05/22/201211CHNG 4CC PHNG PHP TM BINThs. Phm Vn TipKhoa Cng ngh
thng tini hc i Nam2NI DUNG BI GING1. Khi nim bin2. Cc k thut pht
hin bin Pht hin bin trc tip Phng php GradientK thut Gradient+ Phng
php tm bin Roberts+ Phng php tm bin Sobel+Phng php tm bin PrewittK
thut la bn Phng php Laplace31.1. Khi nim bin BinMt im nh c gi l bin
nu c s thay i t ngt v cp xm.Tp hp cc im bin to thnh mt ng bin (ng
bao) ca nh.1.1. Khi nim bin- i vi hm lin tc, s bin thin ca hm c
xcnh thng qua o hm cc cp. - nh: hm lin tc hai bