Nhận dạng và xử lý ảnh vật thể ứng dụng trong điều khiển

BӜ GIÁO DӨ& 9¬ Ĉ¬2 7ҤO
75ѬӠ1* ĈҤI HӐC NÔNG LÂM THÀNH PHӔ HӖ CHÍ MINH










KHÓA LUҰN TӔT NGHIӊP





NHҰN DҤNG VÀ XӰ LÝ ҦNH VҰT THӆ
ӬNG DӨ1*7521*Ĉ,ӄU KHIӆN








Hӑ và tên sinh viên: Ĉһng Minh Chӭc
PhҥP7Uѭӡng Giang

Niên khóa: 2007-2011




Tháng 5/2011
i

NHҰN DҤNG VÀ XӰ LÝ ҦNH VҰT THӆ ӬNG DӨ1*7521*Ĉ,ӄU KHIӆN









ĈҺNG MINH CHӬC
PHҤ0 75ѬӠNG GIANG

Ts NGUYӈ1 9Ă1 +Ô1*











Tháng 5/2011
ii

LӠI CҦ0Ѫ1

ҫy NguyӉ
ҫ



Xin trân trӑng.
Ĉһng Minh Chӭc
PhҥP7Uѭӡng Giang
iii

TÓM TҲT

ĈӅ tài nghiên cӭX ³QKұn dҥng và xӱ lý ҧnh ӭng dөng trong ÿLӅu khiӇQ´ÿѭӧc thӵc
hiӋn tҥL WUѭӡQJĈҥi Hӑc Nông Lâm Thành Phӕ Hӗ Chí Minh, thӡi gian 3 tháng tӯ tháng 3
ÿӃQQJj\WKiQJQăP
ĈӅ WjL ÿmWKӵc hiӋQ WKjQK F{QJYjÿҥWÿѭӧc kӃt quҧ khҧ TXDQQKѭ ÿLӅu khiӇQÿѭӧc
URERW ÿӃn vӏ trí nhұn dҥng và thӵc hiӋn WKDR WiF KiL Fj FKXD Ĉk\ ÿѭӧc xem là kӃt quҧ
chính cӫDÿӅ WjLÿӇ thӵc hiӋn tӕt kӃt quҧ Qj\WKuFK~QJW{LFNJQJSKҧi thӵc hiӋn thành công
quá trình xӱ lý ҧnh nhұn dҥng v
ұt thӇ, vӏ trí vұt thӇ trong không gian 3 chiӅu bҵng
:HEFDPH WK{QJ TXD FKѭѫQJ WUuQK 0atlab và cҧm biӃQ 65) WK{QJ TXD YL ÿLӅu khiӇn
$70(*$ ĈӇ tӯ ÿyFK~QJ W{LOҩy tín hiӋXÿLӅu khiӇn robot.
1JRjL UD FK~QJW{LFNJQJ WKLӃt kӃ giao diӋn giao tiӃp vӟLQJѭӡi quan sát bҵng ÿӗ thӏ
trong lұp trình GUI cӫa Matlab mӝt cách thân thiӋn ,dӉ hiӇu và dӉ ÿLӅu khiӇn.


iv

MӨC LӨC

LӠI CҦ0Ѫ1 ............................................................................................................................. ii
TÓM TҲT .. ................................................................................................................................. iii
MӨC LӨC .................................................................................................................................. iv
DANH MӨC HÌNH.................................................................................................................. vii
&KѭѫQJ  MӢ ĈҪU ................................................................................................................. 1
1.1 Ĉһt vҩQÿӅ....................................................................................................................... 1
1.2 MөFÿtFK ........................................................................................................................ 2
&KѭѫQJ  TӘNG QUAN ......................................................................................................... 3
2.1 Lý thuyӃt xӱ lý ҧnh. ..................................................................................................... 3
2.1.1 HӋ thӕng xӱ lý ҧnh. ................................................................................................. 3

2.1.2 Thu nhұn ҧQKYjOѭXWUӳ ҧnh. ................................................................................. 4
2.1.3 Phân tích ҧnh............................................................................................................ 9
2.2 ;iFÿӏnh khoҧng cách bҵng sóng siêu âm............................................................. 22
2.2.1 Khái niӋm siêu âm................................................................................................. 22
2.2.2 Cҧm biӃn siêu âm và nguyên tҳc TOF................................................................ 22
2.2.3 Cҧm biӃn siêu âm SRF10. .................................................................................... 28
2.3 Phҫn mӅm Matlap ӭng dөng xӱ lý ҧnh. ................................................................ 31
2.3.1 Khái niӋm MATLAB............................................................................................ 31
2.3.2 Giao diӋn trong Matlab......................................................................................... 31
2.3.3 Khҧ QăQJYjӭng dөng cӫa Matlab. .................................................................... 33
2.3.4 HӋ thӕng lӋnh trong Matlab (Matlab Funtion). ................................................. 33
v

&KѭѫQJ  3+ѬѪ1*7,ӊN 9¬3+ѬѪ1*3+È31*+,Ç1&ӬU. ........................... 36
3.1 Bӕ trí thӵc hiӋQÿӅ tài. ............................................................................................... 36
3.1.1 Thӡi gian. ............................................................................................................... 36
3.1.2 ĈӏDÿLӇm. ................................................................................................................ 36
3.2 3KѭѫQJWLӋn nghiên cӭu. ........................................................................................... 36
3.3 3KѭѫQJSKiSQJKLrQFӭu. ......................................................................................... 37
3.3.1 3KѭѫQJSKiSOêWKX\Ӄt. ......................................................................................... 37
3.3.2 3KѭѫQJSKiSWKӵc nghiӋm ................................................................................... 37
&KѭѫQJ  KӂT QUҦ VÀ THҦO LUҰN. .......................................................................... 39
4.1 Xây dӵng quy trình nhұn dҥng và xӱ lý ҧnh. ...................................................... 39
4.1.1 Quy trình nhұn dҥng và xӱ lý ҧnh. ...................................................................... 39
4.1.2 4X\WUuQK[iFÿӏnh khoҧng cách sӱ dөng cҧm biӃn siêu âm............................ 40
4.2 Kêt quҧ nhұn dҥng và xӱ lý ҧnh. ............................................................................ 41
4.2.1 Quá trình nhұn dҥng và xӱ lý ҧnh. ...................................................................... 41
4.2.2 Quá trình nh
ұn tín hiӋu cҧm biӃn SRF 10. ......................................................... 48
4.2.3 KӃt quҧ FKѭѫQJWUình. ........................................................................................... 50

4.3 KӃt quҧ chӃ tҥRYjÿLӅu khiӇn robot....................................................................... 51
4.3.1 Mô hình chӃ tҥo. .................................................................................................... 51
4.3.2 ĈLӅu khiӇn robot. ................................................................................................... 52
4.3.3 KӃt quҧ khҧo nghiӋPVѫEӝ.................................................................................. 54
4.4 Nhұn xét. ....................................................................................................................... 56
&KѭѫQJ  KӂT LUҰ19¬Ĉӄ NGHӎ................................................................................ 57
5.1 KӃt luұn......................................................................................................................... 57
vi

