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Sinh vin: Nguyn Th Lan CT1102

B GIO DC V O TO

TRNG I HC DN LP HI PHNG

---------o0o---------

TM HIU PHNG PHP BPR (BENDING POTENTIAL RATIO)CHO BI TON TM XNG CA NH

N TT NGHIP I HC H CHNH QUY

NGNH CNG NGH THNG TIN

Sinh vin thc hin: Nguyn Th Lan

Gio vin hng dn: Ths. Ng Trng Giang

M s sinh vin: 110853

HI PHNG - 2011

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LI CM N

Trong li u tin ca bo co n Tt Nghip Tm hiu phngphp BPR(Bending Potential Ratio) cho bi ton tm xng ca nh ny, em

mun gi nhng li cm n v bit n chn thnh nht ca mnh ti tt c

nhng ngi h tr, gip em v kin thc, v tinh thn trong qu trnh

thc hin n.

Trc ht, em xin chn thnh cm n Thy Gio. Ths. Ng Trng

Giang, Ging vin Khoa Cng Ngh Thng Tin, Trng HDL Hi Phng,ngi trc tip hng dn, nhn xt, gip em trong sut qu trnh thc

hin n.

Xin chn thnh cm n cc Thy C trong Khoa Cng Ngh Thng Tin

v ton Thy C trong Trng i Hc Dn Lp Hi Phng gip em

trong sut qu trnh hc tp.

Em cng xin by t lng bit n n gia nh v nhng ngi bn

lun gip ng vin em rt nhiu trong qu trnh hc tp v lm n

Tt Nghip.

Do thi gian thc hin c hn, kin thc cn nhiu hn ch nn n

thc hin chc chn khng trnh khi nhng thiu st nht nh. Em rt mong

nhn c kin ng gp ca Thy C gio v cc bn em c thm kinh

nghim v tip tc hon thin bi bo co ca mnh.

Em xin chn thnh Cm n!

Hi Phng, thng 7/2011

Sinh vin

Nguyn Th Lan

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MUC LC

MUC LC ............................................................................................................................ 3M U ............................................................................................................................... 5

DANH MC HNH V ....................................................................................................... 6CHNG 1: TNG QUAN V X L NH ............................................................. 7

1.1 Cc khi nim c bn trong x l nh .................................................. 71.1.1 X l nh l g? ............................................................................. 71.1.2 nh v im nh ........................................................................... 71.1.3 phn gii .................................................................................. 81.1.4 Mc xm ....................................................................................... 8

1.2 Cc php ton c bn trn nh nh phn ............................................... 91.2.1 Php ton logic trn nh nh phn ................................................. 91.2.2 Cc php ton hnh thi trn nh nh phn.................................... 9

1.3 Cc giai on c bn ca X l nh ................................................... 171.4 Mt s ng dng c bn ca x l nh ............................................... 18

CHNG 2: XNG V CC THUT TON TM XNG ............................. 202.1 Khi nim xng................................................................................. 202.2 Cc hng tip cn trong vic tm xng........................................... 20

2.2.1 Phng php tm xng da trn lm mnh............................... 202.2.2 Tm xng khng da trn lm mnh......................................... 22

2.3 Ct ta xng ca nh ......................................................................... 292.3.1 Khi nim ct ta xng .............................................................. 29

2.3.2

K thut ct ta xng vi DCE.................................................. 29

CHNG 3: K THUT CT TA XNG DA VO UN ...................... 333.1 Gii thiu ............................................................................................ 333.2 Phng php ct ta xng theo BPR (Bending Potential Ratio) ...... 35

3.2.1 nh ngha c bn ....................................................................... 353.2.2 T l un (BPR Bending Potential Ratio) ............................... 373.2.3 xut cho pht trin ct ta xng ........................................... 41

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3.2.4 Kt lun ....................................................................................... 44CHNG 4: KT QU THC NGHIM ................................................................ 45

4.1 Mi trng ci t............................................................................... 454.2 Mt s kt qu th nghim ................................................................. 45

4.2.1 Giao din chng trnh. .............................................................. 454.2.2 Mt s kt qu tm xng khc nhau ca cc phng php....... 464.2.3 Hiu qu ca vic s dng ngng t........................................... 48

KT LUN......................................................................................................................... 50TI LIU THAM KHO ................................................................................................. 51

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MU

Xng c coi nh hnh dng c bn ca mti tng, vi s t cc

im nh c bnv n l cch biu din i tng mt cch c ng. Ta cth ly c cc thng tin v hnh dng nguyn bn ca mt i tng thng

qua xng. V tr, s nh hng, di ca mt on xng c trng cho

on nh . V th m xng c ng dng trong rt nhiu lnh vc nh

ha my tnh, tra cu nh, nhn dng k t, . . . Cc thut ton tm xng

c a ra nhng u gp phi nhng hn ch tng t nhau l c

nhy cm cao i vi nhiu ng bin, nhng bin i nh trn ng binca i tng c th lm thay i ng k xng nhn cnh hng ti

chnh xc ca xng. gii quyt c nhng hn ch v kh khn trn.

n trnh by k thut ct ta xng ca nh bng phng php BPR(Bending

Potential Ratio) lm mn xng v cho ra hnh dng xng ph hp vi

cu trc ca i tng.

n bao gm 4 chng:Chng 1: Tng quan v x l nh

Chng 2: Xng v cc k thut tm xng

Chng 3: K thut ct ta xng ca nh da vo un

Chng 4: Kt qu thc nghim

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DANH MC HNH V

Hnh 1.1. Hnh minh ha cc php ton trn nh nh phn............................... 9Hnh 1.2. Hiu qu ca thao tc nh phn n gin trn mt nh nh............ 10Hnh 1.3. A dn bi B ..................................................................................... 11Hnh 1.4. Dn mt im nh ........................................................................... 12Hnh 1.5. Dn nh s dng phn t cu trc................................................... 12Hnh 1.6. Php co nh phn ............................................................................. 13Hnh 1.7. S dng php ton m.................................................................... 15Hnh 1.8. Php ng........................................................................................ 15Hnh 1.9. Php ng vi su ln ................................................................ 16Hnh 1.10. Cc giai on chnh trong X l nh ............................................ 17Hnh 2.1. Trc trung v.................................................................................... 23Hnh 2.2. Xng Voronoi ri rc nh hng ca cc hm hiu chnh khc

nhau ......................................................................................................... 25Hnh 2.3. Minh ha thut ton trn hai s Voronoi ................................... 27Hnh 2.4. Minh ha thut ton thm mt im bin vo s Voronoi ........ 28Hnh 2.5. Minh ha ct ta xng vi DCE .................................................... 32Hnh 3.1. Minh ha xng ca nh ................................................................. 34Hnh 3.2. nh ngha ca im ghost v BPR................................................ 37Hnh 3.3. Vng ca im ghost....................................................................... 38Hnh 3.4. Mu hnh ch nht vi cng mt nh c thm vo ng bin

ca hnh ................................................................................................... 40Hnh 3.5. Xng chn ca 1 con lc .......................................................... 42Hnh 4.1. Giao din chng trnh ................................................................... 45Hnh 4.2. Xng ca qu to thu c bng cc phng php...................... 46Hnh 4.3. Xng ca con lc thu c bng cc phng php ................. 47Hnh 4.4. Minh ha xng ca i tng trong vic s dng cc ngng khc

nhau, t l gi tr ngng. ......................................................................... 49

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CHNG 1: TNG QUAN V X L NH1.1 Cc khi nim c bn trong x l nh1.1.1 X l nh l g?

Cng nh x l d liu bng ha, x l nh s l mt lnh vc catin hc ng dng. X l d liu bng ha 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 bao gm cc phng php v k thut bin i,

truyn ti hoc m ha cc nh t nhin.

X l nh l lnh vc nghin cu, l qu trnh bin i t mt nh ban

u sang mt nh mi tun th tnh cht v c trng ring ca x l. C

2 mc ch chnh ca x l nh:

Ci thincht lng phc v cho quan st.

Chun b cc iu kin cho vic trch chn cc c trng phc v c ho

vic nhn dng v ra quyt nh.

1.1.2

nh v im nhnh trong thc t l mt nh lin tc v khng gian v v gi tr

sng chng c biu din bng mt hm 2 bin thc hoc phc k hiu l

f(x, y). Trong x, y l cc gi tr ta khng gian v gitr ca f s t l

vi sng ca nh ti im ny.

c th x l nh bng my tnh cn thit phi tin hnh s ha nh .

Trong qu trnh s ha, ngi ta bin i tn hiu lin tc sang tn hiu ri rcthng qua qu trnh ly mu (ri rc ha v khng gian) v lng t ha

thnh phn gi tr m v nguyn tc bng mt thng khng phn bit c

hai im k nhau. Trong qu trnh ny, ngi ta s dng khi nim Picture

element m ta quen gi hay vit tt l Pixel phn t nh.Nh vy, mi nh

l mt tp hp cc Pixel.

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nh s l nh x l bng my tnh thu c t nh lin tc bi qu

trnh s ha, thng c biu din bi mng hai chiu I(n, p): n dng v p

ct.Ngi ta thng k hiu I(x, y) ch mt pixel. Mt pixel c th c

lu tr bng 1, 4, 8, 16 hay 24 bt. Thng c k hiu l I[m, n].

1.1.3 phn gii phn gii (Resolution) l mt ca nh c n nh trn nh s

khi hin th.Nh vy khong cch gia cc im nh c chn sao cho mt

ngi vn thy c s lin tc ca nh . Vic chn ny to nn mt phn

b chnh l phn gii c phn b lin tc theo x, y.

1.1.4 Mc xmMc xm (Gray level): Gi tr I[x, y] biu din cng sng c m

ha ca mi im nh (x, y). Gi tr cn c gi l mc xm (grey level).

I[x, y] c gi tr ri rc v tin x l , ta coi gi tr ca I[x, y] l nguyn:

I[x, y] {0, 1, , L-1} vi L l mc xm ti a dng biu din . nh c

nhiu mc xm gi l nh a cp xm. nh ch c 2 mc xm 0 v 1 gi l

nh nh phn. Cch m ha kinh inthng dng l 16, 32 hay 64 mc. M

ha 256 mc l ph dng nht do l do k thut . V 28 = 256 (0, 1, . . . , 255),

nn vi 256 mc mi pixel s c m ha bi 8bit.

nh nh phn, mi pixel m ha trn 1bit; cn nh 256 mu, mi pixel

m ha trn 8bit.

nhmu l nh t hp t 3 mu c bn: (Red) , lc (Green), lam

(Blue) v thng thu nhn trn cc di bng tn khc nhau . biu din cho

mi im nh mu cn 3byte m t 24bit mu.

nh xm l trng hp c bit ca nh mu. Mi im nh mu c 3

gi tr (Red, Green, Blue), nu 3 gi tr ny bng nhau th ta c nh xm.

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1.2 Cc php ton c bn trn nh nh phn1.2.1 Php ton logic trn nh nh phn

Php ton c bn nht c s dng trong x l nh l: php AND ,

php OR v php ton NOT. Cc tnh chtca chng c nh ngha trongbng di y:

Hnh 1.1 di y minhha nhng thao tc ni trn vi gi tr nh phn

1c mu en, cn gi tr nh phn 0c mu trng.

Hnh 1.1. Hnh minh ha cc php ton trn nh nh phn

1.2.2 Cc php ton hnh thi trn nh nh phnHnh thi (morphology) c ngha l hnh thc v cu trcca mt i

tng, hoc l cch sp xpmi quan h bn trong gia cc phn ca i

tng. Hnh thi c lin quan nhnh dng, v hnh thi s l mt cch

m t hoc phn tch hnh dng ca mti tng s.

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Nhng thao tc hnh thi nh phn c xy dng trn nh ch c 2

mc xm 0 v 1, 0 ng vimu trng, 1 ng vi mu en. Trc ht,

bt u, ta hy xem hnh 1.2a. Tp hp cc im nh en to nn i tng

nh hnh vung v trong hnh 1.2b, i tng nh cng l hnh vung nhngl hnh vung ln hn so vi hnh 1.2a mtim nh v mi pha, ngha l

thay mi ln cn trng ca cc im nh trong hnh 1.2a thnh cc im nh

en. i tng trong hnh 1.2b cng c thao tc tng t, tc l hnh 1.2b

c tng thm mtim nh v mi pha. Thao tc c th coi nh mt

php dn n gin,php dn mt im nh v mi pha. Vic dn c th

c thc hin cho n khi ton b nh c thay bng cc im nh en . Dovy, i tng nh trong hnh 1.2a c th c vit li l{(3, 3) (3, 4) (4, 3)

(4,4)}, vi im nh pha trn bn tri l (0, 0). Tuy nhin, vic vit nh vy

s rt di dng v bt tin nn ta gi n gin i tng nh l A, v cc phn

t trong l cc im nh.

Hnh 1.2. Hiu qu ca thao tc nh phn n gin trn mt nh nh

(a)nh ban u(b)nh dn 1 im nh(c)nh dn 2 im nh so vi nh ban u.

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1.2.2.1Php dn nh phn (Dilation)By gi ta s ch ra thao tc tp hp n gin nhm mc ch nh

ngha php dn nh phn. Php dch A bi im x(hng, ct), c nh ngha

l mt tp:

(A)x ={c | c = a + x, a A} (1.1)

Chng hn nu x c to (1, 2), khi im nh u tin pha trn

bn tri ca As dch n v tr: (3, 3) + (1, 2) = (4, 5). Cc im nh khc

trong A s dch chuyn mt cch tng ng , tc nh c dch sang phi

(ct) im nh v xung pha di (hng) im nh.

By gi ta c th nh ngha php dn (dilation) qua l thuyt tp hp

nh sau:Php dn tp A bi tp B, l tp :

A B = {c | c =a + b, a A, b B} (1.2)

D thy trong ton hc, y l php tng trc tip A v B. A l i

tng nh c thao tc v B c gi l phn t cu trc (vit tt l cu

trc). hiu k hn v iu ny, ta hy coi A l i tng trong hnh 1.2a v

B={(0,0), (0, 1)}

Nhng phn t trong tp C = A B c tnh da trn cng thc (1.1),

c th vit li nh sau:

A B = (A + {(0, 0)}) (A + {(0, 1)}) (1.3)

Hnh 1.3. A dn bi B

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(a)Tp A ban u(b)Tp A cng phn t (0, 0)(c)Tp A cng phn t (0, 1)(d)Hp ca (b) v (c) (kt qu php dn).

Nhn thy rng trong hnh 1.4, c mt s phn t ca i tng ban

u s khng c.

Hnh 1.4. Dn mt im nh

(a)nh A1(b)Phnt cu trcB1(c)A1 c dn bi B1.

T nhng iu trn, gip ta tip cn n mt thao tc dn nh c th

c my tnh ha. Ta hy coi nhng phn t cu trc nh l mt mu v

dch n trn nh. iu ny c th hin kh r trong hnh 1.5.

Hnh 1.5. Dn nh s dng phn t cu trc

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(a)Gc cu trc nh v trn im nh en u tin v nhng imen cu trc c chp sang nh kt qu nhng v tr tng

ng

(b)Qu trnh tng t vi im en tip theo.(c)Qu trnh hnh thnh.

1.2.2.2Php co nh phn (Erotion) Nu nh php dn c th ni l thm im nh vo trong i tng

nh, lm cho i tng nh tr nn ln hn th php co s lm cho i tng

nh tr nn nh hn, t im nh hn. Trong trng hp n gin nht, mt

php co nh phn s tch lp im nh bao quanh i tng nh, chng hn

hnh 1.2b l kt qu ca php co c p dng i vi hnh 1.2c.

Nhn chung,php co mt nh A bi cu trc B c thc nh ngha

nhl tp:

A B = {c |(B)c A} (1.4)

u tin, ta hy xt mt v d n gin sau y:

Hnh 1.6. Php co nh phn

(a)Phn t cu trc c dch chuyn n v tr mt im en trongnh. Trong trng hp ny, cc thnh vin ca cu trc u ph

hp vi nhng im en ca nh cho nn cho kt qu imen.

