nhiu nhng cc k t hu ht

b cha trong cc i tng khc ln hn nhiu chng hn nh picture hay

bng biu . Hnh v di y minh ha cho cho trng hp cc k t b bao

bi i tng l bng biu.

Nh vy, nhim v ca chng ta l phi nhn ra c s bao hm gia

cc i tng v tch bit chng, ly c cc i tng k t ch o b bao

bi cc i tng ln hn. Khi , vic xc nh gc nghing khi p dng

bin i Hough ln cc i tng ny mi cho ta kt qu chnh xc.

y, ta dng mt k thut bc dn nhng i tng ln ngoi c

xc nh nhng k t trong . Mt i tng c gi l c kch thc ngoi

c c quy c l i tng c chiu rng v chiu cao ln hn 200 pixel.

Nu trong qu trnh d bin ta gp mt i tng nh vy, ta s cch li n ra

Hnh 3.5 V d v vn bn nghing c cc i tng bao nhau

47

khi tp i tng ang xt. Cc i tng ny s c dng n nu cui

cng s i tng c chn p dng bin i Hough l qu t. Ta xem

nh i tng ny l mt nh v tip tc duyt cc i tng bn trong n

ly ra nhng i tng k t.

Trong ci t thut ton, ta dng mt k thut gi l bc dn. Bnh

thng, sau khi xc nh c chu tuyn ngoi cho mt i tng ta s khng

duyt nhng im nh bn trong i tng ny bng cch nh du li i

tng . Nhng nu i tng c kch thc rt ln, ta s b qua khu

nh du n v kt lun rng l 1 i tng bao hm i tng khc nh

bng biu chng hn. Thay bng nh du i tng ta thay i mu cho cc

im bin thnh mu nn, xem nh cha xt i tng ny v tip tc xt cc

i tng bn trong n. K thut ny gi l bc dn v mi ln xc nh c

bin ca mt i tng ln ta thay i mu ca cc im bin thnh mu nn

iu c ngha l i tng ny s ho vo nn v xem nh bc dn i

tng ln lm ni bt ln cc k t bn trong n.

nh du cc i tng, ta dng phng php gn nhn cho cc i

tng. Mi mt i tng nu khng phi l mt im c lp s mang mt

nhn l mt s nguyn dng. Cc i tng khc nhau mang cc nhn khc

nhau. Nhng phn t thuc bin ca mt i tng s c gn nhn bng

nhau v bng nhn ca i tng ny.

+ Tin trnh xc nh chu tuyn cho cc i tng thc hin nh sau:

- Duyt cc im nh t trn xung di t tri sang phi. Xt

im hin ti l (x, y).

- Nu gp mt im nh c mu khc mu nn, ta s p dng

thut ton xc nh chu tuyn cho i tng cha im nh ny v gn

tt c cc im bin ca i tng ny cng mt gi tr nhn. Kt thc

hm d bin i tng:

48

- Nu kch thc ca i tng khng phi l qu ln tc l kch

thc ca chng b hn 200 pixel, ta s tip tc qu trnh tm bin cho

cc i tng tip theo bt u t mt im nh lng ging bn phi.

Gi (x1,y1) l im lng ging bn phi ca i tng nh nu: x1=x v

im (x1,y1-1) thuc bin ca i tng nh ang xt.

- Ngc li nu i tng c kch thc qu ln. Ta thit lp li

mu cho cc im bin ca i tng thnh mu nn, khng gn nhn

cho bin v xt tip cc im nh bn trong bt u t (x,y+1).

- Nhng nu gp mt im nh xt ri tc l c gn mt

nhn, ta s b qua i tng tng ng vi nhn xt cc i

tng mi bng cch nhy ti im (x1,y1) vi (x1,y1-1) c nhn bng

nhn (x,y) v y1 ln nht trong s cc im c cng nhn.

