bao ve ban quyen cac sp do hoa vecto

8/7/2019 bao ve ban quyen cac sp do hoa vecto

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i hc Thi Nguynkhoa cng ngh thng tin

NG THI H

NGHIN CU K THUTBO V BN QUYN CC SN PHM

HA VECT

Lun vn thc s : KHOA HC MY TNH

Thi Nguyn - 2009


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i hc Thi Nguynkhoa cng ngh thng tin

NG THI H

NGHIN CU K THUTBO V BN QUYN CC SN PHM

HA VECT

Chuyn ngnh: KHOA HC MY TNHM s: 60 48 01

Lun vn thc s : KHOA HC MY TNH

NGI HNG DN KHOA HC

PGS.TS NG VN C

Thi Nguyn - 2009


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iv

S ha bi Trung tm Hc liu i hc Thi Nguyn http://www.lrc-tnu.edu.vn

DANH MC CC CH VIT TT

Chvit tt

Din gii ngha

DCT Discrete Cosine Transform Bin i Cosin ri rcIDCT Invert Discrete Cosine Transform Bin i ngc DCTDFT Discrete Fourier Transform Bin i Forier ri rcIDFT Invert Discrete Fourier Transform Bin i ngc DFT.DWT Discrete Wavelet Transform Bin i Wavelet ri rc

Steganography Giu tin, Vit phIntrinsic Steganography Giu tin c x lPure Steganography Giu tin n thun

Watermarking nh du n, thy vn, thy n

WatermarkM du bn quyn, mu tinmt

IDWT Invert Discrete Wavelet Transform Bin i ngc DWTPN Pseudo Noise gi nhiuFFT Fast fourier transfer Bin i Fourier nhanhGIS Geographic Information System H thng thng tin a l

PRNS Pseudo random number sequence Dy s gi ngu nhinFT Fourier Transfer Bin i Fourier


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i

MC LC

Trang

Trang ph ba

Li cam oan

Mc lc ........................................................................................................ i

Danh mc cc k hiu, ch vit tt ............................................................... iv

Danh mc cc bng ...................................................................................... v

Danh mc cc hnh (hnh v, hnh chp, th) ........................................... iv

M U: .................................................................................................... 11. T VN ............................................................................... 1

2. MC CH CA LUN VN .............................................................. 2

3. B CC LUN VN............................................................................. 3

NI DUNG..................................................................................................

CHNG 1: TNGQUAN V GIU TIN ................................................ 4

1.1.Cc khi nim c bn v giu tin ........................................................... 4

1.1.1.nh ngha: ....................................................................................... 4

1.1.2.Phn loi cc k thut giu tin ............................................................ 5

1.1.3.Vi nt v lch s giu tin ................................................................... 9

1.1.4.Cc yu cu i vi giu tin cho nh .................................................. 10

1.1.5.M hnh k thut giu tin ................................................................... 12

1.1.6.Cc ng dng ca k thut giu tin..................................................... 13

1.1.7.

Cc kiu nh du n.......................................................................... 15

1.2. Giu tin trong nh nhng c trng v tnh cht ................................... 15

1.2.1.Giu tin trong nh............................................................................... 15

1.2.2.Nhng c trng v tnh cht ............................................................. 16

1.2.3.Cc phng php giu tin ................................................................... 19


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1.3. Kt lun chng .................................................................................... 21

CHNG 2: GIU TIN TRONG BN VC T ................................. 23

2.1. Bn ................................................................................................... 23

2.2. Thy vn bn vc t......................................................................... 25

2.3. c im ring ca thy vn bn Vc t.......................................... 27

2.3.1.D liu bn vc t......................................................................... 27

2.3.2. chnh xc ca bn vc t.......................................................... 28

2.3.3.Cc kh nng giu tin ......................................................................... 29

2.3.3.1.

Giu tinhnh hc ............................................................................. 292.3.3.2.Giu tin vo nh ............................................................................. 30

2.3.3.3.Sp xp i tng ............................................................................ 30

2.3.3.4.Gim nhiu ...................................................................................... 30

2.4. Thut ton thy vn............................................................................ 31

2.4.1.Thut ton trong min khng gian ...................................................... 31

2.4.2.Thut ton trong min bin i (min tn s) .................................... 36

2.4.2.1. Min DFT : ................................................................................... 37

2.4.2.2. Min DWT : .................................................................................. 39

2.4.2.3.Min DCT ...................................................................................... 41

2.4.3.Thut ton nhn c t m hnh ba chiu ........................................ 41

2.6. Kt lun chng .................................................................................... 42

CHNG 3: THUT TON GIU V TCH TIN TRONG BN

VC T ....................................................................................................... 43

3.1. Giu tin trong nh en trng ................................................................. 43

3.1.1.Thut ton giu tin c s.................................................................... 43

a. Tin x l .................................................................................................. 43

b. Qu trnh thc hin giu tin ...................................................................... 43


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iii

3.1.2. Thut ton trch tin ............................................................................ 45

a. Tin x l: ................................................................................................. 45

b. Qu trnh trch tin: .................................................................................... 45

3.2. Bin i Fourier.................................................................................... 45

a. Bin i Fourier....................................................................................... 45

b. Bin i Fourier lin tc ........................................................................... 47

c. Bin i Fourier ri ................................................................................. 49

3.2.1.Nhng bin i Fourier trong vc t................................................... 51

3.3. Kt lun chng .................................................................................... 51CHNG 4: CHNG TRNH TH NGHIM ........................................ 52

4.1. M t bi ton th nghim..................................................................... 52

4.2. nh dng cu trc tp Shapefile .......................................................... 53

4.2.1. T chc d liukhun mu ca Shapefile ......................................... 54

4.2.2. Quy c v tn tp.............................................................................. 54

4.2.3. Kiu d liu ...................................................................................... 55

4.2.4. Cu trc ca Main file ....................................................................... 55

4.2.5. Cu trc ca tp ch s (Index file) .................................................... 64

4.2.6. Cu trc ca tp cha c s d liu .................................................. 65

4.3. Quy trnh giu thng tin......................................................................... 65

a. Phn tch thut ton .................................................................................. 65

b. Giu thng tin........................................................................................... 66

4.4. Quy trnh tch thng tin ......................................................................... 69

4.5. Kt lun chng .................................................................................... 70

KT LUN.................................................................................................. 71


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vi


DANH MC CC HNH V

Tn hnh ngha

Hnh 1.1 Phn loi cc k thut giu tin (Fabien A.P. Petitcolaset al., 1999)

Hnh 1.2 Qu trnh giu tin v tch tin.

Hnh 2.1 Cc lp bn phn lp i tng

Hnh 2.2 Th gii thc v bn vect

Hnh 4.1 Cu trc ca tp chnh

Hnh 4.2 Cu trc ca tp ch s.

Hnh 4.3 M t mt bn vector n gin

Hnh 4.4 Giao din chng trnh DEMO


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1

M U:

1. T VN

Ngy nay, vi s ra i v pht trin ca mng Internet. Mi ngi u cth kt ni vo Internet, tm kim thng tin mt cch d dng thng qua nh

cung cp dch v mng.

S pht trin nhanh chng ca khoa hc k thut trn nhiu lnh vc c

bit l trong lnh vc a phng tin (multimedia) lm cho s sn xut, qun l

v phn phi cc sn phm ny: hnh nh, m thanh rt d dng. Cng vi s

ph bin rng ri cc mng internet tc cao lm cho qu trnh phn phichng tr nn rt nhanh chng, d dng, em li nhng thun li to ln thng

qua h thng thng mi in t.

Vi mi trng m v tin nghi nh th, cc h thng mng hin i tr

thnh phng tin phn phi ti liu mt cch nhanh chng v kinh t. Tuy

nhin, vic phn phi mt cch ph bin cc ti nguyn trn mng hin nay lun

gp phi vn nn sao chp v s dng khng hp php nh: Xm phm bn

quyn, truy cp tri php, xuyn tc, gi mo thng tin

i i vi s pht trin ca cng ngh my tnh th tnh trng s dng b t

hp php cc sn phm s (tp tinti liu, chng trnh, m thanh v hnh nh...)

ngy cng tng, do cc tp tins c th sao chp d dng gia cc my tnh. Dn

ntnh trng vi phm bn quyn s ang xy ra hng ngy, hng gi trn khp

th gii. Nhm bo v cc sn phm s khng b s dng tri php, song song

vi vic ku gi thc t gic thc thi lut bn quyn, cc cng ty cng nghln trn th gii v ang thc hin cc gii php k thut kim sot bn quyn

s. Mt trong nhng vn c t ra l lm sao bo v quyn s hu i vi

cc sn phm a phng tin ny.


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2

ng trc tnh hnh vn v bo mt thng tin hin nay lun nhn

c s quan tm c bit trong nhiu lnh vc. T xaxa c nhiu cch

bo mt thng tin, mt trong nhng phng php dng rt sm bo v quyns hu i vi ni dung ca cc sn phm a phng tin l m ho. Ni dung

ca sn phm c m ho v gi cho ngi s dng. Ngi s dng ch c

c cc thng tin ny khi nhn ckho gii m i km. Phng php m

ho trn ch hiu qu trong vic truyn thng tin nhng khng hiu qu trong

vic bo v quyn s hu. Sau khi ngi s dng gii m c th s nhn

bn v phn phi li sn phm . Ngy nay phng php giu thng tin trongcc sn phm a phng tinc dng ph bin v ngoi vn bo mt cn

bo v bn quyn, chng nhn bn bt hp php, chng truy cp tri php, chng

xuyn tc, chng gi mo thng tin

Gii php bo mt thng tin c s dng ph bin nht l dng cc h

mt m [1], [3]. Vi gii php ny, thng tin ban u s c m ha thnh bn

mt m mang nhng gi tr v ngha. Chnh iu ny lm ny sinhnghi ng v

ngi s dng tm mi cch thm m. Ngc li, nuem thng tin giu vo

trong mt i tng khc, mt bc nh F chng hn, s thu c mt nh F hu

nh khng sai khc vi F khi nhn bng mt thng. y l tng ca phng

php giu tin (data hiding) trong mi trng nh, giu tin mt [5], [6], nh du

bn quyn [7], [8], v nhiu ng dng khc

2. MC CH CA LUN VN

Giu tin l mt lnh vc rng ln, trong lun vnny nghin cu cc kthut giu tin trong nh ri p dng cho bn , mt trong nhng vn c

ng dng kh rng ri. thc hin vic giu tin trong bn , tng c bn l

bin i mt s thuc tnh ca cc im trn bn theo mt s thut ton nht


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3

nh, nhm m bo rng d liu bn , v mt th gic, khng sai khc l m y

so vi bn gc, ng thi, sau khi nhn c bn ch, s dng quy t rnh

gii m vi cc kha ph hp, ta c th trch c thng tin cn du.

Ni dung ca lun vn nytp trung nghin cu cc phng php giu tin

trong nh bitmap, nh vector, cc phng php thy vn s [14], [15], mt s

phng php giu tin da vo cc php bin i DCT, DFT, DWT.

3. B CC LUN VN

Lun vn gm trang, c trnh by trong 3 chng, c phn m u,

phn kt lun, phn mc lc, phn ti liu tham kho. Cc ni dung c bn calun vnc trnh by theo cu trc nh sau:

Chng 1: Tng quan v giu tin

Trnh by tng quan v giu tin, phn tch cc yu cu i vi giu tin cho

nh, trnh by mt s loi hnh giu tin v cc yu cu i vi giu tin trong nh.

Bn cnh trnh by mt s m hnh giu tin v cc ng dng ca chng,

nhng c trng v tnh cht ca giu tin trong nh. Ngoi ra, mt ni dung rt

quan trng trong chng ny l cc phng php giu tin v cc thut ton

giu tin.

Chng 2 : Cc k thut giu tin trong nh

Tp trung phn tch, nh gi cc thut ton giu tin trong nh, k thut

bin i Fourier. Bin i Fourier trong nh vector, cc thut ton giu v tch

thng tin trong nh vector.

Chng 3: Xy dng chng trnh

Trnhby cu trc bn dng shapefile v bin i DFT, xy dng thut ton

nhng tch watermark.