5.2 ĈӅ nghӏ. ......................................................................................................................... 57
TÀI LIӊU THAM KHҦO ....................................................................................................... 58
PHӨ LӨC ................................................................................................................................. 59

vii

DANH MӨC HÌNH

Hình 2.1 6ѫÿӗ hӋ thӕng xӱ lý ҧnh............................................................................................ 3

Hình 2.2 Sensor quét dòng CCD .............................................................................................. 6

Hình 2.3 4X\ѭӟc tӑDÿӝ cho biӇu diӉn ҧnh............................................................................ 7

Hình 2.4 Pixel P và các lân c ұn cӫa P...................................................................................... 9

Hình 2.5 Mô hình màu RGB ................................................................................................... 11

Hình 2.6 Các màu gӕc bù và sӵ pha trӝn giӳa chúng .......................................................... 11

Hình 2.7 Sӵ biӃQÿәi tӯ RGB thành CMY ............................................................................ 12

Hình 2.8 Mô hình màu HSV ................................................................................................... 12

Hình 2.9 Mô hình màu HLS.................................................................................................... 13

Hình 2.10 Mӝt lân cұQNtFKWKѭӟF[TXDQKÿLӇm (x,y) ................................................... 16

Hình 2.11 Các lân cұn cӫa p sӱ dөQJÿӇ làm nhҹn ҧnh nhӏ phân...................................... 19

Hình 2.12 /jPWUѫQKuQKҧnh nhӏ phân.................................................................................. 21

Hình 2.13 Vùng hoҥWÿӝng cӫa cҧm biӃn siêu âm( nguӗn internet)................................... 24

Hình 2.14 Khu vӵc mù cӫa cҧm biӃn siêu âm( nguӗn internet) ......................................... 24

Hình 2.15 Thӡi gian truyӅn trong nguyên lý TOF ............................................................... 26

Hình 2.16 Tҫm quét cӫa cҧm biӃn siêu âm. .......................................................................... 26

Hình 2.17 Cҧm biӃn siêu âm SRF10...................................................................................... 28

Hình 2.18 6ѫÿӗ kӃt nӕi SRF10 .............................................................................................. 30

Hình 2.19 Giao diӋn Matlab.................................................................................................... 32

Hình 3.1 6ѫÿӗ SKѭѫQJSKiSÿLӅu khiӇn robot..................................................................... 37

Hình 3.2 3KѭѫQJSKiSÿLӅu khiӇn hӗi tiӃp........................................................................... 38

Hình 4.1 6ѫÿӗ nhұn dҥng và xӱ lý ҧnh ................................................................................ 39

Hình 4.2 6ѫÿӗ [iFÿӏnh kho ҧng cách sӱ dөng cҧm biӃn SRF10 ...................................... 40

Hình 4.3 6ѫÿӗ mҥFKYLÿLӅu khiӇn ........................................................................................ 41

Hình 4.4 6ѫÿӗ nhұn dҥng và xӱ lý ҧnh ӭng dөQJÿLӅu khiӇn............................................ 41

Hình 4.5 Hình ҧnh thu nhұn tӯ Webcame ............................................................................. 42

viii

Hình 4.6 6ѫÿӗ nhұn dҥQJYjWUtFKÿӕLWѭӧng. ...................................................................... 42

Hình 4.7 Ҧnh sau khi chuyӇn sang ҧnh xám......................................................................... 43

Hình 4.8 Ҧnh khi trích xuҩWJDPPjXÿӓ .............................................................................. 44

Hình 4.9 6ѫÿӗ quá trình xӱ lý phân tích ҧnh ...................................................................... 44

Hình 4.10 Ҧnh sau khi lӑc trung vӏ ........................................................................................ 45

Hình 4.11 Lӑc bӓ YQJGѭӟi 300px ....................................................................................... 46

Hình 4.12 ҦQKÿmÿѭӧFÿӏQKWkPYjÿyQJNKXQJ ............................................................... 46

Hình 4.13 ;iFÿӏnh khoҧng cáchhiӇn thӏ tӑDÿӝ tӟi tâm hình ............................................ 47

Hình 4.14 KӃt quҧ hӋ quyӃWÿӏnh ............................................................................................ 47

Hình 4.15 6ѫÿӗ khӕi qúa trình nhұn tín hiӋu cҧm biӃn SRF10 ......................................... 48

Hình 4.16 KӃt quҧ hiӇn thӏ trên màn hình LCD ................................................................... 49

Hình 4.17 KӃt quҧ hiӇn thӏ tín hiӋu cҧm biӃn trên Matlap .................................................. 49

Hình 4.18 Giao diӋn hiӇn thӏ FKѭѫQJWUuQK[ӱ lý ҧnh .......................................................... 50

Hình 4.19 Giao diӋn hiӇn thӏ kӃt quҧ hӋ thӕng ..................................................................... 51

Hình 4.20 Mô hình robot ӭng dөng xӱ lý ҧnh ...................................................................... 52

Hình 4.21 Giҧi thuұWÿLӅu khiӇn robot ................................................................................... 53

Hình 4.22 BiӇXÿӗ khҧo nghiӋPÿӝ phân giҧi ...................................................................... 55

Hình 4.23 BiӇXÿӗ thӡLJLDQÿiSӭng ..................................................................................... 56


ix

DANH MӨC VIӂT TҲT

CCD Charge Coupled Device
CMOS Complementary Metal-Oxide-Semiconductor
GIF Graphics Interchange Format
P Pixel
CMY Cyan, Magenta, Yellow
TOF Time Of Flight
RLE Run-Length-Encoded
RGB Red, Green, Bule

1



&KѭѫQJ

MӢ ĈҪU
1.1 Ĉһt vҩQ ÿӅ.
7URQJ Pҩ\ WKұS Nӹ JҫQ ÿk\ [ӱ OêҧQKÿm ÿѭӧFQJKLrQFӭX PҥQKPӁYjÿmFyUҩW
QKLӅXӭQJ GөQJWURQJ WKӵFWӃ 1KѭWURQJ \KӑF[ӱOêҧQKVӕÿmÿѭӧFGQJÿӇSKiWKLӋQYj
QKұQ GҥQJ NKӕL X FҧL WKLӋQ ҧQK ; TXDQJ QKұQ GҥQJ ÿѭӡQJ ELrQ PҥFKPiX Wӯ QKӳQJ ҧQK
FKөS PҥFKEҵQJ WLD ; 7URQJFXӝF VӕQJ JLD ÿuQK [ӱOêҧQKÿѭӧFGQJÿӇFҧLWKLӋQҧQK7L
YL 7URQJWUX\ӅQ WK{QJYLGHRQKѭ KӝL QJKӏ YLGHR ÿLӋQ WKRҥL YLGHRWKuPӝWYҩQÿӅFKtQKOj
FҫQ Fy GҧL WҫQ UӝQJ 9LӋF Pm KyD WKҷQJ FiF FKѭѫQJ WUuQK YLGHR FKҩWOѭӧQJTXҧQJEiFҫQ
ÿӃQWULӋXELWV ĈLӅX Qj\ NK{QJ WKӇ ÿiS ӭQJ ÿѭӧF 1KѭQJ EҵQJ FiFK PmKyDVӕYj
NK{LSKөF ҧQKOj QKӳQJ YҩQ ÿӅFӫD [ӱ OêҧQKWKu YLӋFWUrQFyWKӇWKӵFKLӋQFKӍYӟLEăQJ
WҫQQJKuQELWV&zQWURQJOƭQKYӵFNKRDKӑFNӻWKXұW[ӱOê ҧQKÿmYjÿDQJFyQKӳQJ
ÿyQJ JyS TXDQWUӑQJ ÿһF ELӋW Oj WURQJ OƭQKYӵF 5RERW 5RERW WK{QJ PLQK QJj\QD\NK{QJ
WKӇ WKLӃX \ӃX Wӕ [ӱ Oê ҧQK Ĉy Oj FiFYҩQÿӅ QKұQ GҥQJFiF ÿӕLWѭӧQJ QJRjL P{LWUѭӡQJ
7ӯ YLӋF QKұQ GҥQJ Fy WKӇ JLҧL TX\ӃW UҩW QKLӅX EjL WRiQ QKѭ WUiQK YұW FҧQ Gz ÿѭӡQJ WuP
YұW« 7ӯ QKӳQJ Fѫ Vӣ ÿy YLӋF QJKLrQ FӭX EjLWRiQ[ӱ Oê ҧQK WURQJ WKӡL ÿҥL QJj\QD\Oj
UҩWTXDQ WUӑQJYj NK{QJ WKӇWKLӃXWURQJKҫX KӃWFiFOƭQKYӵF
1Jj\ QD\ OƭQK YӵF NKRD KӑF Nӻ WKXұW F{QJ QJKӋ SKiW WULӇQ PӝW FiFKQKDQKFKyQg
YjPҥQK PӁ ÿһFELӋWOjOƭQK YӵF 5RERWWK{QJPLQK ;ӱOêҧQKOjEjLWRiQNK{QJWKӇWKLӃX
WURQJ 5RERW  Qy Fy WKӇ ÿѭӧF [HP Oj FRQPҳWFӫD 5RERW Qy Fy WKӇ JL~S 5RERW TXDQ ViW
WKHRG}LÿӕLWѭӧQJ  GzÿѭӡQJWuPYұWÿLӅXQj\UҩWTXDQWUӑQJFKRÿLӅX NKLӇQ5RERW
9u WKӃ EjL WRiQ [ӱ OêҧQKVӁJL~SFKR WDÿLӅXNKLӇQ 5RERWPӝW FiFKFKtQK[iFYjGӉGjQJ
KѫQ
2

1.2 MөFÿtFK
'ӵD WUrQQKӳQJ \rXFҫXWKӵFWӃQJj\ QD\ WURQJOƭQKYӵF5RERWWK{QJ PLQK
&K~QJ W{L WKӵF KLӋQ ÿӅ WjL ³QKұQ GҥQJ Yj [ӱ Oê ҧQK YұW WKӇ ӭQJ GөQJ WURQJ ÿLӅX
NKLӇQ´ YӟL PөF ÿtFK QKұQ GҥQJ YұW WKӇ WK{QJ TXD PjX VҳFYұWYjÿӏQKGҥQJYӏWUtYұWWKӇ
WURQJNK{QJ JLDQ ÿӇOҩ\WtQKLӋXÿLӅXNKLӇQ 5RERW
9u WKӡLJLDQJLӟLKҥQFNJQJ QKѭ PӭF ÿӝ UӝQJOӟQ FӫDÿӅ WjLQrQ FK~QJHP FKӍ WKӵF
KLӋQQJKLrQ FӭXFiFYҩQ ÿӅFѫEҧQ VDX
6ӱGөQJ :HEFDPHNӃWKӧSSKҫQ PӅP0$7/$% SKiW KLӋQÿӕLWѭӧQJ Yj ÿӏQKYӏ
WUtÿӕLWѭӧQJ WKHRSKѭѫQJ [\
6ӱGөQJ FҧP ELӃQVLrXkP 65)ÿӇ[iFÿӏQKNKRҧQJ FiFKÿӕLWѭӧQJWKHRSKѭѫQJ
z.
ӬQJ GөQJ [ӱ OêҧQK YjRÿLӅXNKLӇQ 52%27
3



&KѭѫQJ

TӘNG QUAN
2.1 Lý thuyӃt xӱ lý ҧnh.
2.1.1 HӋ thӕng xӱ lý ҧnh.
Mӝt hӋ thӕng xӱ lý ҧQKÿLӇQKuQKWKѭӡng bao gӗm nhӳng thành phҫn sau:

Hình 2.1 6ѫÿӗ hӋ thӕng xӱ lý ҧnh.
7ӯ KuQKYӁ WDWKҩ\PӝWKӋWKӕQJ [ӱ OêҧQK EDRJӗPWKX QKұQ ҧQK VӕKyDҧQK SKkQ
WtFKҧQK Yj FXӕLFQJ OjTX\ӃWÿӏQK W\WKXӝFYjR \rXFҫX ӭQJ GөQJ FөWKӇPjÿѭDUD
TX\ӃWÿӏQKFKRSK KӧS
ThiӃt bӏ thu
nhұn ҧnh
(camera,

sensor)
Thu nhұn
ҧnh
Sӕ hóa
Phân
tích
ҧnh
Nhұn
dҥng
LѭX
trӳ
LѭX
trӳ
HӋ quyӃt
ÿӏnh
4

2.1.1.1Thu nhұn ҧnh và sӕ hóa.
9LӋF WKX QKұQ ҧQK Fy WKӇ WK{QJ TXD FDPHUD &iF FDPHUD Fy WKӇ KRһF Oj WѭѫQJ Wӵ
ORҥL FDPHUD  ӕQJ NLӇX &&,5 KRһF Oj Vӕ ORҥL FDPHUD NLӇX &&'B &KDUJH &RXSOHG
'HYLFH ҦQKFNJQJ FyWKӇÿѭӧF WKX TXD FiFWKLӃW Eӏ NKiFQKѭ Pi\ TXpWYY1ӃXҧQKQKұQ
ÿѭӧF Oj WѭѫQJ Wӵ Qy SKҧL ÿѭӧF Vӕ KyD QKӡ TXi WUuQK Oҩ\ PүX Yj OѭӧQJ Wӱ KyDWUѭӟF NKL
SKkQ WtFK[ӱOêKD\ OѭX WUӳҧQK.
2.1.1.2Phân tích ҧnh.
Ӣ JLDL ÿRҥQQj\ҧQKÿѭӧF [ӱ Oê WKHRQKLӅXF{QJ ÿRҥQQKӓ QKѭ FҧLWKLӋQҧQKNK{L
SKөF ҧQK ÿӇOjP QәLEұWPӝW VӕÿһF WtQKFKtQKFӫDҧQKKD\OjPҧQKJҫQYӟLWUҥQJWKiLJӕF
7LӃS WKHROjSKiW KLӋQ FiFÿһFWtQK QKѭ ELrQSKkQ YQJ
2.1.1.3HӋ quyӃWÿӏnh.
&XӕLFQJ W\ WKHRPөFÿtFKFӫDӭQJ GөQJ VӁOjJLDLÿRҥQQKұQ GҥQJ KD\ FiF
TX\ӃWÿӏQKNKiF