(b)Phn t cu trc dch chuyn tiim nh tip theo trong nh, vc mt im khng ph hp v kt qu l im trng.

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(c) ln dch chuyn tip theo, cc thnh vin ca cu trcli phhp nn kt qu l imen.

(d)Tng t c kt qu cui cng l im trng.Ta nhn thy mt iu quan trng l:Php co v php dn khng phi

l nhng thao tc ngc nhau. C th trong mt s trng hp ng l php

co s gii hot hiu qu ca php dn .Nhng nhn chung th iu l khng

ng, ta s quan st chng mt cch c th hn sau . Tuy nhin, gia php

co v php dn c mi quan h qua biu thc sau y:

(B A)c = Bc (1.5)Tc l phn b ca php co nh A bi B c coi nh php dn phn

b ca A bi tp i ca B. Nu nh cu trc B l i xng ( y ta quan

nim i xng theo to ) th tp i ca B khng thay i, ngha l = A

Khi : (B A)c = Bc A (1.6)

Hay,phn b ca php co A bi B c coi nh php dn nn ca nh

A (ta quy c trongnh nh phn rng: i tng nh l nhng im en quan

st, nh A l bao gm c im en v nn).

1.2.2.3Php m (Opening)Nu nh ta p dng php co nh i vi mt nh v sau li p dng

tip php dn nh i vi kt qu trc th thao tc c gi l php m

nh, hay vi I l nh, D l Dilation (dn) v E l Erosion (co).

Opening (I) = D(E(I)) (1.7)

Tn ca php tonm nh dng nh phn nh r tc dng ca

n. Tc dng ca n chnh l mnhng khong trng nh gia cc phn

tip xc trong itng nh, lm cho nh dng nh bt gai. Hiu qu ny

d quan st nht khi s dng cu trc n gin . Hnh 1.7 trnh by nh c

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nhng phn ca n tip xc nhau. Sau thao tc m n gin i tng nh

d nhn hn so vi ban u.

Hnh 1.7. Sdng php ton m(a)Mt nh c nhiu vt th c lin kt(b)Cc vt th c cch ly bi php m vi cu trc n gin(c)Mt nh c nhiu(d)nh nhiu sau khi s dng php m, cc im nhiu.

1.2.2.4Php ng (Closing)Tng t php m nh nhng trong php ng nh , thao tc dn nh

c thc hin trc, sau mi n thao tc co nh v cng lm vic trn

cng mt phn t cu trc.

Close (I) = E(D(I)) (1.8)

Hnh 1.8. Php ng

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(a)Kt qu ngs dng cu trc n gin.(b)nh ca mt bng mch c phn ngng v c ccvt t(c)nh tng t sau khi ng nhng nhng nt t c ni

lin.

Hnh 1.9. Php ng vi su ln

(a)T hnh 1.8a, s dng php ng vi su 2(b)Php ng vi su 3(c)Mt vng bn c(d)Vng bn c c phn ngng th hin nhng im bt quy tc

v mt vi l.

(e)Sau khi thc hin php ng vi su 1(f)Sau khi thc hin php ng vi su 2.

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1.3 Cc giai on c bn ca X l nh

Hnh 1.10. Cc giai on chnh trong X l nh

Trc ht l qu trnh thu nhn nh . nh thu nhn qua camera. Thng

nh thu nhn qua camera l tn hiu tng t (loi camera ng kiu CCIR) ,

nhng cng c th l loi tn hiu s ha (loi CCD - Charge Coupled

Device).

nh cng c th thu nhn t v tinh qua cc b cm ng (sensor) , hay

nh, tranh c qut trn scaner. Tip theo l qu trnh s ha (Digitalizer)

bin i tn hiu tng t sang tn hiu ri rc (ly mu) v s ha bng lng

ha, trc khi chuyn sang giai on x l,phn tch hay lu tr li.

Qu trnh phn tch nh thc cht bao gm nhiu cng on nh. Trc

ht l cng vic tng cng nh (Image Enhancement) nng cao cht lng

nh. Do nhng nguyn nhn khc nhau: c th do cht lng thit b thu nhn

nh, do ngun sng hay do nhiu, nh c th b suy bin. Do vy cn phi

tng cng v khi phc (Image Restoration) li nh lm ni bt mt s

c tnh chnh ca nh, hay lm cho nh gn ging nht vi trng thi gc

trng thi trc khi nh b bin dng. Giai on tip theol pht hin cc c

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tnh nh bin (Edge Detection), phn vng nh (Image Segmentation), trch

chn cc c tnh (Feature Extraction), v. v

Cui cng, ty theo mc ch ca ng dng, s l giai on nhn dng,

phn lp hay cc quyt nh khc.

1.4 Mt s ng dng c bn ca x l nhK thut x l nh trc y ch yu c sdng nng cao cht

lng hnh nh, chnh xc hn l to cm gic v sgia tng cht lng nh

quang hctrong mt ngi quan st. Thi gian gny,phm vi ng dng x

l nh m rng khng ngng, c th ni hinkhng c lnh vc khoa hc no

khng s dng cc thnh tu ca cngnghx l nhs.

Trong y hc cc thut tonx l nh cho php bin i hnh nh c

to ra t ngunbc x X-ray hay ngun bc x siu m thnh hnh nh quang

hc trn b mt film x-quang hoc trc tip trn b mt mn hnh hin th.

Hnh nh cc c quan chc nng ca con ngi sau c th c x ltip

nng cao tng phn, lc, tch cc thnh phn cn thit (chp ctlp)

hoc to ra hnh nh trong khng gian ba chiu (siu m 3 chiu).

Trong lnh vc a cht, hnh nh nhn c t v tinh c th

cphn tch xc nh cu trc b mt tri t. K thut lm ni ng

bin (image enhancement) v khi phc hnh nh (image restoration) cho

php nng cao cht lng nh v tinh v to ra cc bn a hnh 3-D vi

chnh xc cao.

Trong ngnh kh tng hc, nh nhn c t h thng v tinh theo di

thi tit cng cx l, nng cao cht lng v ghp hnh to ra nh b

mt tri t trn mt vng rng ln, qua c th thc hin vic d bo thi

tit mt cch chnh xc hn. Da trn cc kt qu phn tch nh v tinh ti cc

khu vc ng dn c cn c th d on qu trnh tng trng dn s, tc

nhim mi trng cng nh cc yu t nh hng ti mi trng sinh thi.

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X l nh c s dng nhiu trong cc h thng qun l chtlng v

s lnghng ha trong cc dy truyn t ng, v d nh h thng phn tch

nh pht hin bt khbn vt th c bng nha, pht hin cc linh kin

khng t tiu chun (b bin dng) trong qu trnh sn xut hoc h thngm sn phm thng qua hnh nh nhn c t camera quan st.

X l nh cn c s dng rng ri trong lnh vc hnh s v cc h

thng bo mthoc kim sot truy cp: qu trnh x l nh vi mc ch nhn

dng vn tay hay khun mtcho php pht hin nhanh cc i tng nghi vn

cng nh nng cao hiu qu h thngbomt c nhn cng nh kim sot ra

vo. Ngoi ra, c th k n cc ng dng quan trng khc ca k thut x l

nh tnh cng nh nh ng trong i sng nh t ng nhn dng, nhn dng

mc tiu qun s, my nhn cng nghip trong cc h thng iu khin t

ng, nn nh tnh, nh ng lu v truyn trong mng vin thng v. v.

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CHNG 2: XNG V CC THUT TON TM XNG2.1 Khi nim xng

Xng c coi nh hnh dng c bn ca mt i tng, vi s t cc

im nh c bn. Ta c th khi phccc thng tin v hnh dng nguyn bn

ca mt i tng thng qua xng. C mt s nh ngha ton hc khc

nhau v xng trong cc ti liu k thut v c nhiu thut ton khc nhau

cho tnh ton chng. Trong cc ti liuk thut, cc khi nimvxng v

trc trung v thngc s dngthay th cho nhau mt s tc gi, trong

khi mt s tc gi khc li xem chng ch lin quan vi nhau m khng ging

nhau. Tng t, cc khi nim vtm xng v lm mnhcng c coi lnh nhau vimt stc gi v khc nhau i vi mt s tc gi khc.

