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Tm hiu cc php ton hnh thi v ng dng

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Li m u

Trong thc t hnh dng thng c ch trng hn kch thc v con ngnhn ra cc i tng xung quanh cng ch yu thng qua hnh dng. Chnh v vy biu din hnh dng l mt vn quan trng v khng th thiu trong qu trnh nhdng i tng. Trong x l nh s ta s dng cc php ton hnh thi gii quyvn ny.

Cc php ton hnh thi khng nhng quan trng trong lnh vc ton hc m cnrt quan trng trong lnh vc Cng Ngh Thng Tin ni chung v x l nh s niring: gip ta gii quyt cc bi ton nh tm bin nh, lc nhiu trn nh, ci thicht lng hnh nh, ni cc nt t trong vn bn xung cp v pht hin tng chuyn ng v nhiu cc ng dng cc na.

Chnh v vy em la chn ti Tm hiu cc php ton hnh thi v ngdng.

Mc tiu ca n l tm hiu cc php ton hnh thi v ng dng vo x l cci tng trong hnh nh.

Ban u em tm c cc ti liu v sch bo c ni dung lin quan n cckhi nim trong ti, sau a ra phng hng, v rt ra kt lun cho ring mn thc hin ti.

Bo co n gm58 trang, c chia lm 4 chng:

Chng I. Tng quan v x l nh: Chng ny gm c cc khi nim ban uv x l nh s, lch s pht trin, cc ng dng, tm quan trng, v cc bc thc hin trong qu trnh x l nh.

Chng II. Khi nim v php ton hnh thi: Chng ny gm c cc khi

nim v php ton hnh thi, t c bn n nhng khi nim nng cao v ng dntrong thc t. u tin l cc khi nim tp hp nh cc quan h php hp, php giao php b sau l cc php ton logic lin quan n qu trnh x l nh nh phn, tin cho vic phn tch v chng minh cc cng thc chnh ca php ton hnh thi.Ton b chng tp trung lm r cc khi nim v: Php co nh phn, php gin nh phn, php ng nh, php m nh, php trng hoc trt (Hit-or-Miss), Php trch bin, Php lm y, php tch cc thnh phn lin thng, php bao li, php lm mnhv tm xng.


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Chng III. Cc ng dng ca php ton hnh thi: Chng ny nu r ccng dng ca php ton hnh thi tm hiu trong x l nh.

Chng IV. Ci t chng trnh th nghim: Trn c s l thuyt tmhiu em xy dng chng trnh x l nh s dng cc php ton: php co nh phn php gin nh phn, php ng nh, php m nh, v tm xng lm mnh cc itng trn nh nh phn.

Kt Lun.


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Li cm n !

u tin em xinchn thnh cm nPGS. TS. Ng Quc To- ngi trc tiphng dnv nh hng gip em c th nhanh chng tip cn , nm bt kin thcvhon thnh ti Cc php ton hnh thi v ng dng.

Em xin gi li cm n ti khoa Cng Ngh Thng Tin- Trng i Hc in Lc,v to iu kin thun li cho em trong sut qu trnh hc tp ti trng.

E m xin gi li cm n ti ton th thy c gio khoa Cng Ngh Thng Tin -Trng i Hc in Lc, tn tnh ging dy trang b cho em nhng kin thc qubu trong nhng nm hc va qua.

Em xin gi li cm n n nhng ngi thn trong gia nh, bn b ng vinv to mi iu kin gip chng em trong qu trnh hc tp cng nh trong cuc sng

Mc d em c gng hon thnh tt ti nhng cng khng th trnh khinhng sai st nht nh, rt mong c s thng cm v chia s cng qu Thy C vbn b.

Em xin chn thnh cm n!

H Ni, Ngy 15 thng 06 nm 2009

Sinh vin thchin O BO LINH


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MC LC

Li m u................................................................................................................................. 1 Li cm n ! ................................................................................................................................ 3 DANH MC HNH V BNG BIU S DNG TRONG N............................... 6

CHNG I. TNG QUAN V X L NH......................................................................... 8 1.1. S lc v ngun gc ca x l nh s....................................................................... 8 1.2. Khi nim v x l nh s........................................................................................... 9 1.3. Qu trnh x l nh.......................................................................................................... 9

CHNG II. KHI NIM V PHP TON HNH THI................................................... 11 2.1. Khi nim c bn........................................................................................................... 11

2.2. Cc php ton Logic lin quan n nh nh phn.......................................................... 15

2.3. Php gin nh phn (Dilation)........................................................................................ 18 2.4. Php co nh phn (Erosion)........................................................................................... 20 2.5. Mt s tnh cht ca php ton hnh thi....................................................................... 23

2.5.1. Cc mnh ........................................................................................................... 23 2.5.2. nh l .................................................................................................................... 24 2.5.3. H qu..................................................................................................................... 24

2.6. Php m nh (Opening) v php ng nh (Closing)................................................... 25 2.6.1. Php m nh........................................................................................................... 25 2.6.2. Ph p ng nh........................................................................................................ 27 2.6.3. Cc tnh cht ca Php m nh v php ng nh................................................. 29

2.7. Php Bin i trng hoc trt (Hit-or-Miss) ............................................................... 30 2.8. Cc thut ton c bn ca hnh thi hc........................................................................ 31

2.8.1. Trch bin ( Boundary Extraction ) ........................................................................ 31 2.8.2. Lm y (Region Filling)....................................................................................... 32 2.8.3. Tch cc thnh phn lin thng (Extraction of Connected Components).............. 33 2.8.4. Bao Li (Convex Hull)........................................................................................... 34 2.8.5. Lm mnh(Thinning).............................................................................................. 36 2.8.6. Tm khung x ng (Skeletonization) ....................................................................... 38

CHNG III. NG DNG CA PHP TON HNH THI.............................................. 40 3.1. S dng php ton hnh thi trong c lng nghing vn bn............................... 40 3.1.1. M t ph ng php ................................................................................................. 42 3.1.2. p dng php ton hnh thi.................................................................................. 42

3.2. ng dng php ton hnh thi trong tch dng vn bn................................................ 44 3.2.1. S dng php ton hnh thi t lem dng vn bn............................................. 44

CHNG IV. CI T CHNG TRNH .......................................................................... 46 4.1. Gii thiu ch ng trnh ................................................................................................. 46 4.2. Hng dn s dng....................................................................................................... 47 4.3. Thc Nghim................................................................................................................. 48


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Kt lun.................................................................................................................................... 53 Ti liu tham kho:................................................................................................................... 54


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DANH MC HNH V BNG BIU S DNG TRONG N

Hnh 1.1: Bc nh u tin v mt trng ca c quan v tr m NASA. Vo lc 9:09pht sng ngy 31/6/1964. (Digital Image processing second edition, Tr 18) ................... 9 Hnh 1.2: Cc giaion chnh trong x l nh................................................................. 10 Hnh 2.1: nh v i tng trong nh.............................................................................. 12 Hnh 2.2: Quan h gia hai tp hp.................................................................................. 13 Hnh 2.3: Php bin i ca tp hp................................................................................. 14 Bng 2.1: Ba php ton logic c bn:............................................................................... 15 Hnh 2.4: Mt s php ton logic gia cc hnh nh nh phn......................................... 16 Hnh 2.5:Mt vi th d v cc phn t cu trc............................................................. 17 Hnh 2.6: Php gin nh phn........................................................................................... 19 Hnh 2.7: Qu trnh qut ca phn t cu trc trn hnh nh nh phn............................. 20 Hnh 2.8: Php co nh phn trn hai i tng. ............................................................... 21

Hnh 2.9: Qu trnh lc i tng s dng php co nh phn v php gin nh phn...... 22

Hnh 2.10: ng dng ca php co nh di dng s nh phn........................................ 23 Hnh 2.11: Qu trnh thc hip php m nh................................................................... 26 Hnh 2.12: Php m nh trn phng din ngha hnh hc........................................... 27 Hnh 2.13: Qu trnh thc hin php ng nh................................................................ 28 Hnh 2.14: Minh ha php ng nh trn phng din ngha hnh hc........................ 29 Hnh 2.15: Minh ha php bin i trng hoc trt....................................................... 30 Hnh 2.16: Qu trnh tm bin ca i tng trn nh nh phn....................................... 32 Hnh 2.17: Qu trnh lm y i tng trong nh.......................................................... 33 Hnh 2.18: Qu trnh tch cc thnh phn lin thng trong nh bng php ton hnh thi........................................................................................................................................... 34

Hnh 2.19: Mt qu trnh trong php bao li.................................................................... 35 Hnh 2.20: Php bao li i vi i tng trong nh....................................................... 36 Hnh 2.21: Qu trnh lm m nh i tng trong hnh nh............................................. 38 Hnh 2.22: Qu trnh thc hin thut ton tm x ng. ..................................................... 39 Hnh 3.1: Cc dng vn bn c xu hng dnh li vi nhau do nh hng ca du........ 41 Hnh 3.2: Nhng khong gc nghing khc nhau c s dng c lng gcnghing ph hp cho phn t cu trc. ............................................................................. 43 Hnh 3.3: Mt vi v d ca vic s dng php ng v m vi nhng phn t cu trcnghing. Hnh 3.3a v 3.3d l nhng nh a vo ban u. Hnh 3.3b v 3.3e l nhngkt qu ca vic p dng bc tin x l, c lng th, v php ng tng ng vihnh 3.3a v 3.3d. Hnh 3.3c v 3.3f l nhng kt qu ca vic p dng php m t ngng vi hnh 3.3b v 3.3e................................................................................................. 44 Hnh 3.5: Hai dng vn bn c t lem..................................................................... 45 Hnh 3.6: (a) Mt dng ct nhng khng m rng bin, (b) Dng ct c m rngbin. .................................................................................................................................. 45 Hnh 4.1: Thc nghim gin nh phn hnh nh vi cu trc 4x4.................................... 48 Hnh 4.2:Thc hin gin nh phn hnh nh vi phn t cu trc 7x7............................ 49 Hnh 4.3: Thc nghim php co nh phn trn hnh nh vi phn t cutrc 4x4. ......... 49 Hnh 4.4: Thc nghim php m nh trn hnh nh vi phn t cu trc trn 7x7......... 50 Hnh 4.5: Thc nghim m nh lm trn gc ca i tng trong nh nh phn............ 50 Hnh 4.6: Thc nghim php m nh vi phn t cu trc hnh ch thp, kch thc 7x7.......................................................................................................................................... 51 Hnh 4.7: Thc nghim php ng nh trn phn t cu trc trn 7x7............................ 51


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Hnh 4.8: Thc nghim php ng nh vi phn t cu trc hnh dng ch thp, kchthc 7x7.......................................................................................................................... 52 Hnh 4.9: Thc nghim tm xng i tng trn nh nh phn...................................... 52 Hnh 4.10: Thc nghim tm bin ca i tng............................................................. 52


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CHNG I. TNG QUAN V X L NH

Trong nghnh khoa hc my tnh, x l nh l mt dng ca x l tn hiuchou vo l mt nh hoc cc frame ca phim nh. u ra c th l mthnhnh, hoctp hp cc k t hoc cc tham s lin quan tihnhnh. Thng th k thut x lnh c lin quan ti x l tn hiu hai chiu v c p dng bng mt chun ring vk thut x l nh cho n. Cc khi nim c bn x l tn hiu nh, khi nim vtch chp, cc bin i Fourier, bin i Laplace, cc b lc hu hn Ngoi ra cncn ti cc cng c ton hc nh i s tuyn tnh,sc xut, thng k.V mt s kinthc cn thit nh Tr tu nhn tao, Mng n ron nhn to cng c cp trong qutrnh phn tch v nhn dng nh.