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4

CHNG 1: TNG QUAN V GIU TIN

1.1.Cc khi nim c bn v giu tin1.1.1.nh ngha:

Qua nghin cu cc phng php giu tin, ta c th nh ngha n nh

sau:

Giu thng tin lk thut nhng(embedding) mt lng thng tin s no

vo trong mt i tng d liu s khc.[18]

Trong khun kh ca lun vn, cc thut ng giu tin, giu thng tinv giu d liu; thut ng nh du n,thy vn s v thy vn; Tng

t ta cng c m v m nh du bn quync xem ng ngha. Mt

trong nhng yu cu c bn ca giu tin l m bo tnh cht n ca thng tin

c giu ng thi khng lm nh hng n cht lng ca d liu gc.

S khc bit ch yu gia m ho thng tin v giu thng tin l m ho

lm cho cc thng tin hin r l n c c m ho hay khng tc l giu i

ngha ca thng tin cn, cn vi giu thng tin th ngi ta s kh bit c l

c thng tin giu bn trong tc l giu i s hin din ca thng tin. V bn cht

giu tin gn vi nn d liu hn. Tm li giu tin v m ha c mi quan h mt

thit vi nhau, cng xy dng mt h thng an ton v bo mt thng tin.

K thut giu thng tin nhm mc ch m bo an ton v bo mt thng

tin hai kha cnh. Mt l bo mt cho gi liu c em giu (embedded

data), chng hn nh giu tin mt: thng tin mt c giu k trong mt itng khc sao cho ngi khc khng pht hin c (steganography), hai l

bo mt cho chnh i tng c dng giu tin (host data), chng hn nh

ng dng bo v bn quyn, pht hin xuyn tc thng tin (watermarking).... Hai


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5

kha cnh khc nhau ny dn n hai khuynh hng k thut ch yu ca giu

tin. Khuynh hng th nht l giu tin mt (Steganography). Khuynh hng ny

tp trung vo cc k thut giu tin sao cho thng tin giu c nhiu v quantrng l ngi khc kh pht hin c mt i tng c b giu tin bn trong

hay khng. Khuynh hng th hai l thu vn s (watermarking). Khuynh

hng thu vn s nh giu vo i tng nhm khng nh bn quyn s hu

hay pht hin xuyn tc thng tin. Thu vn s c min ng dng ln hn nn

c quan tm nghin cu nhiu hn v thc t c nhiu nhng k thut dnh

cho khuynh hng ny.1.1.2.Phn loi cc k thut giu tin

Do k thut giu thng tin s mi c hnh thnh trong thi gian gn y

nn xu hng pht trin cha n nh.Nhiu phng php mi, theo nhiu kha

cnh khc nhau ang v chc chn s c xut, bi vy mt nh ngha

chnh xc, mt s nh gi phn loi r rng cha th c c. S phn loi

trn c Fabien A. P. Petitcolas xut nm 1999.

C th chia lnh vc giu tin thnh hai hng ln l thy vn s v giu tin

mt [18]. Giu tin mt quan tm n cc ng dng sao cho ngi khc kh pht

hin nht vic c tin c giu v nu c pht hi tin c giu th vic gii tin

cng kh thc hin nht.

Phm vi ng dng ca thy vn a dng hn, ty theo mc ch ca h

thy vn m ngi ta li chia thnh cc hng nh nh thy vn d v v thy

vn bn vng.


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Hnh 1.1 Phn loi cc k thut giu tin ( Fabien A.P. Petitcolaset al., 1999)

S phn loi ny nh mt bc tranh khi qut v ng dng v k

thut giu thng tin.Da trn vic thng k sp xp khong 100 cng trnh

cng b trn mt s tp ch, cng vi thng tin v tn v tm tt ni dung ca

khong 200 cng trnh cng b trn Internet, c th chia lnh vc giu tin ra

lm hai hng ln, l watermarking v steganography.

Steganography(giu tin, vit ph) l lnh vc nghin cu vic nhng ccmu tin mt vo mt mi trng ph. Trong qu trnh giu tin tng bo mt

c th ngi ta dng mt kho vit mt khi ngi ta ni v Intrinsic

Steganography (du tin c x l). Khi gii m ngi dng cng phi c

Giu thng tin

Giu tin mt Thy vn s

Thy vn d v

Thy vn n Thy vn hin

Thy vn bn vng

Thy vn n Thy vn hin


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7

kho vit mt . Ch rng kho ny khng phi l kho dng lp mt m

mu tin, v d n c th l kho sinh ra hm bm phc v ri tin vo mi

trng ph. Ngc li nu khng dng kho vit mt th ngi ta ch du tin nthun vo mi trng ph th khi ngi ta ni v Pure Steganography (du

tin n thun).

Watermarking(thu n) l k thut nhng mt biu tng vo trong nh

mi trng xc nh quyn s hu nh mi trng, chng s gi mo v

xuyn tc thng tin. Kch thc ca biu tng thng nh (t vi bit ti vi

nghn bit). K thut ny cho php m bo nguyn vn biu tng khi nh mitrng b bin i bi cc php thao tc nh lc (filtering), nn mt d liu

(lossy compression), hay cc bin i hnh hc, .... Tuy nhin vic m bo

nguyn vn biu tng khng k n khi c s tn cng da trn vic hiu r

thut ton v c b gii m trong tay. Thng tin giu l mt nh danh duy nht,

v d nh danh ngi dng th khi ngi ta gi l Fingerprinting (nhn dng

vn tay, im ch).

Nu nh watermark (thy vn, thy n) quan tm nhiu n ng dng

giu cc mu tin ngn nhng i hi bn vng ln ca thng tin cn giu

(trc cc bin i thng thng ca tp d liu mi trng) th steganography

li quan tm ti ng dng che giu cc bn tin i hi b mt v dung lng

cng ln cng tt. i vi tng hng ln ny, qu trnh phn loi theo cc tiu

ch khc c th tip tc c thc hin, v d da theo nh hng cc tc ng

t bn ngoi c th chia watermark thnh hai loi, mt loi bn vng vi cctc ng sao chp tri php, loi th hai li cn tnh cht hon ton i lp: d

b ph hu trc cc tc ng ni trn. Cng c th chia watermark theo c


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tnh, mt loi cn c che giu ch c mt s ngi tip xc vi n c th

thy c thng tin, loi th hai i lp, cn c mi ngi nhn thy.

Xt v tnh cht thu n ging giu tin ch tm cch nhng thng tin mtvo mt mi trng. Nhng v bn cht th thu n c nhng nt khc mt s

im:

Mc tiu ca thu n l nhng thng tin khng ln thng l biu tng,ch k hay cc nh du khc vo mi trng ph nhm phc v vic xc

nhn bn quyn

Khc vi giu tin ch giu tin sau cn tch li tin cn thu n tmcch bin tin giu thnh mt thuc tnh ca vt mang

Ch tiu quan trng nht ca mt thu n l tnh bn vng, ca giu tin ldung lng

im khc na gia thu n v giu tin l thu n c th v hnh hoc hu hnh

trn nh mang.

K thut giu tin c p dng cho cc loi d liu nh, audio, vidio.

Chc nng ca giu tin trong nh s khc nhau tu theo cc hnh thc xm phm

d liu nh.

nh b vi phm bn quyn: ni dung ca nh ging vi ni dung nh bn

quyn nhng chng c dng vi mc ch m tc gi khng cho php. bo

v cc sn phm chng li cchnh vi ly cp hoc lm nhi cn phi c mt k

thut dn tem bn quyn vo sn phm ny. Vic dn tem hay chnh l vic

nhng thu vn cn phi m bo khng li mt nh hng ln no n vic

cm nhn sn phm. Yu cu k thut i vi ng dngny l thu vn phi tn

ti bn vng cng vi sn phm, mun b thu vn ny m khng c php ca

ngi ch s hu th ch c cch l ph hu sn phm.


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nh b sa i: ni dung ca nh b xuyn tc. Trong trng hp ny giu

tin c tc dng phn bit nh bn quyn vi nh b sa i ni dung. p dng

cc bc tch tin ging nhau vi cc nh khc nhau, ta s tch c du bnquyn c ng k trc i vi nh b xuyn tc.

Hu ht giu tin c gn cho nh l giu khng nhn thy nhng trn

thc t tn ti mt loi giu tin c th nhn thy, chng khng trong sut hon

ton.Tuy nhin ni dung ca lun vnny ti ch cp ti loi giu tin khng

nhn thy.

1.1.3.Vi nt v lch s giu tinCc k thut giu tin c xut v s dng t xa xa, v sau ny

c pht trin ng dng cho nhiu lnh vc. T Steganography bt ngun t

Hi-Lp vi ngha l ti liu c ph (covered writing). Cc cu chuyn k v

k thut giu thng tin c truyn qua nhiu th h. C l nhng ghi chp sm

nht v kthut giu thng tin (thng tin c hiu theo ngha nguyn thy ca

n) thuc v s gia Hy-Lp Herodotus. Khi bo cha Hy-Lp Histiaeus b vua

Darius bt gi Susa vo th k th nm trc Cng nguyn, ng ta gi mt

thng bo b mt cho con r ca mnh l Aristagoras Miletus. Histiaeus co

trc u ca mt n l tin cy v xm mt thng bo trn da u ca ngi n l

y. Khi tc ca ngi n l ny mc di ngi n l c gi ti Miletus.

Mt cu chuyn khc v thi Hy-Lp c i cng do Herodotus ghi li.

Mi trng ghi vn bn chnh l cc vin thuc c bc trong sp ong.

Demeratus, mt ngi Hy-Lp, cn thng bo cho Sparta rng Xerxes nh xmchim Hy-Lp. trnh b pht hin, anh ta bc lp sp ra khi cc vin

thuc v khc thng bo ln b mt cc vin thuc ny, sau bc li cc vin


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thuc bng mt lp sp mi. Nhng vin thuc c ng v lt qua mi s

kim tra mt cch d dng.

Mc khng mu l phng tin hu hiu cho bo mt thng tin trong mtthi gian di. Ngi Romans c bit s dng nhng cht sn c nh nc

qu, nc tiu v sa vit cc thng bo b mt gia nhng hng vn t thng

thng. Khi b h nng, nhng th mc khng nhn thy ny tr nn sm mu

v c th c d dng.

tng v che giu thng tin c t hng nghn nm v trc nhng k

thut ny c dng ch yu trong qun i v trong cc c quan tnh bo. Micho ti vi thp nin gn y, giu thng tin mi nhn c s quan tm ca cc

nh nghin cu v cc vin cng ngh thng tin vihng lot cng trnh nghin

cu gi tr. Cuc cch mng s ho thng tin v s pht trin nhanh chng ca

mng truyn thng l nguyn nhn chnh dn n s thay i ny. Nhng phin

bn sao chp hon ho, cc k thut thay th, sa i tinh vi, cng vi s lu

thng phn phi trn mng ca cc d liu a phng tin sinh ra nhiu vn

nhc nhi v nn n cp bn quyn, phn phi bt hp php, xuyn tc tri

php...

1.1.4.Cc yu cu i vi giu tin cho nhMc ch ca giu tin cho nh l bo v bn quyncho ch s hu nh.

Nhng yu cu c bn i vi giu tin cho nh l:

Tnh n ca giu tin c chn vo nh: S hin din ca giu tin trongnh khng lm nh hng ti cht lng ca nh chn tin.

Tnh bn ca giu tin: Cho php cc tin c th tn ti c qua cc phpbin i nh, bin dng hnh hc hay cc hnh thc tn cng c khc.


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11

Tnh an ton: khng th xo c tin ra khi nh tr khi nh c bin iti mc khng cn mang thng tin

Tnh n ca tin l mt yu cu rt quan trng ca phng php giu tin.