* Thut ton:

V c bn thut ton pht hin gc nghing vn bn da vo bin i

Hough gm cc bc ch yu sau:

Bc 1: Duyt nh theo th t t trn xung v t tri qua phi, vi

mi im nh.

* Nu gp mt im vng (x,y) cha xt thc hin cc bc:

+ p dng thut ton xc nh chu tuyn vi u vo l (x,y) v mu

tng ng.

+ Dng hnh ch nht ngoi tip kim tra nu i tng c kch thc

bnh thng (tho mn ngng) th p dng bin i Hough ln trung

im cnh y ca hnh ch nht ngoi tip i tng .

+ Cp nht li mng tch lu.

49

* Nu gp mt im xt, tm mt im nh trn cng dng c nhn

bng vi im nh ang xt v tin hnh duyt li t y. ng thi

phi cp nht li gi tr trong mng tch lu.

Bc 2: Da vo kt qu ca php bin i Hough c lng gc

nghing cho vn bn.

Bc 3: Da vo gc nghing xc nh c t bc 2 p dng thut

ton xoay nh.

Tuy nhin, nu p dng bin i Hough cho tt c cc i tng ca

nh, th thut ton s khng chnh xc hoc l tn nhiu thi gian thc hin

hoc c hai. V vy chng ta khng p dng bin i Hough cho tt c cc

i tng sau khi tm c chu tuyn ca chng m loi ra nhng i tng

c kch thc qu ln, hoc l rt b so vi k t thng..

50

S gii thut:

Hnh 3.6 S gii thut tng qut

Image source

D bin

Tm im c trng

p dng bin i Hough

Xc nh ng thng Hough

Kim tra cn i tng

nh cn xt

Lu mng tch ly

Xc nh gc nghing da vo

mng tch ly

Xoay nh Image result

ng

Sai

51

3.5. Chnh sa gc nghing vn bn

Sau khi thao tc vi nh trung gian v xc nh c gc nghing cho

ton vn bn. chnh sa gc nghing cho vn bn ta xoay li nh vi gc

lch tm c. Xoay nh l mt trong nhng k thut ph bin nht ca mi

h thng x l nh. Thut ton xoay nh n gin l chuyn mt im nh

(x,y) t nh ban u thnh im nh mi c ta (x, y) trong nh kt qu

vi (x, y) c xc nh theo cng thc:

x = x.cos + y.sin

y = y.sin - x.cos

Trong ci t, nhng im nh (x, y) u tin c tnh theo cng

thc xoat, v cc gi tr l nhng s thc nn tip theo ta ly phn nguyn ca

chng c mt im trong nh ch v gn cho im nh ny mu ca

im (x, y) trong nh gc. Gi s ta cn xoay nh Image vi chiu rng l M

chiu cao N ta c thut ton xoay nh Image thnh nh DestImage nh sau:

O

x

y

P(x,y)

P(x,y)

Hnh 3.7 Xoay mt im nh quanh gc ta

52

Vi hm Trunc l hm lm trn mt s thc thnh mt s nguyn gn

n nht.

Tuy nhin, c mt vn kinh in trong cc k thut xoay nh m

bt k h thng x l nh no cng gp phi l gii quyt nhng l hng

hay nhng im khng c gn mu trong nh kt qu khi thc hin xoay

nh. L do dn n nhng l hng ny chnh l t cng thc xoay nh, do

phi lm trn cc gi tr thnh s nguyn nn trong nh ch c mt s im

nh khng tng ng c nh x t nh gc sang.

gii quyt vn ny, chng ta lp cc l hng bng cch duyt

nh ch v gn mu cho chng da vo mu ca cc lng ging. Vi nh en

trng, cc l hng c gn mu en. Tuy nhin, trong cc nh mu, nu

cc lng ging ca mt l hng c cc mu khc nhau, vic chn mt mu

cho l hng cng l ty v thng th s ly mu trung bnh gia cc mu

ca cc lng ging.