Xng c s dng nhiu trong ng dng lnh vc my tnh, phn

tch hnh nh, v x l hnh nhs,bao gm nhn dng k tquang hc, nhn

dng vn tay, kim trath gic, nhn dng mu, nn nhnh phn.

2.2 Cc hng tip cn trong vic tm xngCc k thut tm xng lun l ch nghin cu trong x l nh . Do

tnh phc tp ca n, mc d c nhng n lc cho vic pht trin cc thut

ton tm xng nhng cc phng php a ra u b mt mt thng tin. C

th chia thnh hai loi tm thut ton tm xng c bn:

Cc thut ton tm xng da trn lm mnh

Cc thut ton tm xng khng da trn lm mnh

2.2.1 Phng php tm xng da trn lm mnh2.2.1.1S lc v thut ton lm mnh

Nghin cu v lm mnh ta cn ch cc vn sau:

Khng phi tt c cc i tng u c th lm mnh . Lm mnh ch

hu dng vi cc i tng l ng, ngha l chng ch thng hoc

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cong v n khng c tc dng vi cc i tng c hnh dng ng

trong mt vng.

Lm mnh thng thng l bc chun b cho cc bc tip theo x l

mt i tng ca nh. Cc bc tip theo lm vic trn cc thuc tnh

cn thit ca xng.

Thut ton lm mnh nh s nh phn l mt trong cc thut ton quan

trng trong x l nh v nhn dng. Xng chanhng thng tin bt bin v

cu trc ca nh, gip cho qu trnh nhn dng hoc vecto ha sau ny.

Thut ton lm mnh l qu trnh lp duyt v kim tra tt c cc imthuc i tng. Trong mi ln lp tt c cc im i tng s c kim

tra: nu nh chng tha mn iu kin xa no ty thuc vo mi thut

ton th n s b xa i. Qu trnh c lp li cho n khi khng cn im bin

no c xa. i tng c bc dn lp bin cho n khi no b thu mnh

li ch cn cc im bin.

2.2.1.2Tm xng da trn lm mnh

Thut ton lm mnh song song l thut ton m trong cc im

c x l theo phng php song song , tc l c x l cng mt lc. Gi

tr ca mi im sau mtln lp ch ph thuc vo gi tr ca cc lng ging

bn cnh (thng l 8 lng ging) m gi tr ca cc im ny c xc

nh trong mt ln lp trc . Trong my c nhiu b vi x l mi vi x l

sx l mt vng ca i tng, n c quyn c t cc im vng khc

nhau nhng ch c ghi trn vng ca n x l.

Trong thut ton lm mnh tun t cc im thuc i tng s c

kim tra theo mt th t no (chng hn cc im c xt t tri qua

phi, t trn xung di). Gi tr ca imsau mi ln lp khng nhng ph

thuc vo gi tr ca cc lng ging bn cnh m cn ph thuc vo cc im

c xt trc trong chnh ln lp ang xt.

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Cht lng ca thut ton lm mnh c nh gi theo cc tiu chun

c lit k di y nhng khng nht thit phi tha mn ng thi tt c

cc tiu chun:

Bo ton tnh lin thng ca i tng v phn b ca i tng

S tng hp gia xng v cu trc ca nh i tng

Bo ton cc thnh phn lin thng

Bo ton cc im ct

Xng ch gm cc im bin, cng mnh cng tt

Bn vng i vi nhiu

Xng cho php khi phc nh ban u ca i tng

Xng thu c chnh gia ng nt ca i tng c lm mnh

Xng nhn c bt bin vi php quay

2.2.2 Tm xng khng da trn lm mnh tch c xng ca i tng c th s dng ng bin ca i

tng. Vi bt c mtim p no trn i tng, u c th bao n bi

mtng bin.Nu nh c nhiu hn mt im bin c khong cch ngn

nht th p nm trn trc trung v. Tt c cc im nhvy lp thnh trc trung

v ca i tng. iu phi c thc hin vi phn gii cao, hoc

khong cch Euclide l khng bng nhau, v nh th cc im nh xng s

mt i. Ta d dng thu c mt xp x ca trc trung v trn mt li ngin sau 2 bc:

Bc th nht, tnh khong cch t mi im nh ca i tng n

im bin gn nht.Nh vy cn phi tnh ton khong cch ti tt c

cc im bin ca nh.

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Bc th hai, khong cch ca nh c tnh ton v cc im nh

c gi tr ln nht c xem l nm trn xng ca i tng.

Hnh 2.1. Trc trung v

Hu ht cc nh nghin cu u cho rng thay i trc trung v thng

khng mang li mt xng chun, v thi gian tnh ton qu di, tuy nhin n

l mu c bn ca phn ln cc phng php lm mnh.

Phng php thay i trc trung v c coi l mt phng php lm

mnh khng lp, ngoi ra cn c mt vi thut ton duyt cc im bin 2 bn

mu, tnh im trung tm cc ng ni gia cc im bin v xng thu

c l tp hp cc im trung tm (line following) hoc cc phng thc

s dng chui Fourier(Fourier transform) cng c coi l lm mnh khng

lp.

2.2.2.1Khi qut lc VoronoiLc Voronoi l mt cng c hiu qu trong hnh hc tnh ton. Cho

hai im Pi, Pjl 2 phn t ca tp gm n im trong mt phng . Tp cc

im trong mt phng gnhn l na mt phng H (Pi, Pj) cha im v b

gii hn bi ng trung trc ca on thng . Do , tp cc im gn hn

bt k im no c th thu c bng cch giao n-1 cc na mt phng H

(Pi, Pj)

V ( ) = H ( ) i j (i= 1, , n) (2.1)

nh ngha 2.1 [a gic/ S Voronoi]

S Voronoi ca l tp hp tt c cc V ( )

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Vor () = V ( ) (l mt a gic) (2.2)

nh ngha 2.2 [a gic Voronoi tng qut]

Cho tp cc im , a gic Voronoi ca tp con U ca c nhnghanh sau:

V (U)= {P | v U, w \ U : d (P, w)}= V ( ) U (2.3)

2.2.2.2Trc trung v Voronoi ri rcnh ngha 2.3 [Bn khong cch Distance Map]

Cho i tng S, i vi mi (x, y) S, ta tnh gi tr khong cchmap(x, y) vi hm khong cch d (. , . ) nh sau:

(x, y) S: map (x, y)= min d[ (x, y ), ( )] (2.4)

Trong ( ) B (S)tp cc im bin ca S

Tp tt c cc map (x, y), k hiu l DM (S), c gi bn khong

cch ca S.

Ch : Nu hm khong cch d (. , . ) l khong cch Euclide, th

phng trnh (2.4) chnh l khong cch ngn nht t mtim bn trong i

tng ti bin. Do , bn khong cch c gi l bn khong cch

Euclide EDM(S) ca S. nh ngha trn c dng cho c hnh ri rc ln

lin tc.

nh ngha 2.4 [ Tp cc im bin sinh]Cho map (x, y) l khong cch ngn nht t (x, y) n bin (theo nh

ngha 2.3). Ta nh ngha :

Khi tp cc im bin sinh ^B (S) c nh ngha bi:

^B (S)= (x, y), (x, y) S (2.5)

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Do S c th cha cc ng bin ri nhau, nn ^B (S) bao gm nhiu

tp con, mi tp m t mt ng bin phn bit:

^B (S) = { } (2.6)

nh ngha 2.5 [Trc trung v Voronoi ri rc (DVMA)]

Trc trung v Voronoi ri rc c nh ngha l kt qu ca s

Voronoi bc nht ri rc catp cc im bin sinh giao vi hnh sinh S:

DVMA (^B (S))=Vor (^B (S)) S (2.7)

2.2.2.3Xng Voronoi ri rcnh ngha 2.6 [ Xng Voronoiri rac Discrete Voronoi Skeleton]

Xng Voronoi ri rc theo ngng T, k hiu l SkeDVMA (^B (S),T)

(hoc Ske (^B (S), T)) l mt tp con ca trc trung v Voronoi:

SkeDVMA (^B (S), T) = { (x, y)| (x, y) DVMA (^B (S)), (x, y) > T }

(2.8)

: l hm hiu chnhD thy ngng T cng ln th s lng im tham gia trong xng

Voronoi cng t (Hnh 2.2).