2.1.2 Thu nhұn ҧQK YjOѭXWUӳ ҧnh.
2.1.2.1Thu nhұn ҧnh.
ҦQK Fy WKӇ ÿѭӧF WKX QKұQ TXD FDPHUD ӣ GҥQJ WtQ KLӋX WѭѫQJ Wӵ ORҥLFDPHUDӕQJ
FKXҭQ &&,5YӟLWҫQVӕ PӛLҧQKGzQJKRһFӣGҥQJWtQKLӋXVӕORҥL&&'Oj
ORҥL SKRWRGLRGH WҥR UD FѭӡQJ ÿӝ iQK ViQJ WҥL PӛL ÿLӇP ҧQK 0һW NKiF ҧQK FNJQJFy WKӇ
WLӃS QKұQ Wӯ YӋ WLQK TXD FiFEӝ FҧP ӭQJ VHQVRU FyWKӇ TXpW ҧQKWӯ ҧQK FKөSEҵQJPi\
WtQKTXpW ҧQK VFDQHU
&ҩXWҥR&amera (Webcame)
:HEFDPH  :HE FDPHUD ÿѭӧF KLӇX QKѭ PӝW WKLӃW Eӏ WKX QKұQ ҧQK GѭӟL GҥQJ WtQ
KLӋXVӕFҩXWҥRFKXQJ QKѭ VDX
- ӔQJ NtQK/HQV WKѭӡQJ OjP EҵQJYұWOLӋXGҿRFyWKӇÿLӅXFKӍQKWLrXFӵFӫD
FDPHUDEҵQJ FiFK [RD\ ӕQJNtQK
- &ҧP ELӃQ KuQK ҧQK ,PDJH 6HQVRU Fy WKӇ Oj &&' FKDUJH-Coupled
Device)hay là CMOS( Complementary Metal-Oxide-Semiconductor).
5

- 0ӝWVӕWKLӃWEӏNKiF
Cҧm biӃn hình ҧnh là thiӃt bӏ có khҧ QăQJFKөp và sӕ hóa hình ҧnh dӵa trên nguyên
Oê WtFK ÿLӋQ Gѭӟi tác dөng cӫa ánh sáng ( hình ҧnh ) thu nhұQÿѭӧFVDXÿyÿѭӧc sӕ hóa
thông qua tín hiӋXÿLӋQÿmÿѭӧc chuyӇQÿәi. trên nguyên tҳc làm viӋFFKXQJÿyFҧm biӃn
hình ҧQK ÿѭӧc chia làm hai loҥi: CCD và CMOS. Tuy nhiên hai cҧm biӃQQj\ÿѭӧc chӃ
tҥo theo hai kӻ thuұt hoàn toàn khác nhau.
Trong thӵc tӃ hiӋQ QD\ NK{QJ tW QJѭӡL WURQJ FK~QJ WD QJKƭ Uҵng camera CCD có
công nghӋ tiên tiӃQKѫQFDPHUD&0267Kӵc chҩW ÿLӅu này không hҷQ ÿ~QJEӣi vì mӛi
công nghӋ ÿӅXFyѭXQKѭӧF ÿLӇm, thӃ mҥnh riêng tùy theo nhu cҫu và ӭng dөng.
&ҧPELӃQ&&'
7KjQKSKҫQFѫ EҧQFӫD 6HQVRU &&'TXpWGzQJ Oj PӝWKjQJSKkQ Wӱ ҧQKVLOLFJӑLOj
SKRWRVLWHV &iF SKRWR KuQK ҧQKFKR TXD PӝWFҩX WU~FFәQJ ÿDWLQK WKӇ WURQJ VXӕWYjÿѭӧF
KҩS WKө WURQJ WLQK WKӇVLOLFGRÿyWҥRQrQPӝWFһSOӛHOHFWURQ &iF TXDQJ ÿLӋQWӱ WҥR UD
ÿѭӧFWұSKӧSYjRFiFSKRWRVLWHOѭӧQJÿLӋQWtFKÿѭӧFWұSKӧSWURQJPӛLSKRWRVLWHWӹOӋ

YӟL FѭӡQJ ÿӝFKLӃX ViQJWҥLÿLӇP ÿy 0ӝWVHQVRUTXpW GzQJ ÿLӇQKuQKJӗPPӝWKjQJFiF
SKkQWӱ ҧQK SKRWRVLWH KDL FәQJWUX\ӅQ ÿѭӧFVӱ GөQJÿӇ FKӕW OҥL QӝLGXQJFӫDFiFSKҫQWӱ
hình ҧQKYjR FiF WKDQK JKL YұQ FKX\ӇQ Yj PӝWFәQJ QӕL UD ÿѭӧFVӱGөQJÿӇFKӕWQӝLGXQJ
FӫD FiF WKDQK JKL YұQ FKX\ӇQ YjR Eӝ NKX\ӃFK ÿҥL OӕL UD FӫD Eӝ NKX\ӃFKÿҥLQj\OjPӝW
WtQKLӋXÿLӋQiS WӹOӋYӟLFiFQӝLGXQJ FӫDKjQJ SKRWRVLWHV
6


Hình 2.2 Sensor quét dòng CCD
&iFPҧQJ NKӕLJKpS GLӋQ WtFK JLӕQJ FiF VHQVRU TXpW GzQJ QJRҥL WUӯFiFSKRWRVLWH
ÿѭӧFVҳS [ӃSWKHR GҥQJ PD WUұQYjFy PӝWWәKӧS WKDQK JKLYұQFKX\ӇQFәQJJLӳDFiFFӝW
SKRWRVLWH QKѭ WURQJ KuQK 1ӝLGXQJ FӫDFiFSKRWRVLWHOҿÿѭӧFFKӕWOҫQOѭӧWYjRFiFWKDQK
JKLYұQFKX\ӇQGӑF Yj VDX ÿyOҥLÿѭӧFFKӕW YjRFiF WKDQK JKLYұQFKX\ӇQ QJDQJ 1ӝLGXQJ
FӫD FiF WKDQK JKL YұQ FKX\ӇQ QJDQJ Qj\ ÿѭӧF GүQ YjR Eӝ NKX\ӃFK ÿҥL OӕL UD FӫD
EӝNKX\ӃFK ÿҥL Oj PӝW GzQJ Oҿ KuQK ҧQK 7KӵF KLӋQ WѭѫQJ Wӵ YӟL FiF SKRWRVLWH FKҹQ ÿӇ
KRjQ WKjQK WUѭӡQJ WKӭKDLFӫD NKXQJ&ѫFҩX TXpWQj\ÿѭӧFOһSOҥLOҫQPӛLJLk\
&iF FDPHUD TXpW GzQJ FKӍFKR UD PӝWGzQJ KuQK ҧQK FӫDKuQKҧQKOӕLYjR1KӳQJ
WKLӃW Eӏ Qj\ ÿһF ELӋWSKKӧSFKRFiFӭQJGөQJPjFiFÿӕLWѭӧQJFKX\ӇQÿӝQJTXDVHQVRU
QKѭ WURQJ FiF EăQJ WUX\ӅQ  6ӵ FKX\ӇQ ÿӝQJFӫD PӝWÿӕL WѭӧQJWKHR KѭӟQJ YX{QJJyF
YӟL VHQVRU WҥR UD KuQK ҧQK KDL FKLӅX &iF VHQVRU TXpW GzQJ  Fy ÿӝ SKkQJLҧL WKҩS [
WUXQJ EuQK [ Yj FDRSKkQWӱ ҧQK Yj FiF VHQVRUWKtQJKLӋP &&'Fy NKҧQăQJ
ÿҥWÿѭӧFÿӝSKkQ JLҧLNKRҧQJ [KD\FDRKѫQ
Ӣ ÿk\ WDNêKLӋXҧQKOӕLUDKDLFKLӅXFӫDFDPHUDKD\WKLӃWEӏFKRҧQKNKiFOjI[\
WURQJ ÿy [ \ ELӇX WKӏ WRҥ ÿӝNK{QJ JLDQ YtGөPһW SKҷQJ ҧQK YjJLiWUӏIWҥL ÿLӇP [\
7

EҩW NǤ Wӹ OӋ YӟL WRҥ ÿӝ FѭӡQJ ÿӝ VDQJ FӫD KuQK ҧQK WҥL ÿLӇP ÿy  +uQK PLQK KRҥPӝW
ÿLӇPҧQK Yj TX\ѭӟFWRҥÿӝFӫDQy

Hình 2.3 4X\ ѭӟc tӑDÿӝ cho biӇu diӉn ҧnh

ĈӇ Pi\ WtQK  Fy WKӇ [ӱ Oê KjP ҧQK [\ SKҧL ÿѭӧF Vӕ KRi FҧYӅ NK{QJ JLDQ OүQ
ELrQÿӝ FѭӡQJ ÿӝ 9LӋFVӕKRiFiFWRҥÿӝNK{QJJLDQ[\ÿѭӧFFRLQKѭOjYLӋFOҩ\PүX
KuQKҧQK WURQJNKLÿy YLӋFVӕ KRiELrQ ÿӝ ÿѭӧFFRL Oj OѭӧQJWӱKRiFѭӡQJÿӝFKRQKӳQJ
KuQKҧQKÿѫQVҳFYjSKҧQ ҧQK EҧQ FKҩW FӫD FiF ҧQK Qj\OjELӃQWKLrQWӯ ÿHQ WӟL WUҳQJWKHR
FiF PӭF [iP NKiF QKDX +DL WKXұW QJӳ FѭӡQJ ÿӝ ViQJ Yj PӭF [iP Fy WKӇ GXQJ KRiQ
FKX\ӇQ FKRQKDX
*LҧVӱ PӝWKuQK ҧQKOLrQWөFÿѭӧFOҩ\PүX ÿӗQJQKҩWFKR PӝWPҧQJ 1 KjQJ Yj0
FӝW ӣÿk\ PӛLPүX FNJQJÿѭӧF OѭӧQJWӱ KRi YӅELrQ ÿӝ 0ҧQJQj\ÿѭӧFJӑLOjҧQKVӕFy
WKӇÿѭӧFYLӃWQKѭVDX

>II«««««««««I0-1)]
)[\ II«««««««««I0-1)
«««««««««««««
f(N-1,0)f(N-««««««I1-1,M-1)
Ӣÿk\FiFELӃQ UӡLUҥF[ «1-Yj \ «0-1
8

0ӛL SKҫQ Wӱ WURQJ PҧQJ ÿѭӧF JӑL Oj PӝW SKҫQ Wӱ ҧQK KD\ SL[HO 7ӯ PҧQJWDWKҩ\
SL[HOWҥLJӕFFӫDҧQKÿѭӧFELӇXWKӏOjISL[HOErQSKҭLOjIYY7K{QJWKѭӡQJ1
0YjVӕPӭFFѭӡQJÿӝUӡLUҥFFӫDPӛL SL[HOÿmOѭӧQJ WӱKRiOjOXӻWKӯD QJX\rQ FӫD
&ҧP ELӃQ &026FNJQJ JLӕQJ QKѭ FҧP ELӃQ &&' &026 FNJQJ KҩS WKө iQK
ViQJ WK{QJ TXD PҧQJ GLRGH TXDQJ 7X\ QKLrQ ErQ WURQJ PӛL SL[HOGLRGHQj\ÿѭӧFWtFK
KӧS PӝWPҥFKNKXӃFK ÿҥL OӑFQKLӉXYjPҥFKVӕKyDÿӇFy WKӇWӵÿӝQJGzWuPSKRWRQiQK
ViQJ KҩSWKөÿѭӧFFKX\ӇQ ÿәLWKjQKÿLӋQ iS YjWUӵFWLӃSWUX\ӅQWtQKLӋXÿӃQQJ}UD9uWKӃ
WtQKLӋXÿLӋQӣQJ}UDOjWtQKLӋXӣGҥQJ Vӕ
2.1.2.2/ѭXWUӳ ҧnh.
ҦQK WUrQ Pi\ WtQK Oj NӃW TXҧ WKX QKұQ WKHR FiF SKѭѫQJ SKiS Vӕ KRi ÿѭӧF QK~QJ
WURQJFiFWKLӃWEӏNӻWKXұWNKiF QKDX4Xi WUuQKOѭXWUӳҧQK QKҵP PөFÿtFK
7LӃW NLӋPEӝQKӟ
*LҧP WKӡLJLDQ[ӱ Oê

9LӋF OѭX WUӳ WK{QJ WLQ WURQJEӝ QKӟFy ҧQKKѭӣQJUҩWOӟQÿӃQYLӋFKLӇQWKӏLQҩQYj
[ӱ Oê ҧQK ÿѭӧF [HP QKѭ Oj  WұS KӧS FiF ÿLӇP YӟL FQJ NtFK WKѭӟF QӃX Vӱ GөQJ FjQJ
QKLӅX ÿLӇP ҧQK WKu EӭF ҧQK FjQJ ÿҽS FjQJ PӏQ Yj FjQJWKӇKLӋQ U}KѫQFKLWLӃWFӫDҧQK
QJѭӡL WDJӑLÿһFÿLӇPQj\ OjÿӝSKkQ JLҧL
ĈӇ OѭX WUӳ  ҧQK WUrQ Pi\ WtQK PӝWVӕÿӏQKGҥQJ ҧQK VDX QKѭ ,0* 3&; 7,))
GIF.
ĈӏQK GҥQJ ҧQK ,0* GXQJ FKR ҧQK ÿHQ WUҳQJ 3KҫQ ÿҫXFӫD ҧQK ,0* Fy
E\WHFKӭD FiFWK{QJ WLQ
- E\WHÿҫXGQJ ÿӇÿiQKGҩX ÿӏQKGҥQJ ҧQK,0*
-  E\WH WLӃSWKHRFKӭD ÿӝGjL PүX WLQ ĈyOjÿӝGjLFӫDGm\FiFE\WHNӅOLӅQ
QKDXPjGm\Qj\VӁÿѭӧFOһSOҥLPӝWVӕOҫQQjRÿy6ӕOҫQOһSOҥLQj\VӁÿѭӧFOѭXWURQJ
E\WH ÿӃP 1KLӅX Gm\ JLӕQJ QKDX ÿѭӧF OѭX WURQJPӝWE\WH Ĉk\ OjPӝWFiFKOѭXWUӳKuQK
ҧQKGѭӟL GҥQJ QpQ
- E\WHWLӃSWKHRP{WҧNtFKFӥSL[HO
- E\WH WLӃSWKHRFKRELӃWVӕSL[HOWUrQPӝWGzQJҧQK 
9