For x:=1 to M do For y:=1 to N do

Begin c := Getpixel(Image,x,y); x1:= x.cos + y.sin; y1:= y.sin - x.cos; x0:= Trunc(x1); y0:= Trunc(y1); Setpixel(DestImage, x0, y0, c);

End;

53

CHNG 4. XY DNG CHNG TRNH THC NGHIM

Trn c s l thuyt tm hiu, tin hnh xy dng chng trnh x l

gc nghing nh vn bn gm cc chc nng chnh nh: v biu mc xm,

convert sang nh nh phn v nh a cp xm, d bin ca cc i tng trong

nh bng phng php: Sobel, Laplace, Canny, Gradient. V cui cng l

chc nng t ng pht hin v hiu chnh gc nghing cho c nh vn bn

mu v nh en trng thun ty.

4.1. S khi.

nh gc

V biu mc xm

Convert nh

D bin Bin i Hough

Xoay nh

nh nh phn

nh a cp xm

Sobel

Canny

Laplace

Gradient

Hnh 4.1 S tng qut

54

4.2. Thit k chng trnh

4.2.1. Module giao din chnh

Chng trnh c ci t bng b cng c Visual C# 2010 trn nn

Windows vi giao din c thit k thn thin v d s dng theo khun

mu ca phn mm Office 2010 v Visual Studio 2010 ca Microsoft. Cc

chc nng chnh ca chng trnh c th hin trn menu v thanh cng c

dng Ribbon Bar nh hnh di y:

* Cc chc nng ca chng trnh chia lm 2 nhm chnh:

a. Cc chc nng x l c bn: Open, Save, Print, Next, Previous tng

t nh cc phn mm ca Window. Chc nng Open cho php m mt hay

nhiu tp tin nh vn bn chun b cho thao tc x l tip theo. Chc nng

Next v Previous phc v cho thao tc di chuyn qua li gia cc nh vn bn

trong trng hp m nhiu tp tin nh.

Hnh 4.2 Giao din chnh ca chng trnh

55

u vo cho chng trnh x l gc nghing vn bn l cc file nh (c

th l nh mu) c chn bng chc nng Open. Mn hnh giao din khi

chn chc nng Open nh sau:

Hnh 4.4 Mn hnh giao din chng trnh khi chn chc nng Open

File

Open Save

Save all Print Exit

Hnh 4.3 S module x l c bn

56

b. Cc chc nng thao tc trn nh

Hai chc nng chnh ca chng trnh l Edge Detect v Rotate

Image. Chc nng Edge Detect dng d bin cc i tng trong mt nh vi

nhiu thut ton khc nhau cho php ngi dng c ci nhn tng quan v

pht hin bin ca i tng trong nh, mt khc c th a ra s so snh v

kt qu cng nh thi gian thc hin ca mi thut ton. Trong khi , chc

nng Rotate Image dng pht hin gc nghing ca mt hay nhiu nh u

vo v chnh sa nh vn bn b nghing gc. Hai chc nng chnh ny c

b tr trn thanh Ribbon Bar ca chng trnh.

4.2.2. Module chuyn i nh gc v biu mc xm

File nh

Sobel

Edge Detect

Canny

Rotate Image

Laplace Gradient

Hnh 4.5 S thao tc x l trn nh

View

Histogram

Previous Image

Next Image

Image

Convert to Binary

Convert to Grayscale

Hnh 4.6 S convert nh sang nh phn v a cp xm

57

Sau khi chn mt hoc nhiu file nh mu v click chut chn chc

nng Convert to Binary hoc Convert to Grayscale, chng trnh s hin th

nh vn bn kt qu sau khi chuyn i t nh mu sang nh nh phn hoc

nh xm.

4.2.3.

Hnh 4.7 Giao din biu din Histogram ca nh

Hnh 4.8 Giao din convert nh sang nh phn v nh a cp xm

58

Module d bin

Ngoi ra chng trnh cn h tr chc nng xc nh bin ca cc i

tng trong nh trong nh ti liu ngi s dng c ci nhn tng qut v

vic xc nh bin ca i tng lm c s cho vic p dng bin i Hough

pht hin gc nghing ca nh.