S lc v ngun gc ca x l nh s Cc phng php x l nh bt u t cc ng dng chnh: nng cao cht ln

nh v phn tch nh. ng dng u tin c bit n l nng cao cht lng trong nghnh cng nghip bo ch, nhng bc nh ny c truyn qua dy cp ngmgia hai thnh ph Lun n v New York. T nhng nm 1920, h thng Bartlanec gii thiu, l mt h thng truyn nh s qua dy cp gip gim thiu thgian truyn hnh nh, c th thng th truyn mt hnh nh qua bin Alantic m

ti hn mt tun th qua h thng ny ch mt hn 3 gi ng h . y mt h thngchuyn dng c trang b m ha cc bc nh thnh mt dng tn hiu sau truyn qua h thng dy cp, u nhn tn hiu s c mt h thng chuyn dng gii m v khi phc li chng.

Vn mi ny sinh l cht lng ca cc bc nh s ny c lin quan ti phng thc in v phn b mc sng, phn gii ca nh. vo khong nhng n1955 vic nng cao cht lng nh cng c pht trin gii quyt vn ny. Ck thut x l nh khng ngng c ci thin trong nhng nm tip theo. Nhng i

quan trng l nghnh cng ngh my vi tnh cng khng ngng c pht trin, png tt nhu cu ca cng ngh, gi thnh ngy cng gim, theo tc x l cnc ci thin ln nhiu. Cng vi nhng i hi khoa hc nghin cu khng gian tng lc thc y cho k thut x l nh pht trin. C th, vo nm 1964, Nhng bnh u tin chp b mt mt trng c truyn v tri t t v tinh Rangernhng bc nh ny c my tnh x l v nng cao cht lng nh lm ni bin, v lu tr nh.

T nm 1964 n nay, cc ng dng ca x l nh ngy cng c m rngngoi cc ng dng trong thm d nghin cu v tr, cc k thut x l nh cn


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s dng trong nhiu mc ch khc nhau. Hu ht cc bi ton t ra u l phntchv nng cao cht lng nh.Ta c th k n mt vi ng dng nh: Thm d a chsinh hc, y hc, ha hc, vt l

Hnh 1.1: Bc nh u tin v mt trng ca c quan v tr m NASA. Vo lc 9:09pht sng ngy 31/6/1964. (Digital Image processing second edition, Tr 18)

Khi nim v x l nh s

Mt hnh nh c th c nh ngha trn h trc ta bi hm( , ) f x y vi x vy l cc ta . V tr mi im nh c xc nh bi cc cp ta ( x,y) trn h trcta , bin ca mi im nh th c gi l mt cng hoc mc xm(Glever). Ta c th xem nh s nh mt ma trn cc im c ch s hng ch s ct, m phn t thuc ma trn ny c gi l mt im nh (Pixel). i vi nh xm, mim nh tng ng vi mt mc xm nht nh(256 mc xm).

1.3. Qu trnh x l nh X l nh bao gm nhiu lnh vc khc nhau: Phn cng phn mm v cc c s

l thuyt. H thng x l nh cho php tip cn khung cnh hoc nh u vo. Thhin mt dy cc x l a dng to ra mt nh a dng u ra mang nhng thngtin cn thit, t rt ra c cc c trng cho php hiu c khung cnh hoc n

Cc phng php v k thut x l nh nhm thit k cc h thng my c khnng nhn v hiu c hnh nh nh con ngi, gip con ngi quan st c nh


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ni m h khng th ti c. X l nh l mt qu trnh phc tp a dng v linquan n nhiu lnh vc khc nhau , sau yl qu trnh x l nh c bn.

Hnh 1.2 : Cc giai on chnh trong x l nh.

Trc ht l qu trnh thu nhn nh. nh c th c thu nhn qua my nh/mquay phim(Camera)theo dng tn hiu tng t, hoc cng c th l tn hiu s ha,hay tranh nh c qut bng my scanner. Tip theo l qu qu trnh s ha(Digitalizer) bin i tn hiu tng t sang tn hiu ri rc(ly mu) v s ha blng ha, trc khi chuyn sang giai on x l, phn tch v lu tr li.

Mc ch ca x l nh l :

- Bin i v lm p nh. - T ng phn tch nhn dng nh hay on nhn nh v nh gi cc ni dung

ca nh.

Nhn dng nh l qu trnh lin quan n m t cc i tng m ngi ta muc t v n. Qu trnh nhn dng nh thng i sau qu trnh trch chn cc c tnch yu ca i tng. C hai kiu i tngl:

- M t theo tham s ( Nhn dng theo tham s ).

- M t theo cu trc ( Nhn dng theo cu trc ). Nhn bit v nh gi ni dung ca nh l phn tch hnh nh thnh nhng phn

ring phn bit i tng ny vi i tng khc. Da vo ta c th m t ctrc ca hnh nh ban u.

C mt s phng php nhn dng nh c bn nh nhn dng bin ca tng trn nh, tch cnh v phn on hnh nhk thut ny c s dng nhiutrongy hc (x l t bo, nhim sc th ).


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CHNG II. KHI NIM VPHP TON HNH THI

Hiu mt cch y th Morphology l hnh thi hc v cu trc ca i

tng, hay n m t nhng phm vi v cc mi quan h gia cc thnh phn trong mi tng. Hnh thi hc qu quen thuc trong cc lnh vc ngn ng hc v sinh hc.Trong ngn ng hc, hnh thi hc l s nghin cu v cu trc ca t, tp hp t,cu v cng l mt lnh vc nghin cu nhiu nm nay. Cn trong sinh hc, hnhthi hc li ch trng ti hnh dng ca mt c th hn, chng hn c th phn tchnh dng ca mt chic l t c th nhn dng c l loi cy g; nghicu hnh dng ca mt nhm vi khun, da trn cc c im nhn dng phn bichng thuc nhm vi khun no Ty theo trng hp c th m c cch phn lp

ph hp vi n: C th phn lp da trn nhng hnh dng ca mt ct nh (Eliptrn), kiu v mc ca nhng hnh dng bt quy tc (li, lm, ), nhng ctrc trong (l, ng thng, ng cong, ) m c tch ly qua nhiu nm quast.

T nh khoa hc ca Hnh thi hc s mi ch thc s pht huy kh nng ca n kt khi my tnh in t s ra i v lm cho hnh thi hc tr ln thng dng, c nhiutnh nng mi. Nhng i tng trong Hnh thi hc ta c th coi nh l tp hp ccc im nh, nhm li theo cu trc ma trn hai triu. Nhng thao tc ton hc ri r

trn tp hp im c s dng lm r nhng nt c trng ring ca hnh di tng, do vy c th tnh ton c hay nhn bit c chng mt cch d dPhn ln cc php ton hnh thi hc c nh ngha t hai php ton c bn l phpton co nh phn (Erosion) v php ton gin nh phn (Dilation) .

Php ton c s c kt hp vi mt i tng l tiu chun ca cc php totp hp nh php hp(Union), Php giao (InterSection), v php b (Complement)cng vi php tnh tin no . V vy trong phn tip theo s trnh by cc khi nimv tp hp thng c s dng trong php ton hnh thi.

2.1. Khi nim c bn Ta nh ngha nh nh phn l tp hp cc im nh c ta a(x,y). Chng ta

cn c nh ngha khc v nh, theo quan st th c th xem nh nh tp hp cc t ri rc hoc lin tc.

Theo mt nh ngha no th, tp hp ny tng ng vi cc im nh thuv cc i tng hin hu trong nh.


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Hnh 2.1: nh v i tng trong nh.

Hnh v cho thy hai i tng, hay hai tp hp A v B trong nh. y ta c phi xc nh h trc ta nh trong hnh, quan tm n gi tr cc im nh cuthnh ln i tng trong nh v c gii hn trn khng gian ri rc .

u tin, ta c A l mt tp hp trong khng gian ri rc. Nua = (a 1 , a 2) lmt phn t ca tp hp A th ta c th vit nh sau:

a A (0.1)

Nh th, nua khng phi l mt phn t ca tp hp A th ta vit:

a A (0.2)

Tp hp m khng c phn t gi l tp hp rng hoc tp hp trng v biu th bng k t.

Tp hp A c xc nh bi ni dung nm trong 2 du ngoc nhn .

Cc phn t ca tp hp c lin quan n trong chng ny l nhng ta ca cc pixel i din cho i tng hoc cc c trng khc c quan tm trong mhnh nh.

Th d, khi ta vit mt cng thc: w | w ,C d d D (0.3)

Tp hpC l tp hp gm cc phn tw, nh vyw c hnh thnh khi nhntng ta ca cc phn t trong tp hp D vi-1.