- 2 E\WHFXӕLFKRELӃWVӕGzQJ ҧQK WURQJҧQK
ĈӏQK GҥQJ ҧQK 3&; Oj PӝW WURQJ QKӳQJ ÿӏQK GҥQJ ҧQK Fә ÿLӇQ QKҩW ĈӏQK
GҥQJ Qj\ Vӱ GөQJ SKѭѫQJ SKiS Pm ORҥL GjL 5/( 5XQ-Length-(QFRGHG ÿӇ QpQ Gӳ OLӋX
ҧQK 4Xi WUuQK QpQ Yj JLҧL QpQ ÿѭӧFWKӵF KLӋQ WUrQ WӯQJ GzQJҧQK7ӋS3&;JӗPSKҫQ
ÿҫXWӋSKHDGHU GӳOLӋXҧQK LPDJHGDWD Yj EҧQJ PjX PӣUӝQJ
ĈӏQK GҥQJ ҧQK 7,))ÿѭӧF WKLӃWNӃ ÿӇOjP QKҽ EӟWFiF YҩQ ÿӅ OLrQ TXDQ ÿӃQ
YLӋFPӣUӝQJWӋSҧQK FӕÿӏQKĈӏQK GҥQJ Qj\FNJQJ JӗPSKҫQ ,)+ ,)''(
ĈӏQK GҥQJ ҧQK *,) *UDSKLFV ,QWHUFKDQJH )RUPDW ĈӏQK GҥQJ Qj\ ÿѭӧF
ÿѭD UD ÿӇ NKҳF SKөF QKӳQJ YҩQ ÿӅPj FiFÿӏQK GҥQJ ҧQK NKiFJһS SKҧL NKL VӕPjX WURQJ
ҧQKWăQJ OrQ
2.1.3 Phân tích ҧnh.
2.1.3.1Khái niӋm pixel và pixel lân cұn.
3L[HOOjSKkQ WӱQKӓQKҩWFҩXWҥRQrQKuQKҧQK 0ӛLSL[HOFyPӝWWRҥÿӝ[\Yj

PjX [iFÿӏQK
P1
(x-1, y-1)
P2
(x-1, y)
P3
(x-1, y+1)
P4
(x, y-1)
P
(x, y)
P5
(x, y+1)
P6
(x+1, y-1)
P7
(x+1, y)
P8
(x+1, y+1)
Hình 2.4 Pixel P và các lân cұn cӫa P
0ӝW SL[HO SWҥL FiF WRҥÿӝ [ \ Fy{ SL[HO OkQ FұQWKHRFKLӅXGӑFYjFKLӅXQJDQJ
Yj WRҥÿӝWѭѫQJӭQJ FӫDFiFSL[HOQj\ QKѭ KuQKWUrQOj
P2(x-1, y) P7(x+1, y)
P6(x+1, y-1) . P5(x, y+1)
10

7ұSFiFSL[HOQj\JӑLOjOkQ FұQFӫD S YjNêKLӋX Oj1S 0ӛLSL[HOOkQFұQFiFK
[ \ PӝW ÿѫQYӏYjQӃX [ \ӣ PpS FӫDPjQ KuQK WKu VӁFy PӝWVӕSL[HOOkQFұQFӫDS
QҵP ӣ QJRjL KuQK ҧQK 1JRjL  SL[HO OkQ FұQ FӫD S WKHR FKLӅX GӑF Yj FKLrX QJDQJ [XQJ
quanh p còn có 4 pixel chéRJyFFyFiFWRҥÿӝWѭѫQJ ӭQJ Oj

P1(x-1, y-1) P3(x-1, y+1)
P6(x+1, y-1) P8(x+1, y+1)
7ұS FiF SL[HO Qj\ÿѭӧFNê KLӋX Oj 1'S%ӕQSL[HOQj\FQJ YӟL SL[HO ӣWUrQ WҥR
WKjQK  SL[HO OkQ FұQ FXҧ S Yj ÿѭӧF Nê KLӋX Oj 1 S 7ұS KӧS Qj\ FNJQJ VӁ FyPӝW Vӕ
SL[HOӣErQQJRjLKuQKҧQKQӃX [\QҵP ӣPpSFӫD KuQK ҧQK
2.1.3.2Mӝt sӕ không gian màu.
 Không gian màu RGB (Red, Green, Bule).
0jX ÿӓ OөF ± xanh lá cây, lam ± [DQK GD WUӡL 5*% ÿѭӧF Vӱ GөQJ SKә ELӃQ
QKҩW1KӳQJ PjX JӕF 5*% ÿѭӧF WKrP YjR QKӳQJ PjXJӕF NKiFÿLӅX ÿyWҥRQrQVӵÿyQJ
JyS ULrQJFӫD WӯQJ PjXJӕF ÿѭӧFWKrP FQJQKDXÿӇ PDQJ OҥLNӃW TXҧ 7ұSKӧS PjX QKӓ
WKjQK SKҫQ VҳS [ӃS WKHR NKӕL OұS SKѭѫQJÿѫQYӏ ĈѭӡQJ FKpRFKtQKFӫD NKӕL OұS SKѭѫQJ
YӟL Vӵ FkQ EҵQJ YӅ Vӕ OѭӧQJ WӯQJ PjX JӕF WѭѫQJ ӭQJ YӟL FiF PӭF ÿӝ [iP YӟLÿHQOj
YjWUҳQJ

Blue(0,255)
(0, 0, 1)
(0,0,0)
(1,0,0)
Red
(0,1,0) green

11

Hình 2.5 Mô hình màu RGB
 Mô hình màu CMY (Cyan, Magenta, Yellow)
/j SKҫQ E WѭѫQJ ӭQJ FKR FiF PjX ÿӓ OөF ODP YjF~QJ ÿѭӧF Vӱ GөQJQKѭ QKӳQJ
EӝOӑFORҥL WUӯ FiF PjX Qj\ Wӯ iQKViQJ WUҳQJ 9uYұ\&0<FzQ ÿѭӧF JӑL Oj FiF SKҫQ E
ORҥL WUӯ FӫD PjX JӕF 7ұSKӧS PjX WKjQK SKҫQ ELӇX GLӉQ WURQJ KӋWӑDÿӝĈӅ-các cho mô
KuQK PҫX &0< FNJQJ JLӕQJ QKѭ FKR P{ KuQK PjX 5*% QJRҥL WUӯ PjX WUҳQJ iQK ViQJ
WUҳQJ ÿѭӧF WKD\ WKӃ PjX ÿHQ NK{QJ Fy iQK ViQJ ӣ WҥL QJXӗQ ViQJ &iF PjX WKѭӡQJ