* Pht hin bin dng phng php Sobel:

Hnh 4.10 D bin bng phng php Sobel

Edge Detect

Sobel Canny

Emboss Laplacian

Gradient

bin

Hnh 4.9 S d bin

59

* Pht hin bin dng phng php Canny:

* Pht hin bin dng phng php Emboss Laplacian:

Hnh 4.11 D bin bng phng php Canny

Hnh 4.12 D bin bng phng php Emboss Laplacian

60

* Pht hin bin dng phng php Gradient

4.2.4. Module biu din bin i Hough

Bn cnh vic biu din Histogram v cc phng php php hin bin

ca i tng th chng trnh cn cung cp mt chc nng na l v biu

bin i Hough trn nh u vo c chn.

Hnh 4.13 D bin bng phng php Gradient

Hnh 4.14 Biu din bin i Hough ca nh

61

4.2.5. Module hiu chnh gc nghing vn bn

Chc nng xoay nh cho php ngi dng hiu chnh gc nghing ca

mt hay nhiu nh vn bn mt cch t ng. Hin ti chng trnh pht

hin v hiu chnh c cc nh vn bn c gc nghing trong khong 200.

Di y l giao din chng trnh trc v sau khi chn chc nng Rotate

Image.

4.3. nh gi kt qu

Thut ton trnh by trn y c ci t thnh cng bng ngn ng

lp trnh Visual C# ca b Visual Studio 2010 v c kim tra nhiu ln vi

nhiu b d liu khc nhau.

D liu vo cho chng trnh l nh mu vi nhiu i tng k t v

phi k t xen ln nhau. kim tra tnh ng n v thi gian chy ca

chng trnh, ti to cc b d liu a dng.

Hn 100 nh c qut t cc tp ch khoa hc hoc cc ti liu mn

hc, gio trnh hoc cc h s vn phng, cc bng biu thng k, bng im,

Hnh 4.15 Pht hin gc nghing v xoay nh

62

mu nh gi mn hc. Cc nh vn bn ny gm nhiu loi ngn ng, ting

Anh, ting Nht, ting Hn, ting Vit v c mt s vn bn ting Trung

Quc. Trong , nh c cha vn bn, cc loi hnh nh, cng thc ton hc,

cc bng biu v vi nhng font ch v kch thc ch khc nhau. Cc nh c

kch thc khc nhau v trong khong t 300*300 pixel ti 2500*3000 pixel.

Kt qu thc nghim cho thy: V tc x l, chng trnh c th x

l nhanh k c vi nh nhiu mu v nh kch thc ln. Nhng nh c kch

thc bnh thng, c b hn 1000*1000 pixel thi gian chy khong 1s. Vi

nhng nh kch thc ln c 2500*3000 pixel chng trnh ch mt khong t

2.5s n 3s chnh sa c gc nghing cho vn bn. Trn thc t, thi

gian x l tp trung ch yu cc cc giai on ph l tin x l v thut

ton xoay nh. Thi gian d bin v p dng bin i Hough khng ng k

khi kch thc nh ln.

V chnh xc, y l mt u im ni bt ca chng trnh so vi

nhiu thut ton pht hin v chnh sa gc nghing vn bn khc. Chng

trnh cho chnh xc cao, c bit vi nhng vn bn c gc lch trong

khong 200. L do n gin l v hu ht nhng i tng c chn p

dng bin i Hough u l k t. Vi nhng nh c nhiu v nhng i

tng phi k t thut ton cho chnh xc n gc lch ln c 150. c bit

chnh xc thut ton khng ph thuc vo cc loi ngn ng, cc font ch,

kch thc k t, v c s bao hm gia cc i tng nh.