Nu tnh n ca tin khng c m bo th khng nhng n lm nh hng ti

cht lng ca nh m cn d dng to iu kin cho cc hnh thc tn cng

nhm loi b tin ra khi nh. Vi nh c nh du mt cch l tng, nh c

bn quyn v nh gc s khng th phn bit c bng mt thng. Nh vy

gi tr ca bc nh s khng b thay i v vic cc tin nh vy s l ro cn ln

cho nhng k ph hoi trong vic c gng xo hoc sa i cc thng tin v bnquyn nh. Trn thc t khi chn tin vo nh th nh kt qu v nh gc s c

nhng sai khc, khng th nhn ra c nhng thay i v ni dung d liu

ny, ngi ta thng khai thc cc c im v kh nng cm th ca mt ngi.

Tnh bn ca giu tin lin quan n vic tch tin t nh c bn quyn mt

nh sau khi c nh du c th c em ra x l phc v cho cc mc

ch khc nhau nh nn nh, bin i hnh hc, lc nh ci thin nh , cc bin

i c tnh xo du tin ra khi nh,v.v. Vn c t ra liu sau khi nh

b x l ta cn c th tch c lng tin ra khi nh khng v tch c th

cht lng ca tin c m bo tin cy khng nh ta bit khi chn mt du n

vo nh th trc ht phi m bo tnh n ca n, ni cch khc thng tin v

du n c nng lng rt nh so vi thng tin nh. Mt khc tng tnh bn cho

du n ta phi tng nng lng ca thng tin du n c chn vo nh iu ny

i nghch vi yu cu ca tnh n .Do vy vic m bo s tn ti ca du n

trong nh cng ging nh vic m bo truyn tn hiu c nng lng nh trong

mi trng c nhiu ln. y l c s p dng cc phng php x l tn hiu

s trong chn du n.


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Trong trng hp mt nh c chn nhiu k hiu bn quyn th cc k

hiu ny phi m bo c th phn bit c. Tuy nhin vic tng s lng cc

du n cng ng ngha vi vic tng lng ca cc thng tin c chn vo nhdo tnh n ca nh cng b nh hng theo chiu hng gim. Tm li cc

yu cu t ra i vi nh du n cho nh c chiu hng xung t nhau, nu

tho mn tt yu cu ny th khng p ng c yu cu kia v ngc li. Qua

ta c kt lun rng khng th c m hnh nh du n no cho nh mt cch

l tng. c c mt phng php nh du n nh hp l, ngi ta thng

a ra hs cn i v tu theo nhng yu cu c th, h s cn i ny s cchn thch hp.

1.1.5.M hnh k thut giu tinH thng giu tin ni chung bao gm 2 phn chnh: chn tin v tch tin (Hnh

1.2). Giai on chn tin, cc thng tin kho (cng khai hoc b mt) v du tin

c chn vo nh gc c nh c bn quyn. Giai on tch tin, d liu

kho (b mt) v hoc nh gc (nh khng chn tin) s lm d liu c s tch

tin t nh c bn quyn.

a) Chn tin

Mutin mt

nhgc Chn tin nh bn quyn

Kha k


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13

b) Tch tin

Hnh 1.2. Qu trnh giu tin v tch tin.

Mu tin mt: c th l vn bn hoc tp nh hay bt k mt tp nh phnno, v qu trnh x l chng ta u chuyn chng thnh chui cc bit.

nh ph hay nh gc: nh c dng lm mi trng nhng tin mt. Kho K: kho vit mt tham gia vo qu trnh giu tin,tng tnh bo mt nh bn quyn: l nh sau khi nhng tin mt vo

Kho k trong h nh du trn l m bo tnh b mt ca du tin

chng li cc hnh thc khai thc quy lut v k hiu c chn vo nh. y l

hnh thc bo v an ton cho nh bn quyn i vi mi hnh thc tn cng c

nhm xo du tin ra khi nh.

1.1.6.Cc ng dng ca k thut giu tinBo v bn quyn tc gi: y l ng dng c bn nht ca k thut thy

vn s. Mt thng tin no mang ngha quyn s hu tc gi gi l thy vn

s c nhng vo trong cc sn phm, thy vn ch mt mnh ch s hu

hp php cc sn phm c v c dng lm minh chng cho bn quyn sn

phm. Gi s c mt thnh phm d liu dng a phng tin nh nh, m

thanh, video v cn c lu thng trn mng. bo v cc sn phm chng li

cc hnh vi ly cp hoc lm nhi cn phi c mt k thut dn tem bn

nh gc

nh c bn quyn Tch tin Tin

Kha k


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14

quyn vo sn phm ny. Vic dn tem hay chnh l vic nhng thy vn cn

phi m bo khng li mt nh hng ng k no n vic cm nhn sn

phm. Yu cu k thut i vi ng dng ny l thy vn phi tn ti bn vngcng vi sn phm, mun b thy vn ny m khng c php ca ngi ch

s hu th ch c cch l ph hy sn phm[18].

Xc thc thng tin hay pht hin xuyn tc thng tin: Mt tp cc thng

tin s c giu trong phng tin cha sau c s dng nhn bit xem

d liu trn phng tin gc c b thay i khng. Cc thy vn nn c n

trnh s t m ca k th, hn na vic lm gi cc thy vn hp l hayxuyn tc thng tin ngun cng cn c xem xt. Trong cc ng dng thc t

ngi ta mong mun tm c v tr b xuyn tc cng nh phn bit c cc

thay i. Yu cu chung i vi ng dng ny l kh nng giu thng tin cao v

thy vn khng cn bn vng[18].

Giu vn tay hay dn nhn: Thy vn trong nhng ng dng ny c s

dng nhn din ngi gi hay ngi nhn ca mt thng tin no . V d cc

vn khc nhau s c nhng vo cc bn sao khc nhau ca thng tin gc trc

khi chuyn cho nhiu ngi [2]. Vi ng dng ny th yu cu l m bo an

ton cao cho cc thy vn trnh s xa du vt trong khi phn phi.

Kim sot sao chp: Cc thy vn trong trng hp ny c s dng

kim sot sao chp i vi cc thng tin. Cc thit b pht ra thy vn thng

c gn sn vo trong cc h thng c/ghi. V d nh h thng qun l sao

chp DVD c ng dng Nht. Cc ng dng loi ny cng yu cu thyvn phi c m bo an ton v cng s dng phng php pht hin thy vn

giu m khng cn thng tin gc.


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15

Giu tin mt: Cc thng tin giu c trong trng hp ny cng nhiu

cng tt, vic gii m nhn cthng tin cng khng cn phng tin cha

ban u. Cc yu cu mnh v chng tn cng ca k th khng cn thit lmthay vo l thng tin giu phi m bo tnh n.

1.1.7.Cc kiu nh du nK thut nh du n c th chia thnh cc loi khc nhau theo c c

phng php khc nhau. K thut nh du n (Watermarking) c th chia thnh

4 loi theo kiu ti liu (d liu) s c nhng nh sau:

nh du n trong vn bn (Text ) nh du n trong nh (Image) nh du n trong m thanh (Audio ) nh du n trong Video

Trong trng hp hnh nh, c vi phng thc nh du n trong min

khng gian. C th dng nh du n trong min tn s thay cho nh du n

trong min khng gian.

nh du n nhn thy nh du n bn vng v hnh nh du n d v-v hnh

1.2. Giu tin trong nh nhng c trng v tnh cht1.2.1.Giu tin trong nh

Giu tin trong nh, hin nay, l mt b phn chim t l ln nht trong cc

chng trnh ng dng, cc phn mm, h thng giu tin trong d liu a

phng tin bi lng thng tin c trao i bng nh l rt ln. Hn na, giu

thng tin trong nh cng ng vai tr ht sc quan trng trong hu ht cc ng

dng bo v an ton thng tin nh: nhn thc thng tin, xc nh xuyn tc thng


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16

tin, bo v bn quyn tc gi, iu khin truy nhp, giu thng tin mt V th

m vn ny nhn c s quan tm rt ln ca cc c nhn, t chc,

trng i hc, v vin nghin cu trn th gii.

Thng tin s c giu cng vi d liu nh nhng cht lng nh t thay

i v t ai bit c bn trong bc nh mang nhng thng tin c ngha

khc. V ngy nay, khi nh s c s dng ph bin, th giu thng tin

em li rt nhiu nhng ng dng quan trng trong trn nhiu lnh vc trong i

sng x hi. V d nh i vi cc nc pht trin, ch k tay c s ha v

lu tr s dng nh l h s c nhn ca cc dch v ngn hng v ti chnh, nc dng nhn thc trong cc th tn dng ca ngi tiu dng. Thm vo

, li c rt nhiu loi thng tin quan trng cn c bo mt, chng rt d b

ly cp v b thay i bi cc phn mm chuyn dng. Vic nhn thc cng nh

pht hin thng tin xuyn tc tr nn v cng quan trng v cp thit. Mt

c im ca giu thng tin trong nh l thng tin c giu trong nh mt

cch v hnh, n nh l mt cch truyn thng tin mt cho nhau m ngi khc

khng th bit c bi sau khi giu thng tin th cht lng nh gn nh khng

thay i, c bit i vi nh mu hay nh a mc xm.

1.2.2.Nhng c trng v tnh chtGiu tin trong chim v tr ch yu trong cc k thut giu tin, v vy m

cc k thut giu tin phn ln cng tp trung vo cc k thut giu tin trong nh.

Cc phng tin cha khc nhau th cng s c cc k thut giu khc nhau. i

tng nh l mt i tng d liu tnh c ngha l d liu tri gic khng bini theo thi gian. D liu nh c nhiu nh dng, mi nh dng c nhng tnh

cht khc nhau nn cc k thut giu tin trong nh thng ch nhng c trng

v cc tnh cht c bn sau y:


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*) Phng tin c cha d liu tri gic tnh

D liu gc y l d liu tnh, d giu thng tin vo trong nh hay

cha th khi ta xem nh bng th gic, d liu nh khng thay i theo thi gian,iu ny khc vi d liu m thanh v d liu bng hnh v khi ta nghe hay xem

th d liu gc s thay i lin tc vi tri gic ca con ngi theo cc on, cc

bi hay cc cnh [18]

*) K thut giu ph thuc nh

K thut giu tin ph thuc vo cc loi nh khc nhau. Chng hn i vi

nh en trng, nh xm hay nh mu ta cng c nhngk thut ring cho tngloi nh c nhng c trng khc nhau.

*) K thut giu tin li dng tnh cht h thng th gic ca con ngi

Giu tin trong nh t nhiu cng gy ra nhng thay i trn d liu nh

gc. D liu nh c quan st bng h thng th gic ca con ngi nn cc k

thut giu tin phi m bo mt yu cu c bn l nhng thay i trn nh phi

rt nh sao cho bng mt thng kh nhn ra c s thay i v c nh th

th mi m bo c an ton cho thng tin giu. Rt nhiu cc k thut

li dng cc tnh cht ca h thng th gic giu tin chng hn nh mt ngi

cm nhn v s bin i v chi km hn s bin i v mu hay cm nhn

ca mt v mu xanh da tri km nht trong ba mu c bn.

*) Giu thng tin trong nh tc ng ln d liu nh nhng khng thay i kch

thc nh

Cc thut ton thc hin cng vic giu thng tin s c thc hin trnd liu ca nh. Dliu nh bao gmphn header, bng mu (c th c) v d

liu nh. Do vy m kch thc nh trc hay sau khi giu thng tin l nh nhau.


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18

*) m bo cht lng sau khi giu tin

y l mt yu cu quan trng i vi giu tin trong nh. Sau khi giu tin

bn trong, nh phi m bo c yu cu khng b bin i c th b phthin d dng so vi nh gc.Yu cu ny dng nh kh n gin i vi nh

mu hoc nh xm bi mi im nh c biu din bi nhiu bit, nhiu gi tr

v khi ta thay i mt gi tr nh no th cht lng nh thay i khng ng

k, thng tin giu kh b pht hin, nhng i vi nh en trng mi im nh

ch l en hoc trng, v nu ta bin i mt bit t trng thnh en v ngc li

m khng kho th s rt d b pht hin. Do , yu cu i vi cc thut tongiu thng tin trong nh mu hay nh xm v giu thng tin trong nh en trng

l khc nhau. Trong khi i vi nh mu th cc thut ton ch trng vo vic

lm sao giu c cng nhiu thng tin cng tt th cc thut ton p dng cho

nh en trng li tp trung vo vic lm th no thng tin giu kh b pht

hin nht [17], [12], [13].