ÿѭӧF WҥR WKjQK EҵQJ FiFK ORҥL Eӓ KRһF ÿѭӧF E Wӯ iQKViQJ WUҳQJKѫQOjÿѭӧFWKrPYjR
QKӳQJ PjX WӕL

Hình 2.6 Các màu gӕc bù và sӵ pha trӝn giӳa chúng
.KLEӅ PһW ÿѭӧF EDRSKӫEӣL OӟSPӵF PjX [DQK WtP VӁNK{QJ FyWLDPjXÿӓSKҧQ
FKLӃX Wӯ EӅ PһW ÿy 0jX[DQK WtP ÿm ORҥLEӓ SKҫQ PjX ÿӓ SKҧQ[ҥNKLFy WLD ViQJWUҳQJ
Pj EҧQ FKҩW Oj WәQJ FӫD  PjXÿӓOөFODP9uWKӃWDFyWKӇFRL PjX &\DQOj PjX WUҳQJ
WUӯ ÿL PjX ÿӓ Yjÿy FNJQJ OjPjX ODP FӝQJPjX OөF 7ѭѫQJ Wӵ QKѭYұ\WDFyPjXÿӓWKүP
PDJHQWD KҩS WKө PjX OөF Yu WKӃ Qy WѭѫQJ ÿѭѫQJ YӟL PjX ÿӓ FӝQJ PjX ODP 9j FXӕL
FQJ PjX YjQJ \HOORZKҩS WKөPjXODP QyVӁEҵQJ PjX ÿӓFӝQJYӟL OөF
.KL EӅ PһW FӫD WKӵF WKӇ ÿѭӧF EDRSKӫEӣL [DQK WtP YjYjQJ FK~QJ VӁ KҩS WKө KӃW
FiF SKҫQPjX ÿӓYj[DQKODP FӫDEӅ PһW .KLÿy FKӍ WӗQ WҥL GX\ QKҩW PjX OөFEӏSKҧQ[ҥ
Wӯ Vӵ FKLӃX ViQJFӫD iQKViQJ WUҳQJ 7URQJWUѭӡQJ KӧSNKLEӅ PһWÿѭӧFEDR SKӫ EӣLFҧ 
màu xanh tím, YjQJ ÿӓ WKүPKLӋQ WѭӧQJKҩSWKө[ҧ\UDWUrQ Fҧ  PjX ÿӓ OөFYj ODP 'R
ÿyPjX ÿHQVӁPjXFӫDEӅPһW1KӳQJ PӕLOLrQKӋQj\FyWKӇÿѭӧFPLrXWҧEӣL
Black
Green
Blue
Yellow
Magent
Cyan Red
12

B
G
R
Y
M
C
1

1
1

Hình 2.7 Sӵ biӃQÿәi tӯ RGB thành CMY
 Mô hình màu HSV.
&iF P{ KuQKPjX 5*% &0< ÿѭӧF ÿӏQKKѭӟQJFKR SKҫQ FӭQJ WUiL QJѭӧFYӟLP{
KuQK PjX +69 FӫD 6PLWK KD\ FzQ JӑL Oj PүX +6% YӟL % Oj %ULJKWQHVV ÿӝViQJÿѭӧF
ÿӏQKKѭӟQJQJѭӡL Vӱ GөQJGӵD WUrQ FѫVӣQӅ WҧQJ YӅWUӵFJLiFYӅW{QJPjXVҳFÿӝYjVҳF
WKiLVӱGөQJ

Hình 2.8 Mô hình màu HSV
6ҳF PjX  +XHKRһF+ ÿѭӧFÿR EӣL JyF TXDQK WUөF ÿӭQJ YӟLPjX ÿӓOj
o
, màu
OөFOj
o
, màu lam là 240
o
[HPKuQK&iFPjXEәVXQJWURQJKuQKFKyS+69ӣ
o

ÿӕL GLӋQ YӟL PjX NKiF *Li WUӏFӫD 6 Oj PӝWWұSFiF JLi WUӏ ÿLWӯWUrQÿѭӡQJWUөFWkP
WUөF 9 ÿӃQ  WUrQ FiF PһW ErQ WҥL ÿӍQK FӫD KuQK FKyS ViX FҥQK6ӵEmRKzDÿѭӧFÿR
WѭѫQJ ÿӕL FKR JDP PjX WѭѫQJ ӭQJ YӟL P{ KuQK PjX Qj\ 0{ KuQK PjX GҥQJ Kình chóp
ViX FҥQKQj\ ÿѭӡQJ FDR9 YӟLÿӍQKOjÿLӇP JӕFWӑDÿӝ  ĈLӇPӣÿӍQKOjPjXÿHQFy
JLiWUӏWӑDÿӝPjX9 WҥLFiFÿLӇPQj\JLiWUӏFӫD+Yj6OjNK{QJOLrQTXDQYӟLQKDX
.KLÿLӇP Fy6  Yj9  Oj ÿLӇPPjXWUҳQJQKӳQJJLiWUӏWUXQJJLDQ FӫD9ÿӕLYӟL6 
WUrQÿᐮӡQJ WKҷQJ TXDWkP Oj FiFPjX [iP.KL 6  JLiWUӏFӫD+SKөWKXӝFÿ ᐮӧFJӑL
EӣLFiFTX\ ᐮӟFNK{QJ [iF ÿӏQKQJѭӧFOҥLNKL 6NKiF JLiWUӏFӫD+VӁOjSKө WKXӝF
13

1Kѭ Yұ\ PӝW PjX QjRÿy 9   6  Oj JLӕJ QKᐮ PjX WKXҫQ NKLӃW WURQJPӻ WKXұW
ÿѭӧF Vӱ GөQJ QKᐮ ÿLӇP NKӣL ÿҫX WURQJ FiF PjX SKD WUrQ 7KrP PjX WUҳQJ SK KӧS ÿӇ
JLҧP 6  NK{QJFy Vӵ WKD\ ÿәL9WҥRQrQVӵWKD\ÿәLVҳFWKiLFӫDJDPPjX6ӵFKX\ӇQ
PjXÿѭӧFWҥRUDEӣLYLӋFJLӳ6 YjJLҧP9WҥRQrQVӵWKD\ÿәL YӅ VҳF ÿӝYj W{QJ PjX
WҥRWKjQKEӣLYLӋFWKD\ÿәLFҧKDL6Yj9
 Mô hình màu HLS
0{ KuQK PjX +/6 ÿѭӧF [iF ÿӏQK EӣL WұS KӧS KuQK FKyS ViX FҥQK ÿ{L FӫD NK{QJ
JLDQ KuQK WUө6ҳF PjX Oj JyF TXDQKWUөF ÿӭQJ FҧXKuQKFKyS ViX FҥQKÿ{LYӟLPjXÿӓWҥL
góc 0
o
. Các mjX VӁ[iF ÿӏQKWKHRWKӭWӵJLӕQJQKѭWURQJELӇXÿӗ&,(NKLUDQKJLӟLFӫDQy
Eӏ [RD\ QJѭӧF FKLӅX NLP ÿӗQJ Kӗ 0jX ÿӓ PjX YjQJ PjX OөF PjX [DQK WtP PjX ODP
Yj ÿӓ WKүP ĈLӅX Qj\ FNJQJ JLӕQJ QKѭ WKӭ Wӵ VҳF [ӃS WURQJ PүX KuQKFKyS ViX FҥQK ÿѫQ
HSV.