Hnh 2.2. Xng Voronoi ri rc nh hng ca cc hm hiu chnh khcnhau

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(a)nh nh phn.(b)S Voronoi(c)Hiu chnh bi hm Potential, T= 9.0(d)Hiu chnh bi hm Potential, T=18.0

2.2.2.4Thut ton tm xngThut ton tm xng da trn mt s tng sau:

Tng trng: Vic tnh ton s Voronoi c bt u t mt im

sinh trong mt phng. Sau im sinh th hai c thm vo v qu trnh

tnh ton tip tc vi a gic Voronoi tm c vi im va c thm

vo . C nh th, qu trnh tnh ton s Voronoi c thc hin cho n

khi khng cn im sinh no c thm vo. Nhcim ca chin lc ny

l mi khi im mi c thm vo, n c th gy ra s phn vng ton b

cc a gic Voronoi c tnh.

Chia tr: Tp cc im bin u tin c chia thnh hai tp im c

kch c bng nhau. Sau thut ton tnh ton s Voronoi cho c hai tp

con im bin . Cui cng, ngi ta thc hin vic ghp c hai s

Voronoi trn thu ht c kt qu mong mun. Tuy nhin, vic chia tp

cc im bin thnh hai phn khng phi c thc hin mt ln , m c

lp li nhiuln cho n khi vic tnh ton s Voronoi tr nn n gin. V

th, vic tnh s Voronoi tr thnh vn lm th no trn hai s

Voronoi li vi nhau.

Thut ton s trnh by y l s kt hp ca 2 tng trn . Tuy

nhin, n s mang li nhiu dng dp ca thut ton chia tr

Hnh 2.3 minh ha tng ca thut ton ny. Mi mt im bin

c chia thnh 2 phn (bn tri: 1-6,bn phi: 7-11) bi ng gp khc ,

v hai s Voronoi tng ng Vor ( ) v Vor( ). thu c s

Voronoi Vor( ), ta thc hin vic trn hai s trn v xc nh li

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mt s a gic s b sa i do nh hng ca cc im bn cnh thuc s

kia. Mi phn t ca s l mt b phn ca ng trung trc ni hai im

m mt im thuc Vor ( ) v mt thuc Vor ( ). Trc khi xy dng , ta

tm ra phn t u v cui ca n . Nhn vo hnh 2.3, ta nhn thy rng cnh

l cc tia. D nhn thy rng vic tm cc cnh u v cui ca tr

thnh vic tm cnh vo .

Hnh 2.3. Minh ha thut ton trn hai s Voronoi

Sau khi tm c , cc im cui ca c s dng xy

dng phn t u tin trong hnh bn). Sau thut ton tm im giao

ca vi Vor ( ) v Vor ( ). Trong v d trn, u tin giao vi V(3). K

t y, cc im nm trn phn ko di s gn im 6 hn im 3. Do ,

phn t tip theo ca s thuc vo ng trung trc ca im 6 v

im 7. Sau im giao tip theo ca s thuc vo Vor ( ); s i vo

V(9) v s c thay th bi . Qu trnh ny s kt thc khi gp phn

t cui .

Trn y ch l minh ha cho thut ton trn hai s Voronoi trong

chin lc chia tr. Tuy nhin, trong thut ton s trnh by y th s

thc hin c khc mt cht. Tp ccim nh khng phi c a ngay vo

t u m s c qut vo tng dng mt. Gi s ti bc th i, ta thu

c mt s Voronoi gm i-1 hng cc im sinh Vor ( ). Tip theo, ta

qut ly mt hng cc im nh t tp cc im bin cn li. Thc hin

vic tnh ton s Voronoi Vor ( ) cho hng ny, sau trn Vor ( )

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vi Vor ( ). Kt qu ta s c mt s mi, v li thc hin vic qut

hng cc im sinh cn li v. v. . Qu trnh ny s kt thc khi khng cn

im bin no thm vo s Voronoi. Do Vor ( ) s c dng rng lc

(nu c k im th Vor ( ) s gm k-1 ng thng ng), nn vic trn

Vor ( ) vi Vor ( ) c phn n gin hn.

Hnh 2.4. Minh ha thut ton thm mt im bin vo s Voronoi

Gii thut trn c th c m t bng ngn ng ta Pascal nh sau:

Procedure VORONOI

(*Si: Tp cc im cua i dng qut u tin, 0

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While (i < imax) do

Begin

Increment i; GetScanLine Li;

Vor (Li) := cc ng trung trc sinh bi cc im sinh thuc Li

Vor (Si) := VoroLink (Vor (Si-1), Vor (Li));

End

End.

Gi s xt trn h trc ta thc. nh vo c qut t di ln. Ta y (bin i) tng ng vi tng dng qutc tng dn theo tng dng.

Trong th tc trn, hm quan trng nht l hm VoroLink, hm ny thc hin

vic trn s Voronoi ca dng d c qut trc vi s

Voronoi ca dng hin ti th i. Trong vng lp trn, hm VoroPreScan l

mtbin c th ca hm VoroLink, c nhim v khi to s Voronoi v

thot khi vng lp ngay khi n thnh lp c s Voronoi cha t nht

mt nh. Hm VoroLink thc hin vic trn hai s Voronoi Vor (Si-1) v

Vor (Li) vi nhau thnh Vor (Si).

2.3 Ct ta xngca nh2.3.1 Khi nim ct ta xng

Ct ta xng ca nh l loi b i mt t nhiu hoc vi s thay i ca

ng bin dn n to ra nhng nhnh tha ci m c th lm nh hng

nghim trng ti hnh dng c bn ca xng.

2.3.2 K thut ct ta xng vi DCE2.3.2.1 tng chnh ca phng php

Nhm tc gi Xiang Baia, Login Jan Latec ki, Wen-Yu Liu xut

mt phng php loi b hon ton nhng im li ra m khng loi b

nhngim bin, v vy khng loi b nhng im xng chnh.Nhng im

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sai hoc tha ra hon ton b loi b trong khi nhng nhnh xng chnh

khng b ngn i. Phng php ny c th ct ta xng da trn vic phn

chia ng bin thnh nhng on cong. tng chnh ca phng php l

di chuyn tt c cc im xng ca im tng trng nm trn cng onng bin. T t ra cu hi l lm th no tm ra cc on phn

chia ng bin tt nht.Nhm tc gi tm ra c s phn chia nh vy

nh qu trnh DCE.

Phng php ct ta xng c th c p dng vi bt k b xng

u vo no. Miim xng l trung tm ca vng trn ln nht v nhng

im ng bin tip tuyn vi ng trn u c a ra. Ct ta xng

khng phi thc hin sau khi tnh c b xng m c thc hin ng

thi vi qu trnh tng trngxng.

2.3.2.2Ri rc ha ng congDCE c gii thiu bi cc nhm tc gi Xiang Bai v cc cng s.

ng bin ca i tng trong nh s b thay i bi nhiu v cc li phn

on. DCE loi b nhng thay i trong khi vn m bo c hnh dng

ban u ca i tng bi n gin ha hnh dng. Bt k ng cong ca

nh s c th c coi l mt a gic m khng b mt thng tin, nhng phi

c s nh ln nghin cu s pht trin ca hnh dng. tng c bn ca

s pht trin xut l cc a gic u n gin hn.

Trc tin tc gi Xiang Bai a ra php o lin quan K:

(2.9)

Trong s1, s2 l nhng cnh ca a gic lin quan ti nh v; (s1, s2)

l gc quay ti nh chung ca on s1, s2; l l tng di ca ng cong a

gic C.

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u vo l ng bin a gic P vi n nh , DCE to ra mt chui cc

a gic n gin vi K l nh nht.