*) Thng tin trong nh s b bin i nu c bt c bin i no trn nh

V phng php giu thng tin trong nh da trn vic iu chnh cc gi

tr ca cc bit theo mt quy tc no v khi gii m s theo cc gi tr tm

c thng tin giu. Theo , nu mt php bin i no trn nh lm thay

i gi tr ca cc bit th s lm cho thng tin giu b sai lch. Nh c im ny

m giu thng tin trong nh c tc dng nhn thc v pht hin xuyn tc thng

tin[16].

*) Vai tr ca nh gc khi gii tin

Cc k thut giu tin phi xc nh r rng qu trnh lc nh ly thng

tin giu cn n nh gc hay khng cn. a s cc k thut giu tin mt th

thng khng cn nh gc gii m. Thng tin c giu trong nh s c


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19

mang cng vi d liu nh, khi gii m ch cn nh mang thng tin giu m

khng cn dng n nh gc so snh i chiu.

1.2.3.Cc phng php giu tinCc phng php giu tin trong nh hin nay u thuc vo mt trong ba

nhm:

Giu tin trong min quan st. V d: Nhng vo cc bt c trng s thp

(Least Significant Bit)

Cc phng php da vo k thut bin i nh, v d bin i t min

khng gian sang min tn sCc phng php s dng mt n gic quan.

Nhm phng php nhng thng tin vo cc bt c trng s thp ca nh

hay c p dng trn cc nh bitmap khng nn, cc nh dngbng mu.

tng chnh ca phng php ny l ly tng bt ca mu tin mt ri ri

n ln nh mang, thay i bt c trng s thp ca nh bng cc bt ca mu tin

mt. v khi thay i cc bit c trng s thp th khng nh hng n cht lng

nh, v mt ngi khng cm nhn c.

Nhm phng php da trn cc php bin i nh li dng vic bin i

nh t min biu din ny sang min biu din khc giu cc bt tin. Mt v

d ca h thng s dng phng php ny l "Jpeg-Jsteg", phn mm ny

nhng thng tin bng cch iu ch cc h s ca php bin i Cosin ri rc

theo cc bt tin cn giu v s lm trn li khi lng ho. Mt s cc phng

php khc thuc nhm ny s dng nh nh m hnh vt l vi cc di ph thhin mc nng lng. Khi giu tin ging nh vic iu ch mt tn hiu di

hp vo mt di tn rng (nh ph).


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Nhm phng php dng mt n gic quan da trn nguyn l nh la h

thng gic quan ca con ngi. "Mt n" y m ch hin tng mt ngi

khng cm nhn c mt tn hiu nu n bn cnh mt tnh hiu nht nhno .

Nu phn chia cc phng php theo nh dng nh th c hai nhm chnh:

*) Nhm phng php ph thuc nh dng nh: c im ca nhm ny l

thng tin giu d b "tn thng" bi cc php bin i nh. Trong nhm ny li

chia ra theo dng nh, c cc phng php cho .

nh da vo bng mu nh JPEG

*) Cc phng php c lp vi nh dng nh: c trng ca cc phng php

nhm ny l li dng vo vic bin i nh giu tin vo trong , v d giu

vo cc h s bin i. Nh vy c bao nhiu php bin i nh th cng c th

c by nhiu phng php giu nh. Cc php bin i nh:

Phng php bin i theo min khng gian (spacial domain) Phng php bin i theo min tn s (DCT, DFT, Wavelet) Cc bin i hnh hc

Cc phng php nhm th hai c nhiu u im hn v tnh bn vng,

nhng lng thng tin giu c s t hn v ci t cng s phc tp hn.Nu

phn cc phng php theo c im k thut c:

*) Phng php thay th

Thay th cc bit d liu trong bn bit (bit plane) Thay th bng mu (palette)

*) Phng php x l tn hiu

Cc phng php bin i nh (Transform)


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Cc k thut iu ch diph*) Cc phng php m ho (coding)

Lng ho, dithering M ho sa li

*) Cc phng php thng k - kim th gi thuyt

*) Phng php sinh mt n - Fractal

1.3. Kt lun chng

Trong chng 1, lun vn trnh by n cc ni dung nh khi nim v

giu tin, phn loi cc k thut giu tin, mt vi nt v lch s giu tin, giu tintrong nh v mt s tnh cht ca n. Ni dung chng ny trnh by l do ti

sao phi giu tin, mc ch giu tin v cc phng php giu tin mt t ngn

xa.

Trong lch s loi ngi bit vn dng sng to tr tu ca mnh giu

nhng thng ip v cng quan trng, nh co u v xm ch ln da u, hay

khc ch ln vin thuc ri bc li bng sp ong

Ngy nay, khi s pht trin ca Cng ngh Thng tin v cng nhanh

chng v mnh m, loi ngi li phi tm cch bo v nhng sn phm tr tu

ca mnh ni chung v bo v bn quyn nhng sn phm ha vector ni

ring.

Khi giu tin cho nh cn phi tha mn ba yu cu l tnh n ca thng

tin c giu, tnhbn v tnh an ton. Bn cnh chng ny cn trnh by v

m hnh k thut giu v tch tin.

K thut giu tin c ng dng trong rt nhiu lnh vc khc nhau nh:

Bo v bn quyn tc gi y chnh l ng dng c s dng nhiu nht v l

ng dngc bn nht ca k thut thy vn s. ng dng th hai l Xc thc


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thng tin hay pht hin xuyn tc ng dng ny c dng pht hin nhng

sn phm b nh cp bn quyn hay s dng sai mc ch hoc b thay i

ni dung m khng c s cho phpca tc gi. Giu vn tay hay dn nhnc dng nhn din ngi gi hoc ngi nhn. Kim sot sao chp v

Giu tin mt l hai ng dng c dng qun l cc sn phm trnh trng

hp sao chp tri php ca ngi s dng.


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23

CHNG 2: GIU TIN TRONG BN VC T

2.1. Bn

Cc i tng bn khi tn ti di dng s c th hin v lu tr

trn cc lp thng tin khc nhau.

Bn l mt chnh th bao gm nhiu lp thng tin chng xp ln nhau

m t th gii thc. Thng tin trnbn c phn ra thnh 4 lpc bn

sau:

Hnh 2.1. Cc lp bn phn lp i tng

i tng dng im (point): th hin cc i tng chim din tch nhnhng l thng tin rt quan trng khng th thiu nh: tr s c quan,cc cng trnh xy dng, cu cng...


32/84


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i tng dng ng (line): th hin cc i tng khng khp knhnh hc, chng c th l cc ng thng, cc ng gp khc v cc

cung, v d nh ng giao thng, sng, sui...

i tng dng vng (region): th hin cc i tng khp kn hnh hcbao ph mtvng din tch nht nh,c th l cc polygon, ellipse v

hnh ch nht, nhlnh th a gii 1 x, h nc, khu rng...

i tng dng ch (text): th hin cc i tng khng phi l a lca bn nh nhn, tiu , ghi ch...

Bn s c m t bng m hnh d liu vc t, m hnh ny da trnc s cc vc thay to cc im trong h trc to khng gian hai chiu

hoc ba chiu.

Trong m hnh vc tcc im, on thng v cc vng c lu tr di

dng tp hp to im. S dng cc ng thng ri rc hay cc im m

t v tr ca i tng. Cc im ni vi nhau to nn cc i tng khc nh

ng (line/polyline), vng hay min (polygon/area). Cc i tng ri rc

(ng bin hnh chnh, sng sui, ng giao thng) c hnh thnh bng

cch ni cc on thng ri rc. V tr mt im c biu din bi mt to

im, ng thng c biu din bi tp hp to im, cn cc vng th

c lu nh mt vng khp kn cccp to . Cc i tng im, ng v

min c s dng th hin cc thc th a l ca th gii thc. M hnh vc

tc hnh thnh trn c s quan st i tng ca th gii thc.

Trong m hnh vect, cc bnh vin, trng hc c vtr l ta thc

trn b mt Tri t v chng c m t bi im d liu. Sng ngi, ng

sc n gin ha thnh cc i tng ng gp khc (polyline). Cc


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vng a l nh ao h, cc n v hnh chnh c tru tng ha thnh cc lp

ng bin, tp hp cc i tng min(hnh 2.1)

Hnh 2.2. Th gii thc v bn vect

Cu trc m hnh vc thay c s dng dng nhiu nht biu din cc

thc th a l thnh cc thc th ca c s d liu l spaghetti v topology.

2.2. Thy vn bn vc tS pht trin nhanh chng ca trao i thng tin bng my tnh v Internet

lm cho d liu b thay i hoc tht lc thng qua ng mng. Mt khc, n

cng tr thnh yu t quyt nh trong vic bo v cc bn sao s ca cc tp a

phng tin s khc nhau. Thy vn c nghin cu hn mi nm tr li

y nh l mt gii php thch hp cho cc n phm khi pht hnh. Bn cnh

vic bo v cc bn sao, thy vn cng c th c thit k cho nhng mc ch

khc nh giu i s trao i thng tin, xc nhn d liu, du vn tay Rt

nhiu kiu d liu c th c s dng nhm che du d liu ca thy vn nh

B.V

sng

tnh

sng

tnhB.V

Th giithc

Bn vect

Lp bn


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nh s, m thanh, cc on phim, vn bn, bng m, kiu 3D, d liu CAD, d

liu vecto 2D, phn mm Nhng d liu kiu ny, mt vi d liu a phng

tin tng quan nh nh s, m thanh, cc on phim, vn bn, bng m, kiu 3Dc ch nhiu hn cc kiu khc. Trong lun vn ny trnh by v cch s

dng thy vn cho bn vecto 2D, l d liu quan trng nht ca h thng

thng tin a l (GIS).

Bn lun quy nh mt vi kiu d liu c th cho cc bn sao ca

ngi s dng, n to ra s an ton cho cc tp hp d liu c phn b pht

hnh. u tin, lm ra c mt bn vecto l mt qu trnh vi chi ph cao.Mt cng c c chnh xc cao l cn thit cho qu trnh o t v mt s

lng ln vt cht, cc ngun ti nguyn tr tu th ph thuc vo thng tin a l

gc. Vic s ha v vecto ha thng tin gc l mt cng vic kh khn thu

c cc bn vecto. Cc bn s trong h thng thng tin a l thng

thng khng th c s dng mt cch min ph. Thm vo , trong mt vi

tnh hung c bit th nhu cu bo mt ln hn l cn thit. V d, nhng ng

dng ca nhng bn s quns b mt ph thuc vo kh nng chnh xc ca

d liu bn gc cng ton vn bao nhiu th cng tt by nhiu. N cng l

mt trong nhng l do chnh bn vecto s khng th thy c nhng

vng min quan trng, then cht nh trong bn giy truyn thng. So snh

mt cch tng qut cc loi d liu a phng tin c mt cht lin quan n

cng vic c lm trong mt vng ca bn vecto thy vn.

S hi ha ca nhng vng m c ng du thy vn, nhng phngthc c kch hot cho thy vn bn vecto c th c xp hng nh sau:

thut ton trong phm vi khng gian, trong phm vi DFT, trong phm vi DWT,

trong phm vi DCT v mt vi phng thc ly c t thy vn 3D. Khc vi


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nhng kiu d liu a phng tin tng quan, thy vn bn vecto c nhng

c im khc bit ring ca n nh cu trc d liu c bit, nhng mi trng

ng dng ca d liu bn .

2.3. c im ring ca thy vn bn Vecto nh du thy vn cho bn vecto s, mt loi cc c im ring

nn c quan tm. Tnh trng ca nhng c trng ny chnh l nhng vn

then cht c c cu trc d liu c bit v mi trng ng dng ca bn

vecto s. Kt qu l c s khc bit r nt gia thy vn a phng tin ni

chung v thy vn bn vecto s ni ring rt nhiu phng thc giu vtch d liu, tiu chun ca vic c lng cht lng d liu, phng thc c

th giu tin

2.3.1.D liu bn vc tD liu nh vecto l s bin son thng thng ca khng gian d liu,

tp hp d liu v thm vo mt vid liu c s dng nh ch s, s m t.