Nu mi phn t ca tp hp A cng l mt phn t trong tp hp B th ta c thni A l tp con ca B, v c biu th nh sau:

A B , (0.4)


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Hp (Union) ca hai tp hp A v B l tp hp ca cc phn t thuc A, B hocc A v B, c biu th nh sau:

C A B , (0.5)

Nh vy giao(Intersection)ca hai tp hp A v B l tp hp cc phn t thucc A v B, c biu th nh sau:

D A B , (0.6)

Hai tp hp A v B tr thnh phn chia (Disjoint) hoc loi tr ln nhau (Mutually exclusive)nu chng c chung cc phn t, nh trong trng hp sau:

A B , (0.7)

Hnh 2.2: Quan h gia hai tp hp a) Giaogia tp hp A v tp hp B;b) Hp gia tp hp A v tp hp B; c) Phn btuyt i ca A;d) Phn b tng i ca tp hpA trongtp hpB (Php tr hai tp

hp A v B).

Phn b tuyt i(complement)ca mt tp hp A l tp hp cc phn tkhng bao gm cc phn t trong A:

w|w Ac A , (0.8)

)a

B

A

A

B B

A

A

B

A A

B

A B

A B c A

A


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Phn b tng i (difference) ca tp hp A trong tp hp B c biu th l A B nh trong biu thc sau:

w | w ,w A B A B A B , (0.9)

Viw l tp hp cc phn t thuc tp hp A nhng khng thuc tp hp B,khi nim ny c minh ha trnHnh 2.2(d).Phn c mu l kt qu ca php tongia hai tp hp.

Sau y l hai nh ngha cn b sung v n c s dng rng ri trong phpton hnh thi, nhng ni chung l vn cha tm c ci cn bn trn thuyt tp hp.

Phn x (reflection) ca tp hp B c biu th l , v c nh ngha bng biu thc sau:

w | w , B b b B , (0.10) Ngha l phn t w c hnh thnh khi nhn tng ta ca tp hp B vi-1

khi v tr tng i gia cc im trong tp hp B c xu hng i ngc li so vi ban u, gi l tnh phn x ca tp hp. Hay ni cch khc tp hp B s quay quanhgc ta mt gc 180o.

Mt im z(z1,z2) thuc tp hp A, khi z tnh tin th php tnh tin ca tp hp A c biu th l z A , v c nh ngha bng biu thc sau:

| , z A c c a z a A , (0.11)

Khi mt im z c ta z(z1,z2) hnh thnh trong tp hp A tnh tin mt lngl z th tp hp A cng tnh tin theo hng ca im z vi mt lng tng ng Hnh 2.3cho thy hai nh ngha trn v s dng hai tp hp A v B Hnh 2.3, chmmu en trn hnh v l biu th phn x ca tp hp B v s tnh tin ca 1 im ttp hp A. (Some basic concept from set theory/ Digital image processing SecondEdition, tr 520~521)

Hnh 2.3: Php bin i ca tp hp

z A

)a )b

1 z

B A

B

2 z


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a) Tnh tin ca tp hp A t mt im z; b) Phn x ca tp hpB.

Lu : Nhng phn t ring l hp thnh B khng ch c cc im nh m cn ccc vector khi chng c v tr ta xc nh vi im gc [0,0].

Bng 2.1: Ba php ton logic c bn:

p q p q p q p

0 0 0 0 1

0 1 0 1 1

1 0 0 1 0

1 1 1 1 0

2.2. Cc php ton Logic lin quan n nh nh phn Cc php ton logicc s dng trong x l nh l AND(), OR( ), v NOT(

). Thuc tnh ca ccphp tonny c minh ha trong Bng 2.1.Cc phpton l cung cp y cc chc nng, chng c th c kt hp di bt k dngno caphp ton logic.

Ton t logic c thc hin trn mt im nh bng im nh c s giaccim nh tng ng ca hai hoc nhiu hnh nh(Ngoi tr NOT, l ton t trncc im nh ca mt hnh nh n gin ). Bi v ton t AND ca hai bin nh phch l 1 khi c hai bin l 1, v vy trong mt hnh nh bt k v tr no th vi tont AND gia cc im nh tng ng, ta thu c kt qu l 1 khi v ch khi cc imnh u vo u c gi tr l 1. Hnh 2.4l v d minh ha cho cc php ton logic, phn c mu xm l phn c gi tr l 1, phn mu trng l phn c gi tr l 0.Cc php ton logic khc c xy dng da trn cc php ton c nh ngha t

bng 2.1. Cho mt v d:Php ton XOR ( da trn php ton AND v NOT ), gi trca n l 1 nu gi tr ca mt trong hai im nh c gi tr l 1(Khng phi l c haiv gi tr ca n l 0 khi c hai im nh u c gi tr l 0 hoc 1.Php ton ny khcphp ton OR,gi tr tr v s l1 khi mt trong hai im nh u vol 1,hoc khic hai im nh u vol 1. Php ton NOT-AND ch tr v gi tr l 0 khi c haiim nh u vo l 1.


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A B

A( ) NOT A

NOT

A B

AND

OR

A B

XOR

A B

NOT

AND

A AND B

A OR B

A XOR B

A N AND B

Hnh 2.4: Mt s php ton logic gia cc hnh nh nh phn. Phn c muxm cccgi tr l 1, v phn mu trng cccgi tr l 0.

Php ton hnh thicung cp hai php ton c bnl php ginnh phnv phpconh phn, hai php tonny l c s ban u cho nhiu thut ton v hnh thi khc.

i vo tm hiu cc php ton hnh thi, u tin ta lm quen vi mt s khinim quan trng thng c s dng trong bi vit.

Phn t cu trc(Constructing elements):i khi c gi l mt nhn (Kernel).

Nhng thut ng ny thng c s dng cho cc i tng trong tch ch


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(Convolutions).Cc phn t cu trc thng c quy nh theo mt mu ring datrnta ca mt s im c lin quan ti i tng no . Ta c th quan st v dt hnh minh ha pha di, l cc mu c trng cho cc phn t cu trc c kchthc khc nhau.

Hnh 2.5 : Mt vi th d v cc phn t cu trc.Hnh 2.5c ara hai kiu phn t cu trc c trng c kch thc l3x3 v

9x9, ccvng trn nh du gc ca phn t cu trc hai kiu ny khc nhau, nhnguc c im chung l vng nh du tm im lun c t im c ta trung tmca phn t cu trc.

Lu : mi ta im trn phn t cu trc u c th c mt gi trring.Mt th d n gin nht v ng dng ca phn t cutrc,nh s dngvo php covi nh nh phn. Ngoi ra cn c nhiucc phn t cu trc phc tp phc v cho ccmc ch khc, chng hn nh s dng tm xng hoc ng dngcho cc php tonhnh thi trn nh xm.

Mt im quan trng na cn lu l cc phn t cu trc cng c th c dnhnh ch nht, hnh trnTrn v d minh hath trong cc phn t cu trc c mts im b b trng,v bn cht th nhng ch b trng c th coi nh c gi tr l 0 hoc mt gi tr no khng thuc phn t cu trc, nu a vo sgy khhiu vini dung cn cp, nn y cc phn t c trng.

Khi mt php ton hnh thi c thc hin th cc gc ca phn t cu trcthng dch chuyn ln lttrn ccim nh. V khi gi tr ca cc im nh vac qut qua s c so snh vi nhau, cc kt qu thu c sau khi so snh phthuc vo php ton hnh thi ang c s dng.

1

1 1

1 1

1 1 1

1

1 1

1

1

1

1 1 1 1

1

111

11111

1 1 1 11

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

111111

1 1 1 1 1

1

1

1

1

1

1 1

111 1 1 1 1

1

1

1

1

1

1

0

0

1

1

1

1

1

10

1

1


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2.3. Php gin nh phn (Dilation)Tp hp B thng th c coi nh l mt phn t cu trc(structuring element)

trong gin nh phn, cng nh trong cc php ton hnh thi khc, tp hp A l tp hpcc phn t ca hnh nh gc.

Vi A v B l cc tp hp trong , th php ginnh phn ca A theo B ( A B )c nh nghaquacng thcsau:

| z

A B z B A

, (0.12)

Nh vy php gin nh phn ca tp hp A bi phn t cu trc B l tp hp catt c cc imz (z l tm im ca phn t cu trc B trn tp hp A) sao cho phn xca B z giao vi tp A ti t nht mt im.Hay ni cch khc, php gin nh phn lschng cho t t nht mt phn t t phn x ca phn t cu trc B vi tp hp A.ng thi cc phn t ny phi l tp con ca tp hp A.

Cng thc (1.12) c th c vit li:

| z

A B z B A A

, (0.13)

Phpgin nh phn ca tp hp A bi tp hp B l tn ti cc imw thuc sao chow l tng ca hai im tng ng bt k thuc tp hp A v tp hp B, nhngha ny c m t qua cng thc:

2w Z | w , , A B a b a A b B , (0.14)

Tng qut hn, nu A l mt hnh nh v B l phn t cu trc c tm im nmtrn hnh nh A, khi php gin ca hnh nh A bi phn t cu trc B c th chiu nh qu tch ca cc im c ph bi phn t cu trc B khi tm im ca B dichuyn trn cnh ca hnh nh A.


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Hnh 2.6 : Php gin nh phn.

Hnh 2.6agm:+ Tp hp A c hai cnh bn kch thc l d.

+ Phn t cu trc vung B kch thcd/4 , trng hp ny th phn t cu trc B v tng phn ca n bng nhauv B c tp hp cc phn t i xng nhau quatmim(du chm en gia).

+ Cui cng l kt qu ca php gin nh phn gia tp hp A v phn t cutrc B.

Hnh 2.6 b cng gm nhng thnh phn tng t nhng vi phn t cu trc B l hnh ch nht, nhng cho ta mt ktkhc. Nh vy, mi kiu phn t cu trc khcnhau s cho ta mt kt qu khc nhau, sau khi thut ton c thi hnh.

T ta c cng thc:

bb B

A B A , (0.15)

thc t ha nhng l thuyt nu trn, ta coi nhng phn t cu trc nh

mt mu sn v dch chuyn tnh tin trn b mt hnh nh. Khi gc ca phn t c

)a

)b

d/8 d/8

d/4

d/4

d

d

d

d

d

d

d

d

d/8 d/8

d/8

d/8

d/2

d/4

d/4

d/4


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trc (chm en tm im) khp vi im nh ti cnh ca hnh nh th cc im tng ng vi vi gc ny s c nh du v thay th. Sau khi ton b im nh c qut qua bi phn t cu trc th, thao tc gin hnh nh c hon tt.