Tc gi cn ch ra rng mt tnh cht quan trng ca DCE l phn chia

trnh t vi a gic u vo P. {v1, . . . . , vn} l nh ca P, {u1, . . . . , um}

{v1, . . . . , vn} l nh li ca Pn-k sao cho m n-k.

Nhn thy DCE v phn chia trnh t c th c nh ngha cho mt

tp hu hn ca ng cong a gic. Trong mi bc DCE mt vectn

c loi b t mt a gic m php o lin quan l nh nht. Phng php

ct ta xut c thc p dng cho mt phng D, vi ng bin D bao

gm s cc a gic ng n gin.

DCE c th loi b hiu qu nhiu v tng phn khng quan trng ca

nh, nhng vn cn phi c mt gii hn T dng ng cch ph hp vi

nhng ng dng c th. Ni cch khc tm kim k a gic n gin Pn-k

miu t chi tit nhng ng bin u vo.

2.3.2.3Phng php ct ta xng vi DCECho mt b xng S(D) ca mt mt phng D v a ra mt DCE a

gic n gin Pk, th hin ct ta xng bng cch di chuyn tt c nhng

im s S(D), nh vy to ra nhng im tng trng tan(s) ca s cha trong

cng on DCE m. Mi im ct ta s l kt qu t phn ng bin cc b

vi s phn chia DCE, v do , s c th coi nh l im xng khng quan

trng v c th loi b. Qu trnh lm n gin ng bin vi DCE hon

thnh ct ta nhnh ca xng. c bit, loi b mt nh li v t Pn-k ti

Pn-(k+1)bi DCE, tc l hon thnh loi b nhng nhnh xng m kt thc ti

v. Trong hnh 2.5 minh ha vic s dng DCE thu c mt hnh a gic vi

7 nh v xng ca i tng c ct ta da trn a gic . Ch c 5

nhnh xng kt thc ti 5 nh li ca a gic n gin.

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Hnh 2.5. Minh ha ct ta xng vi DCE

Tc gi thc hin phn tch on DCE da trn cc nh li bi n

gin ha DCE. Khi mt nh li tr thnh mt nh lm trong qu trnh phttrin ca DCE, th nhng nhnh xng kt thc ti nh b loi b . Cch

tip cn ny cho php loi b nhng nhnh nh trong qu trnh pht trin

DCE.

Mt thuc tnh quan trngca DCE l gy ra phn chia ng bin v

mi phn chia lm gim cc nh ca ng bin a gic, kt qu c mt

nhnh xng kt thc ti mi im phn chia . Theo cc kt qu thc nghimm tc gi nghin cu, trong mt bc tin ha DCE nu nh uica a

gic b xa (tc l ui Pn-kPn- (k+1)) hoc tr thnh lm (do vic xa i mt

trong nhng nh bn cnh ca n) th cung [u i-1, ui+1] thay th cung [ui-1, ui],

[ui, ui+1]. Khi ct ta xng s loi b ton b nhnh xng kt thc ti ui.

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CHNG 3: K THUT CT TA XNGDA VO UN

Chng ny trnh by k thut ct ta xng c xut bi tc gi

Wei Shena, Xiang Baia, Rong Hu, Hongyuan Wang, Login Jan Latec ki [4].

3.1 Gii thiuXng cn c gi l trc trung v, ln u tin cxc nhbi tc

gi Blum[6], l cch m t hnh dng rt hu ch , v n cha cc c trng

hnh dng ca i tng gc.Nh vy, xng l mt dng cn thit biu

din v phn tch hnh dng trong nhiu lnh vc ng dng nh h thng tra

cu nh da trn ni dung, h thng nhn dng k t. . .Nhng thp k qua,c rt nhiu phng php trch chn xng c xut.

Cc thut ton ton tm xng c th c phn thnh 5 loi:

1. Thut ton lm mnh2. Thut ton min ri rc da trn lc Voronoi3. Thut ton da trn khong cch bin i4.

Thut ton co ng bin ca i tng c lp i lp li5. Da trn php ton hnh thi hcHu ht cc phng php ny c mt hn chchung l c nhy

cm cao i vi nhiu ng bin: nhng bin i nh trn ng bin ca

i tng c th lm thay i ng k xng nhn c. Do cc phng php

ny thng to ra cc nhnh xng gi, nh hng ti vic nhn dng i

tng da trn cu trc xng. V d nh xng trong hnh 3.1(a) c nhiunhnh xng tha c pht sinh ra bi nhiu ng bin.

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(a) (b)

Hnh 3.1. Minh ha xng ca nh

Bxng (a) c nhiu nhnh tha, loi bchng phng php ct

ta xng c p dng. Hnh (b) minh ha kt qu ct ta xng.

Nhiu phng php ca cc tc gi c xut pht trin ct ta

xng. Mt trong scc phng php l cn lm mn ng bin trc

khi tnh ton cc im xng, nhm mc ch loi b nhiu ng bin khng

mong mun. Tuy nhin, lm mn ng bin c thlm thay i vtr ng

bin v do v tr ca xng c th b dch chuyn, l kh khn trong

vic phn bit nhiu t cc thng tin hnh dng tn s thp trn ng bao.

Mt skhc gn oc nghacho cc im xng hoc nhnh xng, sau

nhng im xng hoc nhnh xng sc ct ta khi gi tr ngha

nhhn gi trngng. Mt vi phng php quan trng da trn o

c xut: Tc giOgniewicz v Kubler trnh by mt vi o da

trn chiu di nh chiu di cung gia hai im v chiu di on ng bao

ngn nht gia hai im. Tc gi Shaked v Bruckstein tng hp nhiu

phng php, v h ngh chn dy bo mn cc i nh l l o.

Tc gi Couprie v Zrour cng xut o c gi l gc phn gic, l

gc gia ng kt ni cc im xng vi cc im c to ra n. Nhng

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o ca cc phng php c cc tc gi xut u c hn chtng t

nhau:

Th nht, l mt snhnh xng tha khng c loi b hon ton,

nh hng ti qu trnh i snh hnh dng da trn cu trc xng.

Th hai, kt qu ca vic ct ta l khng th hin c cc chi tit nh.

Th ba, i khi kt qu ca vic ct ta tri vi trc gic ca con ngi.

khc phc cc hn ch nu trn ca cc phng php ct ta xng

hin ti nn nhm tc gi Wei Shena, Xiang Baia, Rong Hu, Hongyuan

Wang, Login Jan Latec ki xutmt phng php ct ta xng da trn o nghagi l t l un (BPRBending Potential Ratio). Vic a ra

quyt nh v vic mt nhnh xng nn c ct ta hay khng l da vo

ng cnh ca on ng bin tng ng vi nhnh xng . Phng php

BPR ch ra s ng gp ca on ng bin vi nh gi trn hnh

dng ton cc, ch khng ch nh gi trn hnh dng cc b nh phng

php ct ta xng khc. Ni chung n ph thuc vo vtr c th trong tonb ng bao (v d, mt on c th c coi l khng ngha trn mt v

tr ny nhng n c th tr thnh ngha trong mtv tr khc). BPR l o

ngha khng ging nh cc o ngha khc ch cha thng tin hnh dng

cc b ca nhng ng bao trong ng cnh c th, n m t kh nng un

ca mt on ng bao. BPR c th nh gi c hai thng tin hnh dng cc

b vton cc. V vy theo tc gi Wei Shena [4] th xngkhng nhy cm

vi bin dng ng bin cc b.

3.2 Phng php ct ta xng theo BPR(Bending Potential Ratio)3.2.1 nh ngha c bn

n gin tc gi Wei Shena gi thitrng ng bin ca mt

i tng 2D l mt ng cong ng C trong R2. Tp F c bao bc bn

trong ng bao C biu din vng ca i tng . Tt c cc nh ngha v

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pht biu sau s c p dng cho mt tp phng F c ngbao bao gm

mt s hu hn ng cong khp kn , ngha l F c th c mt s hu hn cc

l, v nu mt im xng c ngun gc t hai ng cong khc nhau n s

khng bao gi b loi b khi xng . Do , bt k mt im xng noc ly ra bt u t mt ng cong duy nht , n sb dch chuyn v do

thut ton ch tp trung gii quyt vo trng hp ca mt ng cong

n C.