M t khng gian d liu, cc vng a l ca bn i tng m t i tng

a l trong th gii thc v lun nm ly 3 yu t a l c bn l im, ng

v a gic. Tt c cc i tng bn ny u c nh dng bi cc nh c

th t. Khng gian d liu l mt chui thc s cc ta ca nhng nh c s

ny trong mt h thng a l.

Tp hp d liu m t thuc tnh ca i tng bn nh tn, loi, v

mt vi thng tin khc. Hin nhin, nhng thng tin c ghi li bi tp hp d

liu rt quan trng v khng th thay i ty tin, tng t cho nhng d liuc thm vo k ra trn. Tt c cc thut ton thy vn c xut,

khng gian ng du thy vn c quy nh bi khng gian d liu nh ta

ca cc nh. Mt bn vecto bt k u c mt dung sai r rng, chng


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a ra rng ti a cho s lm mo ta cho php. Lm mo ta dt

khot phi nh hn dung sai th s khng lm suy gim i cht lng ca bn .

Dung sai r ca d liu bn vecto dch chuyn nh l M hnh che ph trcquan bn trong nh thy vn s a ra mt cht d tha cho vic giu thng tin

thng l

2.3.2. chnh xc ca bn vc tNgun gc chung ca thy vn s l s xp xp c h thng l s a v o

nhng mu tin n c th khng lm nh hng n cht lng ca d liu. Trong

th gii thy vn chnh xc gii hn thng c s dng o cht lngca d liu. Tuy nhin, ty theo cc kiu d liu khc nhau v cch s dng

ring ca chng, chnh xc gii hn c th c nhng ngha khc. i vi

nh s, cc on phim, m thanh, v cc tp hp d liu a phng tin khc,

ngi s dng hng vo d liu l cc cm nhn thng qua nhng b phn gic

quan ca con ngi. Trong gic quan ny, mt ngi c th c dng o

chnh xc ca nh. Nu nh mt ngi khng th phn bit c hai nh, hai nh

c th c coi nh c gi tr s dng nh nhau, c th l c chnh xc

cao. Ni chung, mt vi thng s chnh xc nh PSNR hoc MSE c dng

o s khc bit ca 2 tp hp d liu.

Tuy nhin nh gi cht lng ca d liu nh vecto, con ngi khng

th cm nhn c v PSNR cng khng th l n v o thch hp. u tin,

ngi s dng hng vo nh vecto khng phi l cc b phn gic quan ca con

ngi m l my tnh. Trong mt t l c trng, thm ch hai bn s khging nhau khi nhn bng mt th vn tn ti nhng ta khc nhau gia hai

bn c th vt qu s dung sai. Th hai, gii hn PSNR ch yu l phn

hi li nng lng ca cc li. N s thch hp hn nh gi nh, nhng


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ngc li i vi nh vecto bi v thm ch c vi mt PSNR cao ca bn

vecto khng th m bo chnh xc nhng nh li th c gi tr nh trong dung

sai ca bn .Thm vo , khi chng ta nh gi chnh xc ca bn vecto mt

vi nhn t c th c ly ra nh nt v hnh dng ca cc i tng bn ,

nh du thy vn cho bn s thc s l mt cng vic ht sc vt v.

PSNR khng th khi phc li s bp mo chi tit v nt ca hai bn vecto

. Trong mt lnh vc khc, mt bn vi chnh xc thp cng c th c

PSNR cao. Cho n tn by gi vn cha c n v o ph hp cho chnh xcca bn vecto.

2.3.3.Cc kh nng giu tinMt s giu tin thnh cng c ngha l thy vn c th c g b trong

khi tnh hp php ca d liu bao ph vn c bo v. Khng gian d liu ca

bn vecto gn nh l d liu im tri vi s chnh xc chc chn. Do ,

nhng cch thc v c trng ca cc kh nng giu tin bn vecto thy vn l

khc nhau cho mi loi thy vn a phng tin.

2.3.3.1. Giu tinhnh hcMt vi php bin i nh php dch, php quay l nhng khun dng

chnh ca giu tin hnh hc. i vi nhng nh thy vn s giu tin hnh hc rt

kh c th bo v, bi nhng php bin i ny lun c s thm vo cc gi tr

cho im nh m khng th x l ngc li c v lun l nguyn nhn lm

mt mt thng tin. Tuy nhin i vi bn vecto, vn giu tin a ra trngn nh l php bin i ta , ni m hu nh thng tin khng th b mt. V

vy giu tin hnh hc c lin quan n vn bo v trong vic phi hp nh

du thy vn cho bn vc t.


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2.3.3.2. Giu tin vonhGiu tin nh l giu tin vo cc lp nh nh l thm cc nh vo bn

hay g b bt cc nh. Khi giu tin, c bit l i vi bn n gin hoc sct xn rt nguy him i vi thy vn bn vc t. Mt khc, cc bn n

gin cng c cch hot ng chung bn trong nhng ng dng nhm tng tc

x l d liu bn . Tm li kh nng bao qut bn n gin l rt quan

trng i vi vic sp xp thy vn th.

2.3.3.3. Sp xp i tngy l cch giu tin vo lp i tng, khng gian d liu ca bn vc

t c to lp t rt nhiu ta ca cc nh th t m t cc i tng bn

. Tt c cc i tng c lu tr trong tp bn theo mt trnh t nht

nh. S sp xp li cc i tng trong bn hoc s sp xp li cc nh bn

trong mt i tng c th to nn mt bn mi m khng lm suy gim

chnh xc ca d liu. Mt vi s sp xp thy vn quyt nh th t ca cc i

tng, hot ng ny s l s giu tin nguy him.

2.3.3.4. Gim nhiuC hai nguyn nhn chnh c th gy nn hin tng nhiu bn trong bn

vc t. u tin l mt vi loi cng vic hng ngy. V d nhc rt nhiu

cc nh dng file thng dng trong th gii GIS. Nhng bin i nm trong cc

khun dng ny c th to ra d liu b nhiu. Th hai l cc hnh thc giu tin

him c. Nhng ngi giu tin c gng ph hy du thy vn bng cch thm

nhiu vo cc tp hp d liu. Gim nhiu l s giu tin nghim tc nhng likhng phi l s la chn tt cho nhng ngi giu tin.


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Hai nhn t lm tng mnh nhiu ca thut ton. Nhn t u tin l

khng hn ch kch thc ca mt n. Nhn t th hai l phng thc chung ca

thy vn v tiu chun tng ng s dng trong vic tm cc th tc. Bc utin sinh ra thy vn l lp li cc bit c giu thng tin ca nhng ln

chc chn. Tng t, phn ln cc tiu chun c s dng tm ra cc th tc

thy vn. Chng to ra cc thut ton giu tin nhiu.

tng bo mt c m bo bi hai dy s ngu nhin gi to bng hai

kha. Kha th nht c s dng m ha li cc bit thy vn. Kha th hai

c s dng hon v nhng khi c chia tch, m ha trt t ca dliu c a vo.

Mt PSNR c ly t gi tr chnh xc ca nh k thut s c s

dng tnh ton cht lng ca bn sau khi giu tin nhiu.

RMSE

yVxMaxLogPSNR

),(20 10 (2.1)

v

2

,

2

,,

yx

d

yxyx

V

VVRMSE (2.2)

Khi yxV , l ta gc vd

yxV , l ta nhiu. nh ngha ny cung ging

nh ngha PSNR cho nh v n l bn cht, nh x mnh ca nhiu. Khi

chng ta c mt s m t trc, s tnh ton ny l khng cho cc gi tr

chnh xc ca bn vc t bi n khng th cung cp mt s thng tin quan

trng nh cc li ccln v lm mo nt

L mt tng thy vn khng tt c th a vo nhiu bit thy vn.

S thun li ln ca tng ny l mnh c th a vo cc im nhiu

v n gin ha bn . Nhc im ln nht ca n l s thay i cc nh l


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mt th tc o ngc i vi cch to ra cc li ca d liu a vo cao hn

kch thc ca bn . Mt khc, iu khin cc li l rt kh.

Ohbuchi a ra rt nhiu thut ton cho thy vn bn vc t haichiu. Trong min khng gian, tng c s tm ra s tng quan c

xut. Mt dy s gi ngu nhin (PRNS) c dng ci thin tnh bo mt,

pht hin s tin cy trong tng. Cc bn sao chp, u tin c phn chia

bn trong cc khi hnh ch nht vi s nh chnh xc. to ra thy vn,

di ca thng tin a vo l c nh vi cc s ca cc khi c phn chia

bng cch lp li chng. Dy c lp li sau c chuyn thnh d liulng cc, l thy vn cui cng. Mi khi bn u c dng du mt bit

thy vn. i vi mt khi xc nh th d liu a vo l mt th tc cng.

..' ijii pbVV (2.3)

iV v '

iV l phn bit ta gc v ta thy vn ca cc nh c trong

khi th i, bil bit thy vn th i v pil bit th ica PRNS, l i lng

ln. Trong th tc tch thy vn bn gc l cn thit v cn mt PRNS tngt gii m. Nhng bit thy vn c tch ra sau khi gii m v x l tch ly,

c th c xem nh l nhng th tc pht hin tng quan. ly c nhng

gi tr tch ly cho s pht hin cng ci thin tnh chnh xc ca my d tm.

Nhc im ln nht ca thut ton ny l n khng phi l thut ton r rng

khi bn gc l cn thit cho s pht hin thy vn v mnh ca thut ton

quyt nh mt phm vi ln trong bn gc. Tuy nhin tng thy vn

c cng khai th khng th s dng.

Micheal Voigt v Christoph Busch [10] xut thut ton c th a

vo nhiu bit d liu c s hng vo hnh nh rng ca dy v thay i s

pht hin tng quan. Mt pht biu quan trng l cc ng pht hin tng


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vi kch thc ca cc min nh. R rng, by gi hai tp hp A v B c

son tho bi rt nhiu nh vi nhng gi tr ta quan h nh. Nu khng c

d liu c a vo, ta trong tp hp A v B u c phn chia gingnhau trong mt min v c rt nhiu c im ging nhau. Khi mt bit 1 c

a vo, s thay i ca cc nh c ly ra khng gian bn trong cc min

con. Sau khi bin i, s ging nhau ca cc gi tr ta trong tp hp A tng

cn trong tp hp B th gim xung.

S dng nhng c trng tnh ca ta , thut ton ci thin mnh

giu tin bao gm bn thay i, ni suy d liu, n gin ha, thm nhiu vi ln no , v bn ct mt vi phm vi no . Cc nguyn nhn gy li

khi giu d liu c th c iu khin mt cch chnh xc. Bn gc l khng

cn thit trong th tc pht hin, tng l khng r rng. Thm na, thut ton

c th m rng thm vo nhiu bit. Nhc im chnh ca tng ny l

thay i cc nh cc b khng ly ra t nt ca cc i tng bn . Do ,

tng khng n khp vi bn thy vn m nt ca nhng i tng l

trn.

Bn trong mt di, cc nh ph thuc vo n c bin i n mt vng

c bit miu t bit 1 hoc bit 0 l mi bit mt di. tng ny thm

vo mt nhiu vi ln nh hn 1/3 rng ca di, tng ny cng tn ti

bn thay i v n gin ha, ct xn mt vi phm vi bn . Mt vng chn

l c s dng ci tin cch tm kim tin cy. Hn na, nhng m cm bn

trong vng m c dng gii quyt cc vn i xng. Mc ch chnh ca tng ny l cung cp mt cch khc lu tr d liu bin i ca bn vc

t. D liu bin i bao gm s minh ha v bn vc t.


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N c khuynh hng b mt mt trong khi x l bin i gia cc nh

dng bn khc nhau. C th khc phc nhng vn ny bng cch a d

liu thay i vo khng gian d liu vi hiu ng nh bng cch thay i nhdng. Mt phn mm thng mi c pht trin cung cp bn quyn cho cc

bn vc t. tng ny s tr thnh bng sng ch v chng ta c th hiu

rng nn chp nhn thut ton thy vn trong bn ni suy. Ni chung, cc

tng ny dng miu t cc bit thy vn bng cch cng thm cc nh vo

trong cc bn che ph gc. nh u tin v nh cui cng l hai nh lin k

trong bn gc. Tt c cc nh c t en suy ra cc nh mi trong khi thmvo th tc.