Mt v d v php gin trn mt hnh nh nh phn s dng phn t cu trcdng ma trn vung 3x3 nh sau:

Hnh 2.7: Q u trnh qut ca phn t cu trc trn hnh nh nh phn. v d trn ta cc im nh mu trng mang gi tr l 1 l cc im thuc i

tng ang cn quan tm trn nh, v phn mu en mang gi tr 0 l phn nm ngoi tng. Khithut ton c thi hnh th phn t cu trc s ln lt qut qua ccim nh ngoi cng( i theo ng k mu trn hnh v) ca i tng sau thay th cc im nh trn i tng ny theo mu phn t cu trc. T ta ngdng ni cc nt bi t gy ca on vn do qu trnhxung cp, vi khong cch ln nht ca cc nt b t gy tm hai im nh.

2.4. Php co nh phn (Erosion)Ta cng xt tp hp A v tp hp B (Phn t cu trc) trong , th php conh

phn ca tp hp A bi phn t cu trc B c k hiu A B v vit di dngcngthc nh sau:

A B = | z z B A , (0.16)Vi , z B b z b B , (0.17)

Php conh phn ca tp hp A bi phn t cu trc B l tp hp cc im z(znm tm im ca phn t cu trc B)sao cho B z l tp con ca A.

Xt hnh v sau:


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Hnh 2.8: Php co nh phn trn hai i tng.Hnh 2.8a gm:

+ Tp hp A c hai cnh bn kch thc ld .

+ Phn t cu trc vung B kch thcd/4 (Du chm en gia l tm im). + Cui cng l kt qu ca phpco nh phn gia tp hp A v phn t cu trc

B.

Phn c mu nht hn l kt qu sau khi thc hin co hnh nh bi phn t ctrc B. Hnh 2.8bgm nhng thnh phn tng t nhng vi phn t cu trc B lhnh ch nht, v cho ta mt kt qu khc.

Vy php co nh phn ca nh A vi phn t cu trc B l qu tch cc im

c to ra bi tm im ca phn t cu trc B khi tnh tin trn hnh nh A.T ta c cng thc:

A B Bb B

A , (0.18)

Php co nh phn v gin nh phn c th c vi nhau qua php b v php phn x ca tp hp, lun l ny s c minh ha qua cng thcsau:

( A B)c=Ac B , (0.19)

Ta chng minh cng thc trn l ng:

d/8

d/4

d/2

d

Hng

3d/4

d/8

d/4

d

d

d

d/8d/8

3d/

d/8

d/8

d/

d/4

d/4

d/2


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T cng thc co nh phn ta c:

( A B)c = | z z B Ac, (0.20)

Nu tp hp B z l tp con tp hp A th ta c, B z Ac= , cho nn, trong trnghp ny ta s c:

( A B)c= | c z z B A c, (0.21)

V phn b ca php gin nh phn gia tp hp A v tp hp B lun tha mn:

( B z Ac= )c = B z Ac

cho nn:

( A B)c= | c z z B A

Mt khc theo cng thc1.12 ta c:

| z

A B z B A

Suy ra: ( A B)c= Ac B , .+

Nh vy, phn b ca php co nh phn gia tp hp A v Phn t cu trc B l php gin nh phn gia phn b ca tp hp A vi phn x ca phn t cu trc B.

Mt ng dng quan trng ca php co nh phn l dng loi tr cc chi titkhng cn thit trn hnh nh. Th d, Trn mt hnh nh , ta c cc i tng c c tng ng 1,4,6 v 11 im nh, By gi nu mun loi tr cc i tng nh khngcn thit trn nh, ch li cc i tng c kch thc ln, nh trong hnh v tng ta cn gi li l nhng i tng c kch thc11 im nh. Ta s s dung phnt cu trc c kch thc10x10im nh thc hin php co nh phn ( Erosion ).Kt qu s ch cn li 3 i tng c kch thc 1 im nh(Hnh 2.9b).Sau cci tng tr li kch thc ban u ta s dng php gin nh phn( Dilation ) vi

phn t cu trc c kch c tng ng(Hnh 2.9c).

Hnh 2.9: Q u trnh lc i tng s dng php co nh phn v php gin nh phn.

)b)a )c


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Qu trnhthc hin c th c minh ha r rng qua hnh v sau:

Hnh 2.10 : ng dng ca php co nh di dng s nh phn. a) Hnh nh ban u; b) Hnh nh qu trnh co nh phn trn i tng vi phn

t cu trc 10x10, phn t c t dm mu s c gi tr 1 sauqu trnhco nh phn;c) Phng to i tng v gi tr ca i tng sau qu trnh co nh phn vi phn tcu trc 10x10.

2.5. Mt s tnh cht ca php ton hnh thi thun tin trong vic ci t ta c th phn tch v n gin ha cc mu ph

tp, di yl mt s tnh cht c s ca php ton hnh thi.

2.5.1. Cc mnh -Mnh 1:T nh cht gia tng

a) ' X X X B ' X B , B

' , X B X B

B b) ' B B X B ' X B , X

', X B X B X

-Mnh 2: Tnh cht phn phi vi php

a) ( ) ( ) ( ), X B B X B X B

b) X B B =(X B ) ( X B ),

- Mnh 3: Tnh cht phn phi vi php giao


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( X Y ) B =(X B ) (Y B ),

- Mnh 4: Tnh cht kt hp

a) ( ) ( ), X B B X B B

b) (X B ) B = X ( B B ),

2.5.2. nh l Gi s, X l mt i tng trong nh, B l phn t cu trc, khi X s b chn

trn v chn di bi tp close ca X theo B.

Ta c,( ) X B B X ( X B ) B ,

Chng minh,

Ta c: , x x X B X B (V x x X X B B )

( ) x X B B (Theo nh ngha ca php co),

( ) X B B X , (0.22)

Mt khc, y ( X B ) B ,

Suy ra: x X B sao cho, x y B ( V ( X B ) B = x x X B

B )

, x B X y X Suy ra: ( X X ) , B B (0.23)

T (1.22) v (1.23) ta c:

( ) X B B X ( X B ) B ,

2.5.3. H qu Tnh Bt bin: a) ( ( ) X B B ) B =( ) X B ,

b) ( ( X B ) B ) B =( X B ),

Tht vy, t nh l trn ta c: ( ) X X B B ,

Do , theo tnh cht gia tng ta c:

(( ) X B X B B ) B , (0.24)


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Mt khc cng theo nh l trn ta c: (X B ) B X X

(( X B ) B ) B X B , (0.25)

T (1.24) v (1.25) ta c:

(( ) X B B ) B = X B .

V ((X B ) B ) B = X B . ( Pht trin k thut d bin, pht hin bin v ng dng/Tr. 15)

2.6. Php m nh (Opening) v php ng nh (Closing) cc ch trn nu mt s khi nim cng nh phng thc gin nh phn

v co nh phn cc i tng trn mt nh. Sau yl hai khi nim cng rt quantrng trong php ton hnh thi, l php m nh (Opening) v php ng nh (Closing).Php m nh v php ng nh l hai php ton c m rng t hai phpton hnh thi c bn l php co nh phn v php dn nh phn. Php m nh thnglm trn bin ca i tng trong nh, nh loi b nhng phn nh ra c kch thcnh. Php ng nh cng tng t lm trn bin ca i tng trong nh nhng ngvi php m. Php ton ny thng lm hp nht cc on gy hp, loi b cc lhng nh v lm y cc khe h trong chu tuyn.

2.6.1. Php m nh Bi ton t ra l lm th no c th lm trn bin ca i tng loi b

nhng im nh tha, c kch thc nh khng cn thit. T , ta t ra gii phpnh sau:S dng php co nh phn, lc b cc im nh bn gn pha ngoi b mi tng, ch li ch gi li cc phn t c bn cu hnh ln hnh dng ca tng. T cc phn t sau khi co nh phn ta ta s s dng php gin nh phn tcng ln i tng. Cui cng ta s c i tng mi t cc phn t c bn , itng ny s p ng c yu cu bi ton t ra.

Nh vy, thc hin php ng nh ta phi tri qua hai giai on l co nh vgin nh. u tin s dng php co v phn t cu trcc k ch thc tng ng tcng ln i tng trong nh ng theo yu cu. Tng t vi php gin nh phn tas thu c kt qu(Hnh 3.0).

Vi tp hp A l i tng trong hnh nhv B l phn t cu trc, ( ) l k hiuca php m nh gia tp hp A v phn t cu trc B, php m nh c xc nh bi cng thc:

A B = (A B) B, (0.26)


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Hnh 2.11: Q u trnh thc hip php m nh.

Trn phng din ngha hnh hc, gi s ta c phn t cu trc B dng mthnh trn, Khi bin ca tp hp A B gm qu tch cc im thuc bin ca phn tcu trc B, khi B tnh tin trn ng bin tp hp A, v cch bin ca tp hp A khong cch xa nht(Hnh 2.12), hnh 2.12al i tng ban u, hnh2.12cl itng sau khi thc hin php m nh. Tt c cc hng gc ngoi u c lm trn, trong khi nhng gc hng vo trong u khng b nh hng. Nhng ch nhn nhtha nh ra s b lc b.

T lun im ny tac cng thc:

x

x B A

A B B , (0.26)


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Hnh 2.12 : Php m nh trn phng din ngha hnh hc.

Khu vc t m l i tng mi sau khi thc hin php ton; khu vc trong vin nt t li tng c trc khi thc hin php ton.

2.6.2. Php ng nh Tng t nh php m nh, nhng qu trnh thc hin php ng nhc xu

hng ngc li, vi mc ch, lp y nhng ch thiu ht ca i tng trn nh da vo cc phn t c bn ban u.

Vi tp hp A l i tng trong nh, B l phn t cu trc. l k hiu phpng nh. Khi php ng nh ca tp hp A bi Phn t cu trc B, k hiu l( ) A B , xc nh bi:

( ) A B =( ) A B B , (1.28)

Cho mt hnh nh nh phn, vi i tng trong nh c nhng khu vc b tgy, khng lin mch. khc phc hin tng ny ta p dng php ng nh, vi A l i tng ban u, B l phn t cu trc c kch thc3x3 (Hnh 2.13a). Khi pdng php ng nh, u tin i tng ny s c m rng bng php gin nh phtheo phn t cu trc B. Lc ny nhng khu vc thiu ht s c b ln, v khu vct s c ni li (Hnh2.13b).Sau p dng php co nh phn a i tngv trng thi ban u (Hnh 2.13c).

)a

)b )c


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Hnh 2.13: Q u trnh thc hin php ng nh.

Trn phng din ngha hnh hc tng t nh php m nh, ngoi tr vic phn t cu trc trong php ng nh ny c cch thc thc hin i nghch vi phm nh.

Cho mt i tng trong nh tng t nh i tng hnh2.12. Khi thc hin php ng nh th hnh trn(phn t cu trc) c xu hng qut bn ngoi ng bica i tng(Hnh2.14).

)a

)b )c

A B A1 B

)a

)b

)c


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Hnh 2.14 : Minh ha php ng nh trn phng din ngha hnh hc. Quan st trn hnh v ta c th thy cc gc hng vo ca i tng c lm

trn, cc gc hng ra th khng c tc ng g. lm do phn t cu trc to ra bn tri i tng nh hn bn phi, v th kch thc phn t cu trc cng rt qutrng trong trn ca gc.

Mt imw c coi l mt phn t ca (A B ) khi v ch khi z B A , vimiw z B khi z B tnh tin.

Nh trong quan h gia php gin nh phn v php co nh phn. Phn b ca php ng gia hai tp hp l php m gia php b v php phn x ca hai tp hp;tc l:

( A B)c = ( Ac ), (1.29)

2.6.3. Cc tnh cht ca Php m nh v php ng nh*Tnh cht 1: i vi php m nh

a) A B A ,

c) NuC D th C B D B ,

d) ( ) A B B A B,

*Tnh cht 2: i vi php ng nh

a) A A B ,

b) NuC D th C B D B ,

c) ( ) A B B A B ,

d) A B Khi v ch khi z B A ,

Cc tnh cht trn gii thch cc kt qu nhn c khi php ton m v ng nc s dng xy dng lc php ton hnh thi. Th d, xt cu trc lc ca phm nh. Khi tnh cht(1a) ch ra kt qu s l tp hp con ca tp hp ban u. Tnh cht(1b)ngha l tnh n iu c bo ton. Tnh cht 1c cho thy php tonm nh ch c s dng khng hn 1 ln, nhng ln sau kt qu vn gi nguyTng t i vi php ng nh.


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2.7. Php Bin i trng hoc trt (Hit-or-Miss)Php bin i trng hoc trt c a ra bi Serra v l mt cng c c bn

ng dng vo pht hin hnh dng ca i tng.

Cho phn t cu trc B vi B=( B1, B2), trong B1 l tp hp c to t cc phn t ca B c lin kt vi i tng ( B1 A) , v B2 l tp hp c to t cc phn t ca B vi bc ch lin kt ti phn b ca i tng ( B2 c A ). Hay ni cchkhc,nu cho B1 l phn t cu trc c p dng ln i tng, th B2 s l phn tcu trc c cu to t cc phn t nm trn phn b ca phn t cu trc B1 . Viiu kin ny, ty thuc vo cch chn phn t cu trc B1 v B2 m chng ta s cnhiu i tng mi khc nhau vi cc cp phn t cu trc tng ng. Chnh v vy,trng hoc trt l php bin ic s xy dng cc thut ton nh: Thut ton

bao li, lm mnh Vi A s* B l k hiu ca trng hoc trt gia tp hp A v phn t cu trc

B. Khi trng hoc trt c nh ngha nh sau:

A s* B= ( A B1 ) ( Ac B2), (1.30)

Lu , php co nh phn ca phn b ca A v tp hp B2 l mt trng hp c bit ca trng hoc trt bi v phn t cu trc ln tp hp B2 l rng.

Mt khc( Ac B2) = (A )c nncng thc (1.30) c th c vit li nh sau:

A s* B= ( A B1 ) ( A )c, (1.31)

Suy ra: A s* B= ( A B1 ) - (A ), (1.32)

Hnh 2.15: Min h ha php bin i trng hoc trt


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A l i tng trong nh (tp hp cc phn c nhn l 1 v c bi m); Ac B ca A trong nh; B1, B2 Phn t cu trc; A1: Kt qu ca php co nh phn gia phn t cu trc B1 v A; A2: Kt qu ca php gin nh phn gia phn t cu trc B2 vi Phn b ca A.

2.8. Cc thut ton c bn ca hnh thi hc ng dng ch yu ca hnh thi hc i vi nh nh phnl phn tch cc thnh

phn ca nh,chnh vn rt c hiu qu trong biu din v m t hnh dng i tng cho nn phn ny s tp trung a ra cc thut ton v hnh thi trchng bin,cc thnh phn lin thng, ng bao li, hay tm xng lm mnh.

2.8.1. Trch bin ( Boundary Extraction )

Vi nh u vo l nh xm, th ta c th x l phn on nh bng cc ngnca nh. Trong hnh nh mi im nh c gi tr xm ring, gi tr ny c gii htrong khon 0 ti 255. V vy ta c th thng qua lc mu la chn cc mxmthch hp. Khi chuyn sang nh nh phn cc im nh c gi tr ln hn ngngny u c gn l 255 hoc nu khng th s c gn l 0. ngc li nhng imnh no c gi trnm trong ngng u c t l 1, nhng im nh ny l imnh cu thnh i tng trong nh nh phn.

Trong nh nh phn, i tng c cu thnh bi cc im nh lin thng c gi

tr l 1, Xt mtth d hnh2.16c 9 im nh dc, 9 im nh ngang. Nhng imnh to ln bin l nhng im nh thuc i tng nhng trong 8 im ln cn phi c t nht mt im nh c gi tr l 0.

Bin ca tp hp A ph thuc vo kch thc ca phn t cu trc. dy cang vin bao quanh i tng ph thuc vo kch thc ca phn t cu trc. Chth d, nu mt phn t cu trc c kch thc 3x3 sinh ra dy ng vin l 1 tvi phn t cu trc c kch thc 5x5 s sinh ra ng vin ca i tng c l 3.

Khi , bin ca tp hp A, k hiu l A , c xc nh bi cng thc:

( A A A ) B , (1.33


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Hnh 2.16: Qu trnh tm bin ca i tng trn nh nh phn.

2.8 .2. Lm y ( Region Filling) Lm y vng ca mt i tng tbinl b xung gi tr 1 vo ton b vng

pha bn trong bin ca i tng. Cho mt nh nh phn A, cc im nh bin cai tng trong hnh nh A c gi tr l 1 v cc im nh khc c gi tr l 0. Ta btu qu trnh lm y bng cch gn gi tr 1 vo im nh p bn trong bin ca itng, sau lp i lp li php gin nh phn gia im nh vi phn t cu trc B di gii hn t ra bi php b ca tp hp A ( Ac). Bi v nu hn ch khng ct th chng trnh s lp i lp li php gn ny, dn ti sy ra hin tng trn qcc cng khc trn nh, thm ch ton b nh.

Vi X0= p v B l phn t cu trc, php lm y vng trong nh s c xcnh bi cng thc:

X k =( X k-1 B) c A , Vik =1,2,3,k -1. (1.34)

Thut ton s dng khi X k =X k-1. Th d, hnh2.17, A l nh ban u ch cha bin ca i tng ( gi tr l 1 ),

B l phn t cu trc c kch thc 3x3 v hnh dng ch thp.

Khi thut ton s thc hin ln lt theo trnh t nh sau:

Bc 1: Thut ton s gn gi tr 1 cho mt im nh p bn trong vng bin.

Bc 2: p dng php gin nh phn t im nh p vi phn t cu trc B, ngthi ly giao ca kt qu php gin vi phn b ca tp hp A. Nh vy, sau khi ly

giao ca hai tp hp th phn no c gi tr l1 tng xng vi gi tr 1 ca phnb

1 A A

B A

1 A

A B


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tp hp A th c gi nguyn, phn no c gi tr 1 tng xng vi gi tr 0 ca ph b tp hp A th s c gn l 0. Qu trnh ny s c lp i lp li cho n khi c cc im nh tng ng bn trong bin ca i tng c gn l 1.

Bc 3: Cui cng ly hp gia X7 v bin A ta s c i tng c lmy t bin vng trong nh(Hnh 2.17).

Hnh 2.17 : Qu trnh lm y i tng trong nh.

2.8 .3. Tch cc thnh phn lin thng (Extraction of Connected Components) Trong thc t, bi ton tch thnh phn lin thng trong nh nh phn ng vai

tr quan trng trong cc ng dng phn tch nh t ng.Tng t nh php lm vng.Qu trnh thc hin thut ton cng c lp i lp li vi php tch cc thnh phn linthng.


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Cho mt nh nh phn trong i tng l tp hp A bao gm mt s thnh phn lin thng. Nhng im nh no thuc i tng th c nh dul 1 vimnh no nm ngoi i tng th c nh dul 0. Ta c th tch cc thnh phnlin thng bng cch gn mt im nh trong i tng ri t im nh , lp i lpli php gin nh phn vi phn t cu trc di hn ch t ra bi tp hp A.

Vi X 0= p v B l phn t cu trc. Khi php tch cc thnh phn lin thngc xc nh bicng thc:

X k = 1( ) ,k X B A k = 1,2,3 (1.35)

Hnh 2.18 : Qu trnh tch cc thnh phn lin thng trong nh bng php ton hnhthi.

2.8.4 . Bao Li ( Convex Hull) Ta c th hnh dung bao li ca mt i tng ging nh mt di bng cao s

bao quanh i tng.V th di bng cao su ny c cng qua cc phn lm theo ccvin li ca i tng. Kt qu l to ra mt hnh dng i tng khng c on no b lm. Bao li c th c bin i bi php ton Hit-or-Missvi 4 phn t cu trc


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lun phin quay 900. Cho A l mt nh nh phn v phn t cu trc Bi vi i=1,2,3,4,khi ta c 4 phn t cu trc tng ng nh sau:

(1.36)Trong cc phn t cu trc trn nhng phn t c nh du l nhng phn

t khng cn quan tm. u tin cho0i X A , sau lp i lp li thut ton theo cngthc sau:

(ik X X s* B) A , i=1,2,3,4 vk =1,2,3k-1 (1.37)

Khi 1i ik k X X tc l chng ng quy(converge)th qu trnh x l dng li v

t i iconv D X , Khi bao li ca A s l: 4

1

( ) i

i

C A D , (1.38)

Ni cch khc, thut ton s thc hin php bin i Hit-or-Miss gia tp hp A vi phn t cu trc B1 trn ton b i tng cho n khi i tng khng c g thayi na th dng li v ti iconv D X , sau hp tp hp A vi kt qu i D , qu trnhny s c thc hin ln lt vi2 3 4, , B B B . Cui cng hp ca 4 tpi D cho ta bao

li ca A. Xt th d trong mt chu trnh x l nh s dng php bao li (Hnh2.19). Vi

tp hp A l tp hp cc phn t to ln mt i tng trong nh, Ac l phn b ca tp hp A. B l phn t cu trc gm c B1, v B2.

Hnh 2.19 : Mt qu trnh trong php bao li.


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Th d trn cho thy mt chu trnh trong qu trnh thc hin php bao li i vii tng trong nh. Qu trnh ny s c lp i lp li ln lt vi cc phn t trc khc nhau (1.37). Khi thut ton kt thc, tt c cc ch b lm hay thiu ht chtit s c lm y. Xt mt th d tng qut t th d trong hnh2.19, vi

, v :

Hnh 2.20 : Php bao li i vi i tng trong nh.

2.8.5. Lm mnh( Thinning) Thut ton lm mnh thng bao gm nhiu ln lp, mi ln lp tt c cc i

nh ca i tng s c kim tra, Cc phn t cu trc c thit k tm ccim bin m khi loi b im nh trn i tng th s khng lm nh hng ti cclin thng. Nu im nhno mtha mn iu kin ca phn t cu trc th s bloi b. Qu trnh ny c lp i lp li cho ti khi khng cn im bin no c xna.

Lm mnh tp hp A bi phn t cu trc B, k kiu , xc nh bi cngthc sau:

= , (1.39)


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c th lm mnh mt i tng A mt cch hiu qu hn, ta da vo dy cc phn t cu trc.

{ } { }, (1.40)

Trong Nhn c t , qua php quay quanh tm im ca n. Vikhi nim ny ta nh ngha php lm mnh bi mt dy cc phn t cu trc theocng thc.

{ } , (1.41)

Ni cch khc, qu trnh lm mnh A bi , kt qu li tip tc c c lm mnh bi cho n . Lc nyi tng trong nh hu nh khng thay i na.

Xt th d qu trnh lm mnh (Hnh2.21). Qu trnhlm mnh i tng s

c lp i lp li cho n khi i tng khng c s thay i no th dng li.

Theo cng th c tng qut ta c:

{ } ,

Nh vy, Trong th d ny qu trnh lm mnh c lp i lp li 2 lt. Tronmi ln lp i tng phi tri qua qu trnh lm mnh vi 8 phn t cu tr

.


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nh i tng trong hnh nh.

2.8.6. Tm khung xng ( Skeletonization) Tm khungxng cng tng t nh lm mnh, nhng n c dng tm r

cc chi tit cu trc ca i tng.Khung xng ca i tng l tp hp cc imnh cch u bin ca i tng. V c th biu din bng php co nh phn v phpm nh.

Xt A l mt nh nh phn bao gm cc im nh thuc i tng, c t nhnl cc s1. Cc im nh khng thuc i tng c t nhn l cc s 0. B l phnt cu trc 3x3. Khi , nu k hiuS ( A) l khungxng ca tp hp A th thut tontm khungxng c xc nh qua cng thc:


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, (1.42)

Trong : { [ ]}, (1.43)

(A kB ) l php co k ln lin tip trn A. Tc l:

( A kB )=((..( A B B . B

V K l Bc lp cui cng trc khi A b n mn thnh tp rng. Ni cchkhc:

K = max{k | (A kB ) }

Cng thc (1.42) v (1.43) khng nh rng khung xngS ( A) c th nhn ct hp cc b khung xng conS k ( A). C th chng minh rng A c th xy dng lit cc tp conny bng cch s dng cng thc:

A = , (1.44)

Trong k hiu k ln gin nh phnS k ( A), tc l:

=((..( S k (A) B B . B.

Xt th d :

Hnh 2.22 : Qu trnh thc hin thut ton tm xng.


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CHNG III. NG DNG CA PHP TON HNH THI

Thut ng hnh thi hc (Morphology) c s dng trong sinh hc cpn qu trnh nghin cu dng cu trc ng thc vt. Tng t trong x l nh chta gi l Php ton hnh thi (Mathematical Morphology). Chng ta s dng php tonhnh thi nh mt cng c tch cc thnh phn ca nh cho php biu din v mit hnh dng i tng trong nh thng qua vng, bin,... Ngoi ra chng ta cn sdng php ton hnh thi tc ng ln i tng nh ng nh(Closing), mnh(Opening),tm xng lm mnh

3.1. S dng php ton hnh thi trong c lng nghing vn

bn Trong qu trnh nhn dng v x l nh vn bn cng nh trong hu ht cc phn

mm s dng k thut nhn dng k t(Optical Character Recognition ) haycc hthng phn tch vn bn( Document Analaysis System ), chng ta phi tri qua nhiucng on phc tp v mt trong nhng cng on l c lng gc nghing cton b vn bn. Chnh iu ny s to iu kin thun li cho vic thc hin cc btip theo trong qu trnh nhn dng sau ny. Nguyn nhn ca vic to ra gc nghingvn bn c th do vic copy, in, fax hoc scan .Trong hu ht cc phng php gi

quyt bi tonnhn dng k t, vic vn bn b nghing nh hng rt nghim trngn vic: tch khi, phn tch b cc, thut ton nhn dng k t, ngay c khi gnghing ca vn bn rt nh vo khong 5o.

c nhiu cch tip cn nhm gii quyt vn nhiu mc khc nhau nhcc phng php do Baird hoc ca Hinds v cc ng nghip ngh. Tuy nhinchng u gp nhng kh khn nht nh ( chnh xc khng tt, gc nghing quln ). C hai tiu chun c bn nh gi chnh xc ca vic chnh nghing nvn bn. Tiu chun u tin l gii hn gc c lng v d gc c lng ca v bn gii hn trong khong [-10o, 10o]. Th hai l s lng gc nghing trong ton vn bn ngha l vn bn c mt hay nhiu gc nghing. Trong phm vi ca ti ny, tach quan tm n vn bn c mt gc nghing. i vi mt vi phng php xc nhgc nghing vn bn, phi c mt s rng buc i vi nh vn bn u vo nh cch, khong cch gia cc dng, ngn ng s dng trong vn bn, thm ch b c ca vn bn cng b rng buc, v d nh mt vi thut ton i hi phi c slng thnh phn lin thng l ch hay phi c tht t nhiu.

Trong ti ny, ta s dng thut ton cc php bin i hnh thi c lng

gc nghing vn bn. Thut tonny c bit thch hp cho cc vn bn c du nh


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ting Vit, ting Php, i vi loi vn bn ny, vic xut hin ca cc du, ph ph trn, phn ph di ca ch cng nh nhiu lm cho cc dng ln cn nhau cxu hng dnh li vi nhau (hnh 3.1). Chnh iu ny lm cho cc phng php

xc nh gc nghing vn bn trc y b tht bi. Bng cch s dng cc php biihnh thi, du nhiu s b tch khi nh vn bn. N gip cho vic xc nh ccdng vn bn d dng hn. Qu trnh loi b nhiu v du nh vo cc php bin hnh thic th lm mt mt s thng tin ca vn bn. Tuy nhin, s mt mt khng quan trng, v gc nghing ca vn bn c c trng bi cc dng vn bngay c sau khi loi b phn ph trn v ph di.

Hnh 3.1: C c dng vn bn c xu hng dnh li vi nhau do nh hng ca du

Cc dng vn bn s c hnh dng ha bng cc php bin i nh ng, mVic s dng cc php bin ihnh this rt thun li v nhiu s c loi b. iu

ny rt thch hp trong cc vn bn c du nhtingvit, tingphp,Trong phng php ca Chen, cc php ng, m vi cc phn t cu trc khc nhau c s dngSau khi thc hin cc php bin i ny, cc dng vn bn s bin thnh cc vt thondi ri p dng mt phng php khc xc nh hng ca cc dng vn bnTrong qu trnh p dng, c th xut hin mt s hng sai lch chng c to ra bnhiu v cc thnh phn lin thong khng phi l text. Mt thut ton khc l goodlines selection s c s dng. Trong thut ton ny, cc dng c hng gn ginvi hng c bn ca ton vn bn s c chn ra. Cui cng, gc nghing ca tovn bn s c c lng t cc hng chn ra ny. Tuy nhin, ph ng php nych p dng c cho cc vn bn c nghing l 5o v chnh xc l 0.5o (c kim tra trn b th vin nh UW English Document Image Database).

Das v Chanda cng dng cc php ng, m trn cc dng vn bn vi haithnh phn cu trc dng ng thng v dng hnh vung nh. nh vn bn thc hin php m s c qut theo chiu dc ghi nhn cc pixel c s chuyn t 1 sang 0, cng chnh l base line ca dng vn bn. Cc dng c chiu di lnhn mt ngng cho trc s c chn ra v gc ca ton b vn bn l trung v c


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gc cc dng vn bn ny. Gii hn ca phng php ny l n ch thc hin tt vi cc nh vn bn c gc nghing di 15o.

Najman li hin thc cc php ton hnh thi theo mt cch khc. tng chnhl tm ra gc quay ti u nht ca cc phn t cu trc bng cch cc i ha din tca cc vt thng to ra t cc php tonhnh thi. Trong hng tip cn ny, thutton Run-Length Smoothing closing (RLSA) cng c s dng ti u ha gcquay ca phn t cu trc. Gc quay ny cng chnh l gc nghing ca ton b vn bn. Nhc im ln nht ca c ba phng php va trnh by trn l chng phthuc vo kch c ch, khong cch gia cc dng, khong cch gia cc k t ln cntrong vn bn, Do cc thut ton ny rt ph thuc vo cc tham s thc nghimv khng th xc nh cc tham s ny mt cch t ng.

3.1.1. M t phng php Trc ht l qu trnh tin x l, y l qu trnh dng lc nhiu,tchdu v

nhng thnh phn lin thng ln. Trong qu trnh ny cc tham s nh chiu caovchiu rng c trng ca ch s c t ng xc nh da trn vn bn u vo. Sau, thut ton c lng th s xc nh c khong m gc nghing ca vn bn r vo. Cui cng, vi nhng tham s tm thy bc u tin, ta s thc hin cc phng v m cho cc dng vn bn to thnh cc vt to thun li cho bc xc ngc nghing tip theo. Sau mt thut ton n gin s c dng xc nh g

ca mi dng vn bn v gc nghing ca ton b vn bn cng s c tm thy dtrn gc nghing ca cc dng vn bn. Trong phm vi ti ta ch quan tm n bcs dng php ton hnh thi.

3.1.2 . p dng php ton hnh thi Trong bc ny, chng ta s thc hin cc php ng v m cho cc dng vn

bn. Php ng dng ni cc k t trong mt t, v cc t trong mt dng, php m loi b cc thnh phn lin thng rt nh, cng nh cc phn ph trn hay phn phdi ca k t. Do cc dng vn bn s tr thnh cc vt thon di.

Tuy nhin, thc hin cc php ng, m mt cch hiu qu nht ta cn xcnh kch c v hnh dng ca cc phn t cu trc tht chnh xc. Trong thut tonny, ta s dng mt cch tnh ton n gin c m t nh sau: Trung im ckhong m gc nghing vn bn thuc v tm c trong bc c lng th chnhgc quay ca phn t cu trc. Nu khong m gc nghing vn bn ri vo [30o, 50o],th gc quay ca phn t cu trc s l 40o. Ta chia gc quay ca vn bn thnh 9 phnv mi phn tng ng vi 20o l v mi gc quay ca phn t cu trc c th phhp cho tt c cc vn bn c gc nghing trong khong [ 10o, + 10o], ngha lkhong chnh lch l 20o. Qua thc nghim bng cch quan st v th nghim trn


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mt s lng ln cc nh vn bn, cho thy vic xc nh gc quay cho cc phn tcu trc l rt quan trng. N gip cho kt qu ca cc php ng m l ng nnht. Vi mt phn t cu trc ph hp, th ch cc t trong cng dng mi kt hp l c vi nhau trong khi t trong cc dng khc nhau s vn ri nhau .

Hnh 3.2 : Nhng khong gc nghing khc nhau c s dng c lng gcnghing ph hp cho phn t cu trc.Gi I l nh thu c sau khi kh nhiu, du v nhng thnh phn lin thng ln.

nh I co c to ra nh sau:

oncmco E E I I , (1.45)

Trong nhng phn t cu trc 13 v 22 c chn tng ng vi E c v E o;m v n c xc nh bi max{W / 2 z, H / z} v max{W / 3 z, H / 2 z}; vi z l thu

nh thch hp ca nh, z c tnh nh sau: z = min{W / 4, H / 5}

c tnh bng thut ton c lng th; v cm E v on E l nhngkt qu ca php quay nhng phn t cu trc cm E v on E bi gc (hnh3.3 l mt minh ha ca nh I co).

Mt ln na, c th thy r rng rng kch thc v gc nghing ca phn t ctrc c xc nh mt cch t ng v ch da trn nh a vo ban u. Vi vitnh ton t ng ny, thut ton ny c th p dng gii quyt vn c lnggc nghing ca nhng vn bn c gc nghing ty .

(a) (b) (c)


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(d) (e) (f)

Hnh 3 .3: Mt vi v d ca vic s dng php ng v m vi nhng phn t cutrc nghing. Hnh 3.3a v 3.3d l nhng nh a vo ban u. Hnh 3.3b v 3.3e lnhng kt qu ca vic p dng bc tin x l, c lng th, v php ng tngng vi hnh 3.3a v 3.3d. Hnh 3.3c v 3.3f l nhng kt qu ca vic p dng phpm tng ng vi hnh 3.3b v 3.3e.

3.2. ng dng php ton hnh thi trong tch dng vn bn Thut ton xc nh b cc vn bn thc cht l tm cch chia nh vn bn ra

thnh nhiu khi m mi khi s c trng cho mt vng vn bn. Sau mi khny s c chia thnh nhiu dng, ri mi dng c th c chia thnh mt honhiu t, tng t mi t s c chia thnh nhiu k t.

c rt nhiu phng php a ra tch dng vn bn, phng php tcdng rt n gin da trn cc php ton hnh thi v php chiu ly lc . Phn php gm 3 bc cn bn sau:

Bc 1: Dng cc php ton hnh thi t lem dng vn bn. Bc 2: Ly lc chiu i vi mi khi vn bn theo trc Oy. Bc 3: Xc nh dng vn bn trong mi khi.

Trong ba bc trn ta ch quan tm ti bc 1, l khu t lem dng vn bn.

3.2.1. S dng php ton hnh thi t lem dng vn bn Vic xc nh dng vn bn trong thut ton c a ra y ch yu da v

cc pixel en v mt phn b ca chng. Trong bc u tin ny,ta s tin hnh tcc dng vn bn thnh cc vt lem thon di, mc ch l lm tng s lng pixel enc trong mt dng vn bn. Mt iu lu rng, vic t lem cc dng vn bn chnhm mc ch xc nh cc vt ct ca dng vn bn ch khng lm nh hng tnh vn bn ban u. Chnh vic lm ny s lm tng chnh xc ca thut ton x


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nh dng vn bn nht l i vi cc dng vn bn cui cng trong khi ch c mthai hoc rt t t.

Cch thc t lem dng vn bn trong giai on ny c thc hin kh gingvi cch thc t lem dng vn bn trong giai on xc nh gc nghing vn bn. Tuynhin, c mt s khc bit duy nht l vic t lem ny c thc hin trn vn b c chnh nghing.

Hnh 3.5: Hai dng vn bn c t lem. Sau khi thc hin bc ny, vn bn s c t trng bi cc vt en thon d

nh vic xc nh dng vn bn s c thc hin d dng hn.

Khi tin hnh t lem vn bn da trn cc php ton hnh thi, nhiu b loi b. Cng trong qu trnh t lem, du, cc acender, descender b loi b nn m bo chnh xc ca vic tch dng v khng lm mt du trong vn bn ting vit, atin hnh m rng bin cho dng mt khong T.

(a)

(b)Hnh 3.6: (a) Mt dng ct nhng khng m rng bin, (b) Dng ct c m rng bin.

Trn y l mt on vn bn c tch dng. Kt qu qu trnh tch dngl danh sch cc dng, y chnh l u vo cho vic tch t v tch k t tip theotrong qu trnh xy dng v phn tch b cc vn bn.

- Ngoi ra cn rt nhiu cc ng dng nh pht hin i tng chuyn ng, pht hin hnh dng i tng thng qua xng i tng trong nh


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CHNG IV. CI T CHNG TRNH

4.1. Gii thiu chng trnh Chng trnh c xy dng trn nn C#, minh ha cc php ton hnh thi

gm c, php co nh phn (Erosion), php gin nh phn (Dilation), php ng nh(Closing), php m nh (Opening),tm bin (Edge direction), v tm xng(Skeleton).

Giao din chng trnh nh sau:

Chng trnh gm c 8 phn v c nh s th t tng ng nh hnh minha trn. Trong :

- S1,2,3,4ch ra cc thnh phn iu khin thc hin qu trnh tc ng ln nh gc.

- S6,7 ch ra thnh phn dng hin th hnh nh gc v hnh nh kt qusau khi x l, phn 5 thanh trng thi x l (startus bar).

- Cui cng s 8 l nt thot ng dng.


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4.2. Hng dn s dng S 1:

Open: Np nh cn x l vo picturebox

(S 6).Save: Lu nh x l ra nh dng

Image file.

S 2:

nhm Operation: La chncc phpton tc ng ln nh gc. Php gin nh

phn (Dilation), php co nh phn (Erosion),Php m nh (Opening), Php ng nh(Closing).

Nhm Kernel Shape: La chn ccdng ca phn t cu trc, tc ng ln i tng trong nh. Dng hnh vun(Square), dng hnh trn (Circle), v dng hnh du cng (Cross).

S 3:

Kernel Side: Dng la chn kchthc ca phn t cu trc.

Morphology: Thc hin php ton hnhthi tc ng ln nh khi chn php ton vdng c phn t cu trc tng xng.

S4:

Edge direction: Pht hin bin ca itng trong nh.

Skeleton: Bt u qu trnh lm mnh itng trong nh.

S 5:

Status bar: Thanh trng thi biu th tin x l nh ca chng trnh. Cho mt th d,

nu s dng php co nh phn hay gin nh phn, th tin ny s chy mt ln, b


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v thc hin php co nh phn v php gin th ta ch thc hin thut ton mt ln Nu s dng vi php ng nh v php m nh th s chy hai ln, v thc himt trong hai php ton ny ta phi thc hin hai ln thut ton co v gin nh phn. i vi cc php ton khc th chc nng biu th trng thi ca n cng tng t.

4.3. Thc Nghim Chng trnh c ci t thut ton x l nh nh phn bng cc php to

php gin nh phn, php co nh phn, php ng nh, v php m nh vi cc phn tcu trc dng hnh vung, hnh trn, hnh ch thp, c kch thc khc nhau (3x3,4x4, 5x5, 6x6, 7x7).

Quan st hnh 4.1ta thy: T mt nh nh phn xung cp, sau khi s dng php gin nh phn vi phn t cu trc dng trn, kch thc 4x4, ta c nh mcc nt t c ni lin li v r rng hn. Tng t nh vy, i vi cc phn t cu trc dng vung, dng ch thp. u s cho ta kt qu mi l cc i tng c ci thin r rt , vi phn t cu trc c kch thc cng ln th i tng cgin.