Cho mt im p, hm khong cch k c nh ngha nh sau:

(3.1)

Trong , d (, ) l o khong cch Euclide

i vi mt im , r (p) biu th mt tp hp cc im bin gn p

nht. Khi ,

d (p, r (p)) = k (p) (3.2)

nh ngha 3.1. Tp cc im sinh R (p) nh l mt tp hp ccimnm trn ng baoC m gn vi im p nht hoc l 8- lng ging ca p

nm pha trong ng bao, tc l

R (p) = R8 (p) r (p) = {r (q) | q N8 (p)} r (p), (3.3)

Trong N8 (p) l 8 lng ging ca im p trong ng bao

v R8 (p) = {r (q)| q N8 (p)}.

Do vy, nu p l mt im ca xng, n (R (p)) 2 (3.4)

Trong hm n () biu th s ca cc phn t trong tp hp.

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3.2.2 T l un (BPRBending Potential Ratio)3.2.2.1nh ngha ca t l un

Xt hai im q1, q2 R (p) (n (R (p)) 2) th hin trong hnh 3.2, cc

on ng bao ngt nht gia q1 v q2c k hiu l C (q1, q2). Khi onng bao l mt tp hp cc im nh, chng ta o chiu di ca on

ng bao bng tng khong cch Euclide gia mi cp nh im ln cn .

Khong cch gia hai im lng ging di chuyn theo chiu ngang/dc l 1 v

theo ng cho l . Nu q1, v q2 chia ng bao thnh 2 on c chiu

di bng nhau, mt trong 2 on c k hiu l C (q1, q2).

Hnh 3.2. nh ngha caim ghost v BPR

nh ngha 3.2. Cho mt on ng cong C (q1, q2), gi l (q1, q2) l

chiu di ca cung C (q1, q2). Chng ta xy dng mt hnh tamgic cn vi c

s q1q2v vi nh g R2

d (g, q1)= d (g, q2) = l (q1, q2). (3.5)

Thc t c hai im khc nhau tha mn cng thc (3.5), n c nh

du vi g1 v g2 th hin trong hnh 3.3c. Tc gi Wei Shena nh ngha im

g l im cht ca C (q1, q2).

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Thng thng, im cht g khng nm trn ng bao, tr khi cc

on ng bao l mt on caa gic i xng nh trong hnh 3.3b.Nu g

nm trn ng bao nh hnh 3.3a, th l (g, q1)> d (g, q1), l (g, q2)>d (g, q2),

l(q1, q2 ) >d (g, q1)+d (g, q2), v g s khng tha mn cng thc (3.5).

Hnh 3.3. Vng ca im ghost

nh ngha 3.3. Cho im p nm trong ng congC vi n(R(p)) ,

v gi q1, q2 l hai im thuc R (p). Gi g l im chtca on ng bao

C (q1, q2). T hnh 3.2 cho hg l chiu cao ca tam gic q1pq2. T l un (BPR)(q1, p, q2) c nh ngha nh sau:

. (3.6)

3.2.2.2Xc nh t l un BPRT hnh 3.2, khi tam gic q1pq2l mt tam gic cn, th ta c

hg = (3.7)

D thy hg cung cp thng tin hnh dng cc b ca on ng bao

C(q1, q2), vi chiu di ca cung l (q1, q2), thuc tnh ca on ng bao. Vi

mt khong cch d(q1, q2) c nh, nu l (q1, q2) ln th c kh nng un cong

ca C(q1, q2) l ln. Do , hgphn nh t l un caon ng bao C(q1,q2).

Mt on ng bao cng vi im un cong cc i v c mt kt ni gia

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cong cc i ca ng bao v xng to ramt nhnh xng. Do , hg

c xem xt nh l mt php o nh gi tm quan trng ca on ng

bao.

Theo cng thc lng gic, chng ta c

(3.8)

T ta suy ra

(3.9)

Nu p l mt im xng, l xp x vi, ; v vy c

c

(3.10)

Cng thc (3.10) ch ra rng hp cha khng ch l thng tin ca gc

phn gic m cn l chiu rng ca i tng. D mt on ng bao l

ngha hay khngc xc nh khng ch bi cc thng tin ca chnh n , vd: chiu di ca cung, nhng cng c th trong ng cnh l ni m

c xc nh v tr ca n. onng bao tng tc th nhiu hn, c

th c coi l khng nghanu n nm trong mt phn rng ca hnh dng,

trong khi nu n nm trn mt phn nh ca hnh dng th n c th c coi

nh l mt c trng ring. Do t l hg v hp, t l un tch hp c hai

thng tin hnh dngcc b v ton cc.N c th c s dng xc nhxem mt ng cong to ra mt nhnh xng. c bit, hp lbng 0 nu cc

tip tuyn trn q1 v q2 l song song. Trong trng hp ny gi tr BPR l v

hn, n chra rng p l mt im xng. Hnh 3.4 ch ra hiu qu ca phng

php BPR trong ct ta xng. Cc nh ca hnh 3.4 l tng t nhau, tuy

nhin, chng c hnh dng khc nhau gp phn cho i tng. nh ca

hnh 3.4a c nhiu kh nng l mt chi tit khng ng k trn ng bin, v

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v vy nhnh c ngun gc t n nn c ct ta , trong khi nh vi cng

kch thc nh hnh 3.4 b c nhiu kh nng l c trng hnh dng quan

trng, v nh vy c thto ra mt nhnh xng. nh trong hnh 3.4c l gn

gc bn phi hnso vi nh trong hnh 3.4a, v do n a ra mt nhnhxng, v n thay th gc bn phi nh c trng ca hnh dng .Nh ch

ra trong hnh 3.4, xng thu c biphng php ca tc gi Wei Shena c

th phn bit gia nhnh khng ng k nh trong hnh 3.4a v cc nhnh

quan trngnh trong hnh 3.4 (b, c).

Hnh 3.4. Mu hnh ch nht vi cng mt nh c thm vo ng binca hnh

Hng (1). Xng thu c bng phng php xut.

Hng (2). Xng ca cng mt hnh c ct ta bng o nghaca chiu di on ng bin ngn nht

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3.2.2.3Mi quan h ca BPR vi cc o ngha khcBng cng thc (3.7), (3.8) v (3.11) chng ta c c

(3.11)

Cng thc (3.11) th hin s kt ni gia BPR v o ngha:

khong cch ca dy cung , chiu di ca on ng bin ngn

nht l v gc phn gic . S tch hp ca c 3 o ny l mt

trong nhngng gp chnh caphng phpc xut.N l hp l

tch hp ba o vi nhau theo cch ny, nu gc lnhn, c nhiu

kh nng p l mt im xng, v chc nng ca tip tuyn ny cng cng c

cho phng php ny, c bit khi gc = (gi tr ln nht), gi tr

BPR l v hn. Hn na t l ca l c tnh cht cc ba

phng.

3.2.3 xut cho pht trin ct ta xngTc gi Wei Shena xut mt tng cho pht trin xng quy

bng cch thm im ph hp vimt tiu ch da trn BPR.

3.2.3.1Tiu ch ct ta nhnh xng giMt tiu ch c gii thiu trong [4] cs dng xc nh xem

nicc im cho trc c l mt im ca xng . l l do ti sao tc gi

gi chng l im sinh. Tc gi Wei Shena xem xt cc tiu ch y

trong vng nh: i vi mt im p cho trc bn trong ng bao V vi

n(R (p)) 2, nu c q1 r(p) v q2 R8 tha mn:

(p, q1) - (p, q2) max (abs (x1x2), abs (y1y2)), (3.12)

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im p c coi l mt im xng, ni m (x1y1), v (x2y2) l

ta tng ng ca q1, q2. Da trn cng thc (3.12) th thu c xng,

nhng xng thu c cha qu nhiu nhnh gi, v d cc nhnh c mu

c th hin trong hnh 3.5a. Lu rng cc nhnh xng gi c nhdu cng vi mu sc c to ra t cc on ng bao khng ngha ca

mu sc ging nhau. o ngha BPR c xut gii quyt vn

ny.