Gi s, khong cch gia im xut pht v im u ni suy m t bng

mt bit 1 v mt na khong cch m t bng mt bit 0, d liu thm vo

trong on thng l 1010011. Nu chng ta ch ngh n s chnh xc, th

tng ny l tt nht bi n s khng a ra s mo thng tin. Thm na,

tng ny kh mnh quay v v bn . Tuy nhin c hai nhc im chnh

trong tng ny. Th nht, thm cc khuch i thy vn kch c ca d

liu che du. thm vo mt bit d liu, phi thm vo d liu bn mt

nh mi. Cc thng tin khc c thm vo, d liu bn s ln hn. Th hai,

tng ny dt d v n gin ha bn . Vibt c mt thut ton thng

dng no c s dng cng c th g b mt cch d dng cc nh ni suy,

tc l cc d liu thm vo.

2.4.2.Thut ton trong min bin i (min tn s)Khi nim ny ging nh trong thy vn s cho cc tp tin a phng tin,

tcl nhng d liu thy vn c thm vo khng phi l lp tc thay i ta


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NakNbrbNkaNkW

kW)1()1(,,,);(

0

0

)( (2.4)

*) Giu v tch thng tin: Trong th tc giu thng tin, php cng hoc

php nhn c th c chpnhn thay i ln ca dy |Z(k)|. Trong vic

tch d liu, a ra mt h s DFT Z(k) ca hnh a gic cho vic tm ra cc

du thy vn W(k), tng quan ng thng c ca |Z(k)| v W(k) c tnh ton

trc tin. Sau , v mt l thuyt gi tr ccng c tnh. Tng quan thng

thng c=c/cdng quyt nh lm cn c cho im bt u.

N l mt tng m rng khng c d liu gc no l cn thit. Dy

ln cc c trng ca bin i Fourier ri rc, thut ton ny vn mnh vi rt

nhiu cch giu tin nh l bin i bn , quay, v v iu khin nh khi u

ca a gic thy vn. Chun b xp th t mt nh cng l a vo trong bc

xa b nhng hiu ng l nguyn nhn ca vic xp sp li cc nh. Hn th

na nhng thun li ny, c mt vi nhn t cng c th ly ra t ti khon. u

tin, chp nhn mt my d bn trong thut ton lm cn c cho quan h thngthng. Trong trnh t nhm nhn c s bin i ti u ca vic tm kim. N

yu cu cc h s ln |Z(k)| v thy vn W(k) nn c lp vi nhau v phn

b nh nhau.

S hon thnh iu kin ny c th to ra mt quyt nh d trn d liu

bn c bit. Th hai, tnh tin cy ca my d tm ph thuc vo di ln

hn ca d liu che giu, tc l cn nhiu nh hn.Tuy nhin, s dng my tnh

tnh ton DFT ca mt dy ta di s nhanh hn. Thm na, tng ny

l r rng n gin ha cc bn khc hoc ni suy. Thm mt vi pht hin

chc chn nhm thm mt bit vo nhiu a gic. K thut trn d liu c

chp nhn trong th tc tch thy vn nhm ci thin s chnh xc ca vic d


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tm. Trong tng ny, rt nhiu a gic c la chn nh d liu che giu.

Vi mi a gic, d liu thm vo s dng cng mt phng thc m t nh

nhau bn trong thn ca chng. Sau mi a gic ny s nhn c mt gi trquan h thng thng ci (i = 1, 2, ,M vi M l s cc a gic). Hm trn d

liu f(.) c chn tnh ton cc thng s kt hp c = f(c1, c2, , cM), s

c s dng cho quyt nh cui cng lm c s cho im khi u. Mt vi

quy tc trn d liu nh Kh nng ng dng v rt nhiu quy tc trn kinh

nghim c chp nhn trong tng ny.

thm nhiu bit thy vn vo min DFT. N l mt tng thy vnmt cc bn gc l cn thit trong vic tm kim. Rt nhiu a gic

c la chn lm d liu che giu v tri qua qu trnh tin x l ging nhau

trong tng ca Pitas. Thy vn l mt dy bit mang ngha y thay th

cho mt bit n m t bi dy sgi ngu nhin. Th tc thm vo th kh l

ging vi phng thc c. Nhng ngc li th tc tch thng tin th li kh

khc xa bi v tch thng tin th phi cn ti bn gc. Hu nh, cng vic

chnh ca tng ny l cng c xc nh nhng bit lng ph. Thm na,

tng ny vn kh yu n gin ha v ct xn bn .

2.4.2.2. Min DWT :Mt s cng vic bt buc i vi thy vn cho bn vc t trong min

sng ri rc min (DWT). Thut ton DWT c thit k cho thy vn ca

nh k thut s nh thy vn cho bn vc t s. Mt tng mi thm

nhiu bit thy vn cho bn vc t trong min DWT c xut.S la chn cho d liu che giu v phng thc tin x l l ging nh

i vi tng trong min DFT c m t. Ta ca cc nh c trch

ra t bn bi mt trnh t nht nh v c kt hp vi mt dy s phc tp.


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Mt php phn chia ba lp c thc hin trn dy ny nhn c 4 tp hp h

s l HH1, HH2, HH3, LL3 nhm n mt gi tr dung sai chnh xc, HH2 v

HH3 c la chn a d liu vo

*) Ly ra tp hp h s HH2 nh l mt v d, phng thc thm d liu

c ch ra trn, Z0, Z1, Z2, , Zi l h s ca HH2. Bt u vi Z1, cc bit

thy vn s c thm vo t tt c cc h s khc, cc h s ch s l Z1 , Z3,

Z5 nh mt v d, gi s thm vo bit thy vn u tin w1 {0,1} vo Z1. R

c tnh bi cng thc

220

1zzR (2.5)

khi hai h s lng ging Z0 v Z2 c s dng v l nhn t sc mnh iu

khin ln thm vo. Sau tnh K1 = round(|Z1|/R1) v s dng thuc tnh

chn l ca K1nh l s m t ca bit thy vn, nu w1= 0 th bin |Z1| thnh

K1 l mt s chn. Cn nu w1= 1 th bin |Z1| thnh K1 l mt s l. Cc bit

thy vn khc w2, w3 th c thm vo Z3, Z5, mt cch tng t.

*) D liu tch ra c th c thc hin m khng cn bn gc. S

phn tch cc ln sng nh vy v Ki|i = 1,3, c tnh ton v cc bit thy

vn d dng c tch ra t mi K i.

Trong tng ny, ln ta ca cc h s DWT c thay i

tha mn mt phng thc c th cho cc bit thy vn m t. y l mt

tng m. Cn c vo cc kt qu thc nghim, chng t rng tng ny mnh

i vi mt s bin i cp s nhn. Khi nh gi cht lng ca bn thy

vn, cm nhn ca con ngi v mt PSNR c chp nhn nh mt gii hn,

chng khng nh gi cc bn vc t. Tm li, tng ny khng

mnh giu tin vo cc nh nh n gin ha bn hoc ni suy.


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2.4.2.3.Min DCTTrong mt xut gn y Michael Voigt v Bian Yang thit k mt

tng thy vn tri ngc thm cc bit thy vn vo min bin i Cosin rirc (DCT). tng chnh ca pht kin ny l s dng mt c tnh quan

trng ca d liu bn tc l mi tng quan cao cc ta ca nh. Tng

qut, lm trn nt. Cc ta ca cc nh bn trong cc i tng n

lun tng quan cao. Hn na, bin i Cosin ri rc rt ni ting c mt thuc

tnh tha thun sc mnh cho d liu tng quan cao. Sau bin i DCT, sc

mnh ca bin i d liu s c tp trung vo Cosin ri rc v dy h s thp.Thun li ca c trng ny, thut ton ny xut kt hp tm nh li

thnh mt khi v mi khi mt bit thy vn n s c thm vo bn trong h

s DCT ca tm nh . Phng thc thm d liu c o ngc li, iu

ny c ngha l d liu bn gc c th b mt i sau khi tch thng tin. y l

mt tng khng r rng v l tng nhiu bit. N l thut ton u tin vi

tng o ngc bn trong thy vn bn vc t s. Nhc im ca

tng ny l s xuyn tc do thy vn l rt ln. Hn na, thut ton ny

khng th chng li s n gin ha v ni suy bn .

2.4.3.Thut ton nhn c t m hnh ba chiuMc d mi trng ng dng ca bn vc t hai chiu v m hnh 3

chiu l khc bit nhau rt ln, nhng vn c rt nhiu nhng im tng ng

gia hai kiu d liu ny bi chng u l d liu vc t v c tp hp t rt

nhiu cc nh. V vy chng c kh nng khai thc mt vi tng thy vncho m hnh ba chiu t thy vn bn vc t hai chiu. Ohbuchi xut rt

nhiu tng thy vn cho m hnh ba chiu, trn c s h cng xut cc

tng cho thy vn bn vc t hai chiu trong min li che ph, chng


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c s dng cho m hnh ba chiu. Thut ton mt vi k thut ba chiu

c a vo x l d liu vc t hai chiu. u tin tt c cc nh trong bn

gc s c kt ni vi nhau to thnh li hai chiu. Sau cc bn nyc phn chia v tch hp vo rt nhiu vng s dng quy tc cy k-d. Nhng

bit thy vn ging nhau s c thm vo mi vng to ra nhng tng

phn hi. Ti mi vng s phn tch vng mt li c thc hin u tin n

mt li bn trong vng, nhn c dy h s ca vng mt li m c cng

mt kch thc nhdy ta gc trong vng . Dy ta ca vng th c

nhc n nh l d liu che giu ca thy vn. Phng thc sinh thy vn vthm d liu vo kh ging vi cc k thut trc .

2.5. Kt lun chngChng ny, ch yu trnh by v mt s thut ton nh du cho bn

vc t. Ngoi ra cn cp n mt s vn khc nh: Khi nim bn ,

khun mu ca bn v t chc ca bn Shapefile, thy vn bn vc t,

cc c im rin ca thy vn bn vc t

Trong ni dung ca chng cng cp n mt s tnh cht v c im

ring ca thy vn bn vc t nh: chnh xc, D liu ca bn vc

t Cc kh nng giu tin trnh by tng tm ni a vo thng tin cn

giu.

V ni dung quan trng nht trong chng l cc thut ton giu tin,

tp trung ch yu vo cc thut ton bin i trong min khng gian v min tn

s, cc bin i Fourier nh DFT, DWT, DCT.


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CHNG 3: THUT TON GIU V TCH TIN TRONG

BN VC T

3.1. Giu tin trong nh en trng3.1.1.Thut ton giu tin c s*) Thut ton

Input: File nh Bitmap en trng F

D liu cn giu d c biu din di dng nh phn (dy bt 0/1)

Output: File nh giu tin G = SDH(F, d)

a. Tin x l

c header ca nh (phn cha thng tin nh) ly thng tin nh. Sau

c ton b d liu nh vo mt mng hai chiu A s dng cho vic giu tin.

b. Qu trnh thc hin giu tin

Chia A thnh cc khi kch thc mxn.Vi mi khi B trong A ta xt kh nng giu mt bt d liu d ica d theo

Quy tc cn bng tnh chn lnh sau:

- Gi t l tng s im trng (bt mang gi tr 1) trong B. Nu t v d i cng tnh

chn l th khng sa khi B v coi nh khi ny c giu bt d liu d i.

Trong trng hp ngc li, nu t v d ikhc tnh chn l th o ngu nhin mt

bt trong B t v di tr thnh cng tnh chn l. .