Hnh 4.1: Thc nghim gin nh phn hnh nh vi cu trc 4x4.

Th d nh vn trng hp trn, ta xt thut ton gin nh phn trn nh vi phnt cu trc 7x7 ta s c nh vi cc i tng trong nh c b dy ln hn:


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Hnh 4.2 : Thc hin gin nh phn hnh nh vi phn t cu trc 7x7.Cnghnhnh nh phn nh trn ta s dng php co nh phn hnh nh vi phn

t cu trc 4x4. Bi v vi php ton ny i tng c xu hng co vo nn ta c ths dng lc cc im nh nh tha trong nh nh phn. V vy ty theo yu cu mta ty chn kch thc phn t cu trc tng ng lc cc chi tit quan trng trnnh.

Quan st hnh4.3 ta c th thy, vi phn t cu trc 4x4, khi ta ci t thutton vtc ng ln nh th tp hp nhng im nh c kch thc ln s khng bloi b bi phn t cu trc, trong khi cc tp hp im nh nh hoc im nh rinr s b loi b. Nh trn phn l thuyt chng 2 gii thiu, trong mt s tr

hp ta c th kt hp php co nh phn v php gin nh phn lc cc im nhkhngd tha trong nh. Tt nhin ch t yu cu i vi nh nh phn.

Hnh 4.3 : Thc nghim php co nh phn trn hnh nh vi phn t cu trc 4x4.Xt nh nh phn, i tng l mthnh vung khot (Hnh 4.4), khi ta s dng

thut ton m nh vi phn t cu trc dnghnh trn, kch thc 7x7 th ta c nh

mi vi cc gc hng ra ngoi b lm trn, cn cc gc hng vo trong th vn gi


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nguyn.Vi c trng ny ta c th p dng lm trn cc ngnh hng ra ngoi cai tng u ra, tronghnh 4.2.Cng tng t nh php co nh phn, php gin nh phn, kch thc ca phn t cu trc cng ln th trn gc cnh hng ra ngocng cao.

Hnh 4.4 : Thc nghim php m nh trn hnh nh vi phn t cu trc trn 7x7.

Trong hnh v 4.5 ta thy, cc nghnh hng ra ngoi ca i tng trong nhnh phn (nt ch) c lm trn. Thut ton rt hiu qu trong khi phc vn bnti liu xung cp.

Hnh 4.5 : Thc nghim m nh lm trn gc ca i tng trong nh nh phn.

Ty thuc vo phn t cu trc m ta c i tng mi c thuc tnh khcnhau. Th d, vi phn t cu trc dng hnh vung th cu to i tng trong khng thay, cn i vi phn t cu trc hnh ch thp th s to ra gc cnh ca itng mi mt gc vung hng vo (Hnh 4.6).


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Hnh 4.6 : Thc nghim php m nh vi phn t cu trc hnh ch thp, kchthc 7x7.

Ngc li vi php m nh, php ng nh vi phn t cu trc trn li lm trcc gc hng vo trong i tng (Hnh 4.7), v trn ca i tng trong nhcng ph thuc vo kch thcca phn t cu trc.

Hnh 4.7 : Thc nghim php ng nh trn phn t cu trctrn 7x7.

i vi phn t cu trc hnh dng ch thp, v kch thc 7x7, cc gc hnvo s c phn t cu trc to ln mt gc vung hng ra ngoi (Hnh 4.8).


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Hnh 4.8 : Thc nghim php ng nh vi phn t cu trc hnh dng ch thp,kch thc 7x7.

Tiptheo, ta xt mt hnh nh nh phn i tng l ch A mu trng (Hnh4.9),ta p dng thut ton tm xng trn hnh nh ny. Kt qu thu c l tp hp ccim mu pha bn trongA.

Hnh 4.9: Thc nghim tm xng i tng trn nh nh phn.

Cui cng l thut ton pht hin bin i tng. u tin thut ton s thc hico nh phn gia i tng v phn t cu trc, sau ly i tng ban u tr i kqu co nh phn, ta s c bin ca i tng, dy ca bin ty thuc vo phn

cu trc.

Hnh 4.10 : Thc nghim tm bin ca i tng.


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Kt lun Php ton hnh thi l mt mng v cng quan trng trong x l nh s,cc

ti v php bin i ny cng ang c nhiu ngi quan tm, bi vqua cc thut

ton v php tonc s ta c th m rng v pht trin nhng bi ton khcc linquan n lnh vc quan st thm d, tr tu nhn to, chng hn nh ng dng vicamera theo di qua ccthut ton nhn bit i tng chuyn ng, hoc ghp itng trong hai hnh nh thng qua cc c im hoc im tng ng

Cc kt qu t c:

- Trnh by tng quan v x l nh, lch s pht trin v phng thc hot ng.

- Trnh by h thng cc khi nim c bn ca php ton hnh thi di gc x l nh; cc khi nim, cc tnh cht v ng dng c bn trong x l v biu dinhnh dng i tng. ng thi qua gii thch v minh ha c th v a ra milin h gia cc php ton vi nhau.

- Thc nghim cc php ton, thut ton qua chng trnh xl.

Qua phn tch trn ta c th rt ra kt lun:

Cc php ton gin nh phn (Dilation), co nh phn (Erosion), Php m nh(Opening), php ng nh (Closing), l cc php ton c s trong php ton hnh thi,cc thut ton trch bin (Boundary), lm y (Region filling), tch thnh phn linthng (Extraction of connected compoments), bao li (Convex Hull), lm mnh(Thinning), tm xng (Skeleton), u c xy dng t cc php ton hnh thi c bn. Cc php ton l iu kin, cng nh tin tm hiu nghin cu cc thutton khc c tnh ng dng cao trong x l nh ni ring v trong thc t i sng nchung.

Php ton hnh thi l mt ti rt rng, cn rt nhiu thi gian mi c th tmhiu v nghin cu v n. Trong thi gian ti nu c iu kin em s tip tc tm hicc thut ton lc nhiu, tng cng nh, v phn on nh thng qua cc php tohnh thi.


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Ti liu tham kho:

Ting Vit [1].TS. Nng Ton , TS. Phm Vit Bnh(2007) - Gio Trnh Mn Hc X L

nh , trng H thi nguyn, khoa CNTT , tr. 26 ~ 27, tr. 44 ~ 49.

[2]. PGS. Nguyn Quang Hoan (2006) - Gio Trnh X L nh, hc vin cngngh bu chnh vin thng,tr. 4

[3]. Lng Mnh B, Nguyn Thanh Thy (2003)- Nhp Mn X L nh S, Nh xut bn Khoa hc v K thut, tr. 7 ~ 10.

[4]. Phm Vit Bnh (2006) Pht trin k thut d bin, pht hin bin v ngdng, lun n tin s khoa hc,tr. 5, tr. 13~17

Ting Anh [1].Chen, S.( 1995): Document Layout Analysis Using Recursive Morphological

Transforms, PhD thesis, Univ. of Washington,.

[2]. Das, A., Chanda, B. (2001): A Fast Algorithm for Skew Detection of Document Images Using Morphology. Int. J. Document Analysis and Recognition 4,tr. 109~114.

[3]. Frank Y. Shih(2009) -Image Processing and Mathematical MorphologyFundamentals and Applications , tr. 11~ 24,tr 37~52.

[4]. Hinds, S.C., Fisher, J.L., DAmato, D.P.USA (1990): A Document SkewDetection Method Using Run-Length Encoding and the Hough Transform. In: Proc.10th Int. Conf. on Pattern Recognition, Atlantic City PA, tr. 464~468.

[5]. Najman, L. USA (2004): Using Mathematical Morphology for Document

Skew Estimation. In: Proc. of SPIE Conf. on Document Recognition and Retrieval XI,San Jose, California, tr. 182~191.

[6]. J.B.T.M Roerdink- Computer vision And Mathematical Morphology.

[7]. Rafael C. Gonzalez & Richard E. Woods (1992)- Digital Image ProcessingSecond Edition, tr. 20 ~ 26, tr. 530 ~ 560.


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Website[1]. http://homepages.inf.ed.ac.uk/rbf/HIPR2/skeleton.htm

[2].http://en.wikipedia.org/wiki/Morphological_image_processing#Properties_of

_the_basic _operators [3]. http://www.funmorph.com/

[4]. http://www.ph.tn.tudelft.nl/Courses/FIP/noframes/fip-Morpholo.html
http://homepages.inf.ed.ac.uk/rbf/HIPR2/skeleton.htmhttp://homepages.inf.ed.ac.uk/rbf/HIPR2/skeleton.htmhttp://homepages.inf.ed.ac.uk/rbf/HIPR2/skeleton.htmhttp://en.wikipedia.org/wiki/Morphological_image_processing#Properties_of_the_basic%20%20%20%20%20%20%20%20%20%20_operatorshttp://en.wikipedia.org/wiki/Morphological_image_processing#Properties_of_the_basic%20%20%20%20%20%20%20%20%20%20_operatorshttp://en.wikipedia.org/wiki/Morphological_image_processing#Properties_of_the_basic%20%20%20%20%20%20%20%20%20%20_operatorshttp://en.wikipedia.org/wiki/Morphological_image_processing#Properties_of_the_basic%20%20%20%20%20%20%20%20%20%20_operatorshttp://www.funmorph.com/http://www.funmorph.com/http://www.funmorph.com/http://www.ph.tn.tudelft.nl/Courses/FIP/noframes/fip-Morpholo.htmlhttp://www.ph.tn.tudelft.nl/Courses/FIP/noframes/fip-Morpholo.htmlhttp://www.ph.tn.tudelft.nl/Courses/FIP/noframes/fip-Morpholo.htmlhttp://www.ph.tn.tudelft.nl/Courses/FIP/noframes/fip-Morpholo.htmlhttp://www.funmorph.com/http://en.wikipedia.org/wiki/Morphological_image_processing#Properties_of_the_basic%20%20%20%20%20%20%20%20%20%20_operatorshttp://en.wikipedia.org/wiki/Morphological_image_processing#Properties_of_the_basic%20%20%20%20%20%20%20%20%20%20_operatorshttp://homepages.inf.ed.ac.uk/rbf/HIPR2/skeleton.htm

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