Hnh 3.5. Xng chn ca 1 con lc

a) Xng c ct ta da trn phng php tip cn trong.b) Xng c to ra bi tiu chun 1 c mt s im cn thit ,

nh l mt phn mu xanh l cy.

c) Xng c ct ta bng phng php lm mnh c xut.Tiu ch 1: im p thuc nhnh xng ct ta nu c tn ti q 1 r(p)

v q2 R8(p) tha mn

(3.13)

Trong t l mt ngng cho trc, v v l ta

tng ng ca v .

R rng, tiu ch 1 l mt iu kin cn thit xc nh mt im hnh

l im xng hay khng, v da trn o nghac xut, ch cn cc

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cp ca cc im ng bao kt ni vi on ng bao ngha l c s

dng xc nh xem cc im tng ng l cc im xng . V vy cc

nhnh xng gi khng c sinh ra bng vic thay i tiu chun ny.

3.2.3.2Pht trin xng ct taDa trn tiu ch 1, tc gi Wei Shena cung cp cc tng cho pht

trin ct ta xng kt ni. i vi mt i tng 2D, ng bin F c bao

bc bn trong ng bao Cbiu din vng ca i tng, v Sk l xng ca

i tng.

Thut ton pht trin xng ct ta:

Procedure SkeletonGrow (Input F, Output Sk)

01. Choosen the point pm F, such that k (pm) is maximum02. If pm satisfies Criterion 103. Add (pm, k (pm)) to Sk and push pm to a stack S04. End05. While S not empty06. p pop (S)07. For 8 neighbors x of p that satisfy Criterion 108. Add (x, k (x)) to Sk, push x to S09. End10. End

Xng da trn tng c xut c th hin trong hnh 3.5b,

cc nhnh xng gi c ct ta. Mt phn ca xng thu c c th cha

cc im d tha, nh phn mu xanh l cy trong hnh 3.5b. Trong nhiu

phng php i snh hnh dng da trn cu trc xng, lymt s im

mut xng hocpht hin nhng im c trng (im cui v im giao

nhau) l cn thit. Vic ly cc im giao tha t xng s thun li cho vic

phn tch v i snh ph hp thu c hnh dng ph hp phn tch .

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lm iu ny bt k cc php ton topo u c th c s dng ct ta

xng. Tc gi Wei Shena s dng phng php lm mnh c xut v

kt qu th hin trong hnh 3.5c.

3.2.3.3 phc tp ca BPR tnh ton BPR cn cc thng s ng bin bi chiu di cung,

trong c phc tp O(m), m l sim ng bin. i vi mt im p

c kim tra, xem n c c thm vo xng hay khng, th sim sinh

l n. Kim tra im p tha mn c tiu chun 1 c phc tp O(n).Nh

vy, tng thi gian phc tp ca phng php tip cn l O(nN+m), trong

N l slng im nh bn trong ng bin. Trn thc t, trong ng dngthc t, n thng bng mt gi tr nhhn, thng l 3 hoc 4, v m l t hn

nhiu so vi N.

3.2.4 Kt lunTrong bi ny, tc gi Wei Shena v cc cng s trnh by mt

oc ngha mi cho ct ta xng c gi l t l un . Da trn o

ngha, tc gi xut mt thut ton cho pht trin xng. Th nghimca tcgi trn tp d liu MPEG-7 thu c cho thy xng khng nhy cm vi

nhiu ng bin, theo nhiu quy m, trong nhng nhnh xng khng

ng k c ct ta, trong khi nhnh quan trng vn cn.

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CHNG 4: KT QU THC NGHIM4.1 Mi trng ci t

Chng trnh c ci t trn Mi trng Windows 7, s dng ngn

ng Matlap vi my tnh c cu hnh nh sau:

CPU : i5450M

HDD: 320 GB

Memory: 2GB

Tp d liu c s dng trong th nghim l tp d liu thuc:

MPEG-7

4.2 Mt s kt qu th nghim4.2.1 Giao din chng trnh.

Hnh 4.1. Giao din chng trnh

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4.2.2 Mt s kt qu tm xng khc nhau ca cc phng php

Hnh 4.2. Xng ca qu to thu c bng cc phng php

a. Phng php tm xng theo trc trung v.b. Phng php tm xng theo Matlab.c. Phng php tm xng theo DCE vi N = 15,N l s nh c

la chn bi DCE

d. Phng php tm xng theo BPR vi t = 0. 8, t l gi tr ngngc la chn bi BPR.

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Hnh 4.3. Xng ca con lc thu c bng cc phng php

a. Phng php tm xng theo trc trung v.b. Phng php tm xng theo Matlab.c. Phng php tm xng theo DCE vi N = 15, N l s nh

c la chn bi DCE

d. Phng php tm xng theo BPRvi t = 1. 2, t l gi tr ngngc la chn bi BPR

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4.2.3 Hiu qu ca vic s dng ngng tHiu qu ca cc gi tr ngng t khc nhau trn xng ca mt i

tng c minh ha trong hnh 4.4.Nh gii thiu trong mc 3.1, o

ngha c xut, BPR c th c thc hin nh mt trng hp c bitgia nhng m hnh khc nhau. Do , nhiu chi tit xng c th thu c

bng cch thit lp ngng t c gi tr khc nhau cho BPR. Khi gi tr ngng

t tng, c t hn cc nhnh trong xng, m i in ngha cho cc b

phn ca i tng, v cc b phn khng quan trng b b qua. y l nhng

c tnh ph hp vi nhn thc ca con ngi.

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Hnh 4.4. Minh ha xng ca i tng trong vic s dng cc ngng khcnhau, t l gi tr ngng.

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KTLUN

Sau thi gian tm hiu, nghin cu ti Tm hiu phng php

BPR(Bending Potential Ratio) cho bi ton tm xng ca nhv trin khai

thc hin, em t c mt s kt qu nh sau:

V l thuyt, n ca em trnh by v hiu c:

Tng quan v x l nh s.

Mt shng tip cn trong tmxng ca nh.

Tm hiu thut ton ct ta xng ca nh da vo BPR(Bending

Potential Ratio) do Wei Shena v cc cng s xut [4].V thc nghim, em ci t th nghim chng trnh tm xng v

ct ta xngda vo o BBR v so snh vi kt qu tm xng theo hm

tm xng ca matlab.

Tuy nhin trong qu trnh thc hin, thi gian khng c nhiu, nng lc

chuyn mn cn nhiu hn ch, nn ti mi ch dng li mc c , dch

hiu v tm hiu tm lc v phng php, cha nh gi tng hp c

phng php. Nu c iu kin, em s tm c ti liu nghin cu nhm

tng hp nhiu phng php v a ra c nhng nh gi kt lun da trn

nhng g tm hiu c. Trong thi gian ti ti s pht trin mc cao

hn, v d nh c th tra cu nh da trn cu trc xng.

Em rt mong nhn c s ng gp kin ca cc Thy C v cc

bn em c thm kin thc v kinh nghim tip tc hon thin ni dung

nghin cu trong ti.

Em xin chn thnh Cm n!

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TI LIU THAM KHO

Ti liu Ting Vit

[1]. Nng Ton, Phm Vit Bnh (2007), Gio trnh x l nh, Nh

xut bn i hc Thi Nguyn.

[2]. Lng Mnh B,Nguyn Thanh Thy(2007),Nhp mn x l nh

s,Nh xut bn KHKT.

[3]. Nguyn Th Hoa (2010), n Tt Nghip, Trng HDL Hi

Phng

Ti liu Ting Anh

[4]. Wei Shena, Xiang Bai, Rong Hu, Hongyuan Wang, Login Jan

Latec ki(2010), Skeleton Growing and Prunning with Bending Potential

Ratio, CVPR.

[5]. Xiang Baia, Login Jan Latec ki(2007), Skeleton Prunning byContour Partitionning with Discrete Curve Evolution, CVPR.

[6]. H. Blum, in: A Tranformation for Extrating New Description of

Shape, Models for the Perception of Speech and Visual Form, MIT Press,

1967pp, 363-380.

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44.Nguyen 3