Hình 2.9 Mô hình màu HLS
&K~QJ WD Fy WKӇ [HP PүX +/6 QKѭ PӝW Vӵ ELӃQ GҥQJ FҧX PүX +69 Pj WURQJ ÿy
PmX Qj\ PjX WUҳQJ ÿѭӧF NpR KѭӟQJ OrQ KuQK FKyS ViX FҥQKSKtDWUrQWӯPһW 9 1Kѭ
YӟL PүX KuQK FKyS ViX FҥQK ÿѫQ SKҫQ Eә VXQJ FӫD PӝW PjX VҳF ÿѭӧFÿһWӣYӏWUt
o

KѫQ Oj [XQKTXDQKKuQKFKyS ViX FҥQK ÿ{L Vӵ EmR KzDÿѭӧFÿR [XQJTXDQKWUөF ÿӭQJ Wӯ
 WUrQ WUөF WӟL  WUrQ EӅ PһW Ĉӝ ViQJ EҵQJ NK{QJ FKR PjX ÿHQ Yj EҵQJ PӝW FKR PjX
WUҳQJ
14

2.1.3.3Mӝt sӕ công cө trӧ giúp xӱ lý ҧnh.
 .ӻWKXұWOӑFVӕ
&KҩW OѭӧQJ KuQK ҧQK NpP GR UҩW QKLӅX QJX\rQ QKkQ QKѭ GR QKLӉP ÿLӋQ Wӱ FӫD

Pi\ WKX KD\ FKҩW OѭӧQJ Eӝ Vӕ KyD NpP 1KLӉX ҧQK Vӕ ÿѭӧF [HP QKѭ Oj Vӵ GӏFK FKX\ӇQ
QKDQKFӫD WtQ KLӋX WKX QKұQ WUrQ PӝWNKRҧQJ FiFK QJҳQ 9Ӆ PһW WҫQVӕQKLӉXӭQJYӟLFiF
WKjQK SKҫQ WҫQ Vӕ FDR WURQJ ҧQK1Kѭ Yұ\ÿӇ[ӱ Oê QKLӉX WD FyWKӇ OӑF FiF WKjQK SKҫQ WҫQ
Vӕ FDR 9LӋF OӑF GӵD YjR WtQK Gѭ WKӯD WK{QJ WLQNK{QJ JLDQ FiFSL[HOOkQFұQ Fy WKӇ Fy
FQJ KRһFJҫQFQJ PӝW VӕÿһF WtQK .ӻWKXұW OӑFQj\GQJ PӝWPһWQҥYjGLFKX\ӇQNKҳS
ҧQKJӕF 7\WKHR FiFKWәKӧS ÿLӇP ÿDQJ [pW YӟLFiF ÿLӇP OkQFұQ Pj WD Fy NӻWKXұW OӑF
WX\ӃQWtQKKD\NӻWKXұWOӑF SKL WX\ӃQ ĈLӇP ҧQK FKӏXWiFÿӝQJ FӫDELӃQÿәLOjÿLӇPӣWkP
FӫDPһWQҥ &iFNӻWKXұWOӑFQj\ ÿѭӧFWUuQKEj\ NӻWURQJSKҫQ OjPWUѫQҧQK
 %LӃQÿәL)RXULHU
.KiLQLӋPYj F{QJWKӭF
%LӃQÿәL)RXULHUFKRPӝWWtQKLӋXFyWKӇELӇXGLӉQQKѭ VDX
%LӃQÿәL)RXULHUWKXұQ FKRWtQKLӋXPӝWFKLӅXJӗPPӝWFһSELӃQÿәL
-BiӃQÿәi Fourier thuұn: chuyӇn sӵ biӇu diӉn tӯ không gian thӵc sang không gian
tҫn sӕ (phә và pha) .Các thành phҫn tҫn sӕ Qj\ÿѭӧc gӑi là các biӇu diӉn trong không
gian Fourier cӫa tín hiӋu.
- BiӃQÿәL)RXULHUQJѭӧc: ChuyӇQ ÿәi sӵ biӇu diӉn cӫDÿӕLWѭӧng tӯ không gian
Fourier sang không gian thӵc.
.K{QJ JLDQ PӝWFKiӅu.
Cho mӝt hàm f(x) liên tөc. BiӃQÿәi Fourier cӫa f(x), ký hiӋu F(u) , u biӇu diӉn tҫn
sӕ NK{QJJLDQ ÿѭӧFÿӏQKQJKƭD Oj

F(u) =

7URQJ ÿy
f(x) : biӇu diӉQELrQÿӝ tín hiӋu.
15

ELӇXGLӉQ SKD
%LӃQÿәL)RXULHUQJѭӧc cӫD)XFKRI[ÿѭӧFÿӏQKQJKƭD QKѭ VDX

.K{QJ JLDQ KDLFKLӅX
&KR I[\ Oj KjP ELӇX GLӉQҧQKOLrQWөF WURQJNK{QJJLDQKDLFKLӅXFһSELӃQÿәL
)RXULHUÿѭӧFÿӏQKQJKƭD QKѭ VDX
-%LӃQÿәL)RXrier thuұn:

u,v biӇu diӉn tҫn sӕ không gian
-BiӃQÿәL)RXULHUQJѭӧc

2.1.3.4TiӅn xӱ lý .
¾ 3KѭѫQJ SKiS WLӅQ[ӱOêWURQJPLӅQNK{QJ JLan.
7KXұW QJӳ PLӅQ NK{QJ JLDQ ӣ ÿk\ PXӕQ QyL ÿӃQ Vӕ OѭӧQJ SL[HO WҥRQrQPӝWKuQK
ҧQK&iF SKѭѫQJ SKiS WLӅQ [ӱ Oê WURQJ PLӅQ NK{QJ JLDQ Oj FiFWKӫWөFWiF ÿӝQJ WUӵFWLӃS
OrQ FiF SL[HO WҥR OrQ KuQK ҧQK ÿy &iF KjP WLӅQ [ӱ Oê WURQJ PLӅQ NK{QJ JLDQ ÿѭӧF YLӃW
nhѭVDX
g(x,y) =h[f(x.y)]
Ӣ ÿk\I[\OjKjP ÿLӇm ҧQK FKѭD ÿѭӧc xӱ lý.
J[\ OjKjP ÿLӇm ҧQK ÿmÿѭӧc xӱ lý.
7URQJ ÿyK Oj WRiQ Wӱ áp lên f. DҥQJ ÿѫQ JLҧn nhҩt cӫa h là lân cұn có kích
WKѭӟF[ NKL ÿy J FKӍ phө thuӝc vào giá trӏ cӫa f tҥi (x,y) và h trӣ thành hàm ánh xҥ
FѭӡQJÿӝ ViQJÿLӇm ҧnh.