Ngoi ra, chng trnh cn c tch hp vi h thng qun l im ti

trng i hc Lc Hng h tr vic hiu chnh bng im sinh vin phc v

cho khu nhp im c nhanh chng v chnh xc. Bn cnh , chng

trnh cn c s dng pht hin v chnh gc nghing cho h thng nh

63

gi cht lng ging dy v cc thao tc scan ti liu in t. T hiu qu

cng vic qun l v o to ti trng i hc Lc Hng tng ln ng k.

* Sau y l mt s nh vn bn b nghing v kt qu t c sau khi pht

hin v hiu chnh gc nghing :

Hnh 4.16 Mt nh b nghing gc c cc i tng xen ln vn bng, bng biu v nh kt qu sau khi hiu chnh 1 gc 12.9o

64

Hnh 4.17 Mt nh b nghing gc ting Nht c xen ln hnh nh, k t v nh kt qu sau khi hiu chnh 1 gc 11.3o

Hnh 4.18 Mt bng im b nghing gc khng th nhn dng c ca h thng qun l im v nh kt qu sau khi hiu chnh 1 gc 7.61o

65

Hnh 4.19 Mt mu phiu nh gi cht lng ging dy b nghing gc khng th nhn dng c v nh kt qu sau khi hiu chnh 1 gc 9.72o

Hnh 4.20 Mt nh mu ti liu b nghing v nh kt qu sau khi hiu chnh 1 gc 10.82o

66

Hnh 4.21 Mt nh mu ti liu b nghing gm nhiu biu v nh kt qu sau khi hiu chnh 1 gc 17.6o

67

KT LUN

Bn cnh ngn ng giao tip, cc thng tin di dng hnh nh ng

mt vai tr rt quan trng trong vic trao i thng tin. Trong cng ngh

thng tin, x l nh v ha chim mt v tr rt quan trng bi v cc

c tnh y hp dn to nn mt s phn bit vi cc lnh vc khc.

Chng gii thiu cc phng php v k thut to ra cc nh v x l cc

nh ny. Ta bit rng phn ln cc thng tin m con ngi thu thp c qua

th gic u bt ngun t cc nh. Do vic x l nh v ha l mt b

phn quan trng trong vic trao i thng tin gia ngi v my.

X l nh l mt lnh vc rt rng ln gm nhiu giai on x l.

Trong mi giai on c nhiu vn nghin cu trong x l nh vn

bn l mt b phn quan trng ca ngnh x l nh v c nhiu ng dng

rng ri trong khoa hc v i sng thc tin. Mt cch t nhin v tt yu,

vn u tin v cng l vn khng th trnh khi trong x l nh vn

bn l bi ton gc nghing nh vn bn.

S d c th kt lun rng mt vn bn b nghing gc l v chng ta

da vo mt s i tng ch o trong vn bn v quan st thy ng ni

cc im gia y ca chng lch i mt gc. Trn c s nghin cu cc thut

ton php chiu nghing, phn cm lng ging, bin i Hough, ti chn

v ng dng bin i Hough vo vic pht hin v hiu chnh gc nghing

vn bn vic x l nh vn bn t hiu qu tt nht.

Mc tiu ca lun vn l tm hiu cc k thut pht hin gc nghing

trn c s ng dng vo hiu chnh vn bn nng cao hiu qu cho qu

trnh nhn dng nh tip theo. C th lun vn t c cc kt qu sau:

68

+ Trnh by tng quan v x l nh v bi ton pht hin gc nghing

vn bn. Phn tch u v nhc im v a ra nhn xt c th cho mi

phng php trong qu trnh nghin cu.

+ Trnh by h thng nhng khi nim c bn v bin v cc phng

php pht hin bin ni bt di gc x l nh.

+ Trn c s nhng k thut nghin cu, tin hnh xy dng mt

ng dng pht hin v hiu chnh gc nghing vn bn h tr cng tc qun

l im, chm thi trc nghim v scan ti liu in t.