Gi s cn giu 1 bt d liu b vo khi B. K hiu SUM(B) l tng s

im trng trong khi B, k hiu x=y(mod z) cho bit hai s nguyn x v y ccng s d khi chia cho z (x v y ng d theo modulo z). Nh vy biu thc x

= y(mod 2) cho bit x v y c cng tnh chn l. Ni ring, khi y l mt bit thng

tin , biu thc trn tng ng vi x mod 2 =y. Ta xt hai trng hp sau y:


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Trng hp th nht: SUM(B) = b(mod 2), Khi B tho mn tnh cht giu bt d liu b, ta khng cn sa khi B v xem nh bt b c giu vo

khi B.

Trng hp th hai: SUM(B) b (mod 2). trng hp ny phi sa B thay i tnh chn l ca SUM(B) s tng hoc gim 1 n v. Gi B l khi kt

qu thu c t khi B sau khi o mt bt trong B. Ta c SUM(B) = b (mod 2).

Th d di y minh ha cho hai trng hp trn.

*) Gi s ta phi giu bt d liu b=1 vo khi B nh sau:

Khi B kch thc 4x4, SUM(B)= 8

Ta m s bt 1 trong khi: Trong trng hp trn khi B c 8 bt 1,

SUM(B)=8. Do , SUM(B) 1(mod 2). Nh vy khi B khng tha mn yu

cu giu bt 1. Mun giu bt 1 vo khi ny ta cn phi thay i khi bng

cch

chn mt bt bt k v i t 0 sang 1 hoc t 1 sang 0. Gi s ta sa li phn t

B[2,2] nh sau:

Khi ta c SUM(B) = 7, v do SUM(B) = 1 (mod 2).

1 0 1 1

0 1 0 0

0 0 1 0

1 1 1 0

1 0 1 1

0 0 0 00 0 1 0

1 1 1 0

bt b thay i t 1 thnh 0


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*) Gi s vn l khi B cho trn nhng ta phi giu bt d liu b=0

vo khi . Ta c, do SUM(B) = 8, nn SUM(B) = 0(mod 2). Khi B tho mn

yu cu giu bt 0. V xem nh bt d liu b=0 c giu.

Vi mi bt d liu ta ly mt khi giu theo quy tc trn cho n ht

lng thng tin cn giu. Sau khi giu xong ta c mt ma trn hai chiu cha

d liu nh mi A. Bc tip theo, ta xy dng nh mi bng cch gn header

nh gc c ra lc u vo A thu c file nh mi G.

3.1.2. Thut ton trch tin

Trong thut ton giu tin ny, kho n gin ch l kch thc ca khi,tc lb s (m, n). Nu bit kch thc khi th d dng trch li d liu d theo

thut ton SIDH nh sau:

*) Thut ton

Input: File nh Bitmap en trng c cha tin G

Output: D liu d (dy bt 0/1) trch t nh G, d = SIDH(G)

a. Tin x l:

c header ca nh G (phn cha thng tin) ly thng tin nh. Sau

c tonb d liu nh vo mt mng hai chiu A s dng cho vic trch tin.

b. Qu trnh trch tin:

Chia A thnh cc khi kch thc mxn.Vi mi khi Bi trong A ta tnh di = SUM(B) mod 2

3.2. Bini Fouriera. Bin i Fourier, c t tn theo nh ton hc ngi Php Joseph Fourier,

l mt bin i tch phndng khai trin mt hm stheo cc hm s sin c

s, c ngha l di dng tnghay mttch phn ca cc hm ssin c nhn
http://vi.wikipedia.org/wiki/Jean_Baptiste_Joseph_Fourierhttp://vi.wikipedia.org/wiki/Bi%E1%BA%BFn_%C4%91%E1%BB%95i_t%C3%ADch_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Bi%E1%BA%BFn_%C4%91%E1%BB%95i_t%C3%ADch_ph%C3%A2nhttp://vi.wikipedia.org/wiki/H%C3%A0m_s%E1%BB%91http://vi.wikipedia.org/wiki/H%C3%A0m_s%E1%BB%91http://vi.wikipedia.org/w/index.php?title=H%C3%A0m_c%C6%A1_s%E1%BB%9F&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=H%C3%A0m_c%C6%A1_s%E1%BB%9F&action=edit&redlink=1http://vi.wikipedia.org/wiki/T%E1%BB%95_h%E1%BB%A3p_tuy%E1%BA%BFn_t%C3%ADnhhttp://vi.wikipedia.org/wiki/T%E1%BB%95_h%E1%BB%A3p_tuy%E1%BA%BFn_t%C3%ADnhhttp://vi.wikipedia.org/wiki/T%C3%ADch_ph%C3%A2nhttp://vi.wikipedia.org/wiki/T%C3%ADch_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Sinhttp://vi.wikipedia.org/wiki/Sinhttp://vi.wikipedia.org/wiki/Sinhttp://vi.wikipedia.org/wiki/T%C3%ADch_ph%C3%A2nhttp://vi.wikipedia.org/wiki/T%E1%BB%95_h%E1%BB%A3p_tuy%E1%BA%BFn_t%C3%ADnhhttp://vi.wikipedia.org/w/index.php?title=H%C3%A0m_c%C6%A1_s%E1%BB%9F&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=H%C3%A0m_c%C6%A1_s%E1%BB%9F&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=H%C3%A0m_c%C6%A1_s%E1%BB%9F&action=edit&redlink=1http://vi.wikipedia.org/wiki/H%C3%A0m_s%E1%BB%91http://vi.wikipedia.org/wiki/Bi%E1%BA%BFn_%C4%91%E1%BB%95i_t%C3%ADch_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Jean_Baptiste_Joseph_Fourier


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vi cc hng skhc nhau (hay cn gi l bin ). Bin i Fourier c rt nhiu

dng khc nhau, chng ph thuc vo dng ca hm c khai trin.

Bin i Fourier FT (Fourier Transform) l mt php bin i thunnghch, n cho php s chuyn i thun - nghch gia thng tin gc (min

khng gian hoc min thi gian) v tn hiu c x l (c bin i). Tuy

nhin mt thi im bt k ch tn ti mt min thng tin c th hin.

Ngha l tn hiu trong min khng gian khng c s xut hin thng tin v tn

s v tn hiu sau bin i Fourier khng c s xut hin thng tin v thi gian.

FT cho bit thng tin tn s ca tn hiu, cho bit nhng tn s no c trong tn hiu, tuy nhin n khng cho bit tn s xut hin khi no trong tn

hiu. Nu nh tn hiu l n nh (stationary cc thnh phn tn s khng thay

i theo thi gian) th vic xc nh cc thnh phn tn s xut hin khi no

trong tn hiu l khng cn thit. Php bin i FT thun v nghch c nh

ngha nh sau:

dtetxfX ftj2)()( (3.1)

dfefXtX tfj2)()( (3.2)

Php bin i FT cng c th c pdng cho tn hiu khng n nh

(non - stationary) nu nh chng ta ch quan tm n thnh phn ph no c

trong tn hiu m khng quan tm n n xut hin khi no trong tn hiu. Tuy

nhin, Nu thng tin v thi gian xut hin ca ph trong tn hiu l cn thit,

th php bin i FT khng c kh nng p ng yu cu ny, y cng l hn

ch ca php bin i ny.
http://vi.wikipedia.org/wiki/H%E1%BA%B1ng_s%E1%BB%91http://vi.wikipedia.org/wiki/H%E1%BA%B1ng_s%E1%BB%91http://vi.wikipedia.org/wiki/Bi%C3%AAn_%C4%91%E1%BB%99http://vi.wikipedia.org/wiki/Bi%C3%AAn_%C4%91%E1%BB%99http://vi.wikipedia.org/wiki/H%E1%BA%B1ng_s%E1%BB%91


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b. Bin i Fourier lin tc

Thng thng, tn gi bin i Fourier c gn cho bin i Fourier lin

tc, bin i ny biu din mt hm bnh phng kh tch f(t) bt k theo tngca cc hm e ly tha phc vi tn s gc v bin phc F():

(3.3)

y l bin i nghch o ca bin i Fourier lin tc, trong khi bin i

Fourier biu din hm F() theof(t).

*) Bin i Fourier lin tc

x(n) = 0.8nu(n)

njenxX )()( (3.4)

Nhng X() Lin tc theo tn s khng thch hp cho vic tnh tontrn my tnh. Vy ta phi ly mu min tn s

kN

XkX

2

)()( (3.5)

n

Nknj

Nk enxkN

XX/2

2 )()2(

1,...,1,0 Nk (3.6)

)(kX

1

/2)(

Nn

Nknjenx

+

1

0

/2)(

N

n

Nknjenx +

12

/2)(

N

Nn

Nknjenx

(3.7)

l

NlN

lNn

Nknjenx1

/2)(

=

1

0

/2)()(

N

n

Nknj

l

enxlNnx (3.8)

Thay n = nlN


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Ta c

1

0

/2)()(

N

n

Nknj

p enxkX vi

)()( lNnxnxp (3.9)

xp(n) lp vi chu k ca xpmi N mu th tun hon vi chu k c bn N

1

0

/2)(

N

k

Nknj

kp ecnx 1,...,1,0 Nn (3.10)

1

0

/2)(

1 N

n

Nknj

pk enxN

c 1,...,1,0 Nk (3.11)

)(1

kXN

ck 1,,1,0 NKk (3.12)

1

0

/2

)(1

)(

N

k

Nknj

p ekXNnx

1,,1,0 NKn (3.13)

C th phc hi xp(n) t cc mu ca ph X(w)

(3.14)

C th phc hi X() t cc mu X(k) vi k=0,1, , N-1

Gi s N L x(n) = xp(n) khi 0 n N-1

1

0

2

)(1

)(N

k

N

knj

ekXN

nx

(3.15)

n

jnenxX

)()( = jn

N

n

N

k

Nkn eekXN

1

0

1

0

/2)(

1(3.16)

=

1

0

1

0

)/2(1)(

N

k

N

k

nNknje

NkX

1

0

1)(

N

n

nje

NP

=

j

Nj

e

e

N

1

1*

1(3.17)

= 2/)1()2/sin(

)2/sin( NjeN

N

10 Nn

Khc

)(

0

)(

nxp

nx


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T (3.16) v (3.17) ta c

1

0

)2

()()(N

k

k

N

PkXX

N L (3.18)

1

0

)2(N

kP

0

1,,2,1

k

NKk

(3.19)

X(n) c chiu di L N sau khi bin i tn s c

n

njenxX

)()( ly mu ta c (3.20)

1

0

2

)()(N

n

N

nkj

enxkX

(3.21)

1

0

1)(

N

k

jne

Np

viN

kk

2 (3.22)

Ta c

1

0

2

)(1

)(N

k

N

kjn

ekXN

nx

(3.23)

c. Bin i Fourier ri rc, i khi cn c gi l bin i Fourier hu hn, l

mt bin i trong gii tch Fouriercho cc tn hiu thi gian ri rc. u vo

ca bin i ny l mt chui hu hn cc s thchoc s phc, lm bin iny l mt cng c l tng x l thng tin trn cc my tnh. c bit, bin

i ny c s dng rng ri trong x l tn hiuv cc ngnh lin quan n

phn tch tn s cha trong trong mt tn hiu, giiphng trnh o hm

ring, v lm cc php nh tch chp. Bin i ny c th c tnh nhanh bi

thut ton bin i Fourier nhanh(FFT).