Hng pht trin:

+ Tch hp thm cc thut ton nng cao cht lng nh nhm tng kh

nng pht hin gc nghing.

+ Ci t cc phng php pht hin gc nghing khc: phn cm lng

ging, php ton hnh thi, hnh chiu nghing.

+ Thc hin pht hin gc nghing trn mi loi nh vn bn.

+ Nghin cu thc hin vi nh vn bn c gc lch - 200 v

200.

69

TI LIU THAM KHO

[1] Phm Vit Bnh, Cao L Mnh H, Nng Ton, Mt cch tip cn

mi trong pht hin bin ca nh a cp xm. Hi tho Quc gia ln

th 8 - Mt s vn chn lc ca Cng ngh thng tin v Truyn thng,

Hi Phng 25-27/08 /2005. Nxb KH&KT, H Ni 2006.

[2] Nng Ton, "Bin nh v mt s tnh cht", Tp ch Khoa hc Cng

ngh, Tp 40, s B, 2002.

[3] Nng Ton, Phm Vn Dng, Phm Vit Bnh (2005), ng dng

chu tuyn trong pht hin gc nghing Vn bn. K yu Hi tho Quc

gia ln th 7 - Mt s vn chn lc ca Cng ngh thng tin v

Truyn thng, Nng 18-20/08 /2004. Nxb KH&KT, H Ni 2005.

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Hough Transform, Pattern Analysis & Applications, 2000.

[5] H. Baird, The skew angle of printed documents. Society of

Photographic Scientists and Engineers, 1987.

[6] J. Canny, A Computational Approach To Edge Detection, IEEE Trans.

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[7] Castan, S.; Zhao, J. and Shen, J."New edge detection methods based on

exponential filter", Pattern Recognition, vol.1, Jun 1990.

[8] A.K. Das, B.Chada. A fast algorithm for skew detection of document

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70

[9] S. C. Hinds, J. L. Fisher and D. P. D'Amato. A Document Skew Detection

Method Using Run-Length Encoding and the Hough Transform. 10th

International Conference on Pattern Recognition, vol. 1, 1990.

[10] X. Jaing, H. Bunke, D. Widmer-Kljajo. Skew detection of document

image by focused nearest-neighbour-clustering. Proc. Of the 5th

International Conference on Document Analysis and Recognition,

Bangalore. 1999.

[11] Kimmel, Ron and Bruckstein, Alfred M. "On regularized Laplacian zero

crossings and other optimal edge integrators", International Journal of

Computer Vision, 2003.

[12] D. X. Le, "Automated Document Skew Angle Detection Using

Projection Profiles, Variances, Component Labelling and the Hough

Transform," M.S. thesis, Computer Science Department, George Mason

University, November 17th, 1992.

[13] Shutao Li, Qinghua Shen and Jun Sun. Recognition Letters, Volume 28,

Issue 5, 1 April 2007.

[14] Yue Lu and Chew Lim Tan, A nearest neighbor chain based approach

to skew estimation in document images, Pattern Recognition Letters 24,

2003.

[15] A. Mahmoud Al-Shatnawi and Khairuddin Omar. Skew Detection and

Correction Technique for Arabic Document Images Based on Centre of

Gravity. Journal of Computer Science 5, 2009.

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[16] L. Najman, Using mathematical morphology for document skew

estimation, In procs. SPIE Document Recognition and Retrieval XI,

volume 5296, 2004.

[17] J.R. Paker, Algorithms for Image processing and Computer Vision. John

Wiley & Sons, Inc, 1997.

[18] W. Postl, Detection of linear oblique structures and skew scan in

digitized documents. Document Analysis and Recognition, 1986.

[19] Tahir Rabbani and Frank van den Heuvel, "Efficient hough transform for

automatic detection of cylinders in point clouds", Proceedings of the

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[20] John C. Russ, The Image Procesing Handbook. CRC Press, Inc, 1995.

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state of art. Int. J. Comput. Sci. Network Secur, 2008

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