*)nh nghaDy caNs phc:x0,...,xN 1c bin i thnh chui caNs phcX0,

...,XN1bi cng thc sau y:
http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_h%E1%BB%AFu_h%E1%BA%A1n&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_h%E1%BB%AFu_h%E1%BA%A1n&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Gi%E1%BA%A3i_t%C3%ADch_Fourier&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Gi%E1%BA%A3i_t%C3%ADch_Fourier&action=edit&redlink=1http://vi.wikipedia.org/wiki/S%E1%BB%91_th%E1%BB%B1chttp://vi.wikipedia.org/wiki/S%E1%BB%91_th%E1%BB%B1chttp://vi.wikipedia.org/wiki/S%E1%BB%91_ph%E1%BB%A9chttp://vi.wikipedia.org/wiki/M%C3%A1y_t%C3%ADnhhttp://vi.wikipedia.org/wiki/M%C3%A1y_t%C3%ADnhhttp://vi.wikipedia.org/w/index.php?title=X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u&action=edit&redlink=1http://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1o_h%C3%A0m_ri%C3%AAnghttp://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1o_h%C3%A0m_ri%C3%AAnghttp://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1o_h%C3%A0m_ri%C3%AAnghttp://vi.wikipedia.org/w/index.php?title=T%C3%ADch_ch%E1%BA%ADp&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_nhanh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_nhanh&action=edit&redlink=1http://vi.wikipedia.org/wiki/S%E1%BB%91_ph%E1%BB%A9chttp://vi.wikipedia.org/wiki/S%E1%BB%91_ph%E1%BB%A9chttp://vi.wikipedia.org/wiki/S%E1%BB%91_ph%E1%BB%A9chttp://vi.wikipedia.org/wiki/S%E1%BB%91_ph%E1%BB%A9chttp://vi.wikipedia.org/wiki/S%E1%BB%91_ph%E1%BB%A9chttp://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_nhanh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=T%C3%ADch_ch%E1%BA%ADp&action=edit&redlink=1http://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1o_h%C3%A0m_ri%C3%AAnghttp://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1o_h%C3%A0m_ri%C3%AAnghttp://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1o_h%C3%A0m_ri%C3%AAnghttp://vi.wikipedia.org/w/index.php?title=X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u&action=edit&redlink=1http://vi.wikipedia.org/wiki/M%C3%A1y_t%C3%ADnhhttp://vi.wikipedia.org/wiki/S%E1%BB%91_ph%E1%BB%A9chttp://vi.wikipedia.org/wiki/S%E1%BB%91_th%E1%BB%B1chttp://vi.wikipedia.org/w/index.php?title=Gi%E1%BA%A3i_t%C3%ADch_Fourier&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_h%E1%BB%AFu_h%E1%BA%A1n&action=edit&redlink=1


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(3.24)

vi e lc s ca log t nhin, ln v o(i2 = 1), v l pi.Php bin i

asin or or .i khi c k hiu bi ,

Php bin i Fourier ri rc ngcc cho bi cng thc sau

(3.25)

*) ng dng ca bin i Fourier

Bin i Fourier c rt nhiu ng dng khoa hc, v d nh trong vt l,

s hc,x l tn hiu,xc sut,thng k,mt m,m hc,hi dng hc, quanghc,hnh hcv rt nhiu lnh vc khc. Trong x l tn hiu v cc ngnh lin

quan, bin i Fourier thng c ngh n nh s chuyn i tn hiu thnh

cc thnh phn bin vtn s. S ng dng rng ri ca bin i Fourier bt

ngun t nhng tnh chthu dng ca bin i ny:

- Tnhtuyn tnh: (3.26)-

Tn ti bin i nghch o, v thc t l bin i Fourier nghch o gnnh c cng dng vi bin i thun.

-Nhng hm s sin c s l cchm ring ca phpvi phn, c ngha l khaitrin ny bin nhngphng trnh vi phn tuyn tnh vi cc h s khng i

thnh cc phng trnh i s c bn. V d, trong mt h vt l tuyn tnh

khng ph thuc thi gian, tn sl mt i lng khng i,do nhng thnh

phn tn s khc nhau c th c tnh ton mt cch c lp.

- Theo nh l tch tng chp, bin i Fourier chuyn mt tch tng chpphc tp thnh mt tch i s n gin.

- Bin i Fourier ri rcc th c tnh ton mt cch nhanh chng bngmy tnh nh thut tonFFT (Bin i Fourier nhanh).
http://vi.wikipedia.org/wiki/E_%28h%E1%BA%B1ng_s%E1%BB%91_to%C3%A1n_h%E1%BB%8Dc%29http://vi.wikipedia.org/wiki/E_%28h%E1%BA%B1ng_s%E1%BB%91_to%C3%A1n_h%E1%BB%8Dc%29http://vi.wikipedia.org/wiki/E_%28h%E1%BA%B1ng_s%E1%BB%91_to%C3%A1n_h%E1%BB%8Dc%29http://vi.wikipedia.org/wiki/%C4%90%C6%A1n_v%E1%BB%8B_%E1%BA%A3ohttp://vi.wikipedia.org/wiki/%C4%90%C6%A1n_v%E1%BB%8B_%E1%BA%A3ohttp://vi.wikipedia.org/wiki/%C4%90%C6%A1n_v%E1%BB%8B_%E1%BA%A3ohttp://vi.wikipedia.org/wiki/Pihttp://vi.wikipedia.org/wiki/Khoa_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/V%E1%BA%ADt_l%C3%BDhttp://vi.wikipedia.org/wiki/V%E1%BA%ADt_l%C3%BDhttp://vi.wikipedia.org/w/index.php?title=S%E1%BB%91_h%E1%BB%8Dc&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=S%E1%BB%91_h%E1%BB%8Dc&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u&action=edit&redlink=1http://vi.wikipedia.org/wiki/X%C3%A1c_su%E1%BA%A5thttp://vi.wikipedia.org/wiki/X%C3%A1c_su%E1%BA%A5thttp://vi.wikipedia.org/wiki/X%C3%A1c_su%E1%BA%A5thttp://vi.wikipedia.org/wiki/Th%E1%BB%91ng_k%C3%AAhttp://vi.wikipedia.org/wiki/Th%E1%BB%91ng_k%C3%AAhttp://vi.wikipedia.org/wiki/Th%E1%BB%91ng_k%C3%AAhttp://vi.wikipedia.org/wiki/M%E1%BA%ADt_m%C3%A3http://vi.wikipedia.org/wiki/M%E1%BA%ADt_m%C3%A3http://vi.wikipedia.org/wiki/M%E1%BA%ADt_m%C3%A3http://vi.wikipedia.org/wiki/%C3%82m_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/%C3%82m_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/%C3%82m_h%E1%BB%8Dchttp://vi.wikipedia.org/w/index.php?title=H%E1%BA%A3i_d%C6%B0%C6%A1ng_h%E1%BB%8Dc&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=H%E1%BA%A3i_d%C6%B0%C6%A1ng_h%E1%BB%8Dc&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=H%E1%BA%A3i_d%C6%B0%C6%A1ng_h%E1%BB%8Dc&action=edit&redlink=1http://vi.wikipedia.org/wiki/Quang_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/Quang_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/Quang_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/T%C3%ADn_hi%E1%BB%87uhttp://vi.wikipedia.org/wiki/T%C3%ADn_hi%E1%BB%87uhttp://vi.wikipedia.org/wiki/Bi%C3%AAn_%C4%91%E1%BB%99http://vi.wikipedia.org/wiki/Bi%C3%AAn_%C4%91%E1%BB%99http://vi.wikipedia.org/wiki/T%E1%BA%A7n_s%E1%BB%91http://vi.wikipedia.org/wiki/T%E1%BA%A7n_s%E1%BB%91http://vi.wikipedia.org/w/index.php?title=T%C3%ADnh_ch%E1%BA%A5t&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=T%C3%ADnh_ch%E1%BA%A5t&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Tuy%E1%BA%BFn_t%C3%ADnh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Tuy%E1%BA%BFn_t%C3%ADnh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Tuy%E1%BA%BFn_t%C3%ADnh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=H%C3%A0m_ri%C3%AAng&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=H%C3%A0m_ri%C3%AAng&action=edit&redlink=1http://vi.wikipedia.org/wiki/Vi_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Vi_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Vi_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_vi_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_vi_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1i_s%E1%BB%91http://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1i_s%E1%BB%91http://vi.wikipedia.org/wiki/T%E1%BA%A7n_s%E1%BB%91http://vi.wikipedia.org/wiki/T%E1%BA%A7n_s%E1%BB%91http://vi.wikipedia.org/w/index.php?title=%C4%90%E1%BB%8Bnh_l%C3%BD_t%C3%ADch_t%E1%BB%95ng_ch%E1%BA%ADp&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=T%C3%ADch_t%E1%BB%95ng_ch%E1%BA%ADp&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=T%C3%ADch_t%E1%BB%95ng_ch%E1%BA%ADp&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Fourier_r%E1%BB%9Di_r%E1%BA%A1c&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Fourier_r%E1%BB%9Di_r%E1%BA%A1c&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_nhanh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_nhanh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Bi%E1%BA%BFn_%C4%91%E1%BB%95i_Fourier_nhanh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Fourier_r%E1%BB%9Di_r%E1%BA%A1c&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=T%C3%ADch_t%E1%BB%95ng_ch%E1%BA%ADp&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=%C4%90%E1%BB%8Bnh_l%C3%BD_t%C3%ADch_t%E1%BB%95ng_ch%E1%BA%ADp&action=edit&redlink=1http://vi.wikipedia.org/wiki/T%E1%BA%A7n_s%E1%BB%91http://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1i_s%E1%BB%91http://vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_vi_ph%C3%A2nhttp://vi.wikipedia.org/wiki/Vi_ph%C3%A2nhttp://vi.wikipedia.org/w/index.php?title=H%C3%A0m_ri%C3%AAng&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=Tuy%E1%BA%BFn_t%C3%ADnh&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=T%C3%ADnh_ch%E1%BA%A5t&action=edit&redlink=1http://vi.wikipedia.org/wiki/T%E1%BA%A7n_s%E1%BB%91http://vi.wikipedia.org/wiki/Bi%C3%AAn_%C4%91%E1%BB%99http://vi.wikipedia.org/wiki/T%C3%ADn_hi%E1%BB%87uhttp://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/Quang_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/Quang_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/Quang_h%E1%BB%8Dchttp://vi.wikipedia.org/w/index.php?title=H%E1%BA%A3i_d%C6%B0%C6%A1ng_h%E1%BB%8Dc&action=edit&redlink=1http://vi.wikipedia.org/wiki/%C3%82m_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/M%E1%BA%ADt_m%C3%A3http://vi.wikipedia.org/wiki/Th%E1%BB%91ng_k%C3%AAhttp://vi.wikipedia.org/wiki/X%C3%A1c_su%E1%BA%A5thttp://vi.wikipedia.org/w/index.php?title=X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u&action=edit&redlink=1http://vi.wikipedia.org/w/index.php?title=S%E1%BB%91_h%E1%BB%8Dc&action=edit&redlink=1http://vi.wikipedia.org/wiki/V%E1%BA%ADt_l%C3%BDhttp://vi.wikipedia.org/wiki/Khoa_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/Pihttp://vi.wikipedia.org/wiki/%C4%90%C6%A1n_v%E1%BB%8B_%E1%BA%A3ohttp://vi.wikipedia.org/wiki/E_%28h%E1%BA%B1ng_s%E1%BB%91_to%C3%A1n_h%E1%BB%8Dc%29


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- Theo nh l Parseval-Plancherel, nng lng ca tn hiu (tch phn cabnh phng gi tr tuyt i ca hm) khng i sau bin i Fourier.

3.2.1.Nhng bin i Fourier trong vc tnh vc t l loi nh c lu tr theo cch m t ng bin ca cc

i tng trong nh nh l cc hnh v cc ng hnh hc, v d nh elp

(ellipse), a gic (polygon), hnh cung (arc), ng thng (line), ch nht

(rectangle)... Vic lu tr nh vc tthc cht l lu tr li cc lnh dng v

li nh . nh vc tc lu tr di dng hnh hc nn cht lng lu tr

khng tt lm, nhng b vo , kch thc file nh tng i nh v vic x lnh rt n gin, thng qua cc hm ton hc. Cc file nh vc tph bin hin

nay l WMF, CGM, CDR, GEM Metafile...

i su vo chi tit lu tr, mt file nh bao gi cng c ba phn c bn l

phn u (header), bng mu (palette) v d liu (data). Mt vi nh c s

dng trong Windows hay XWindows to giao din nh Icon, Cursor... th c

thm phn nhn dng resource (resource id).

Phn header cho bit cc thng tin v bn thn nh nh chiu di, chiu

rng, v tr bt u hin trn thit b (mn hnh, my in, my v...), s mu..., v

cho bit v cu trc file nh nh kiu nn d liu, vng bt u d liu, v tr

bng mu...

3.3. Kt lun chngThut ton giu v tch tin c s v Tng quan v bin i Fourier, ng

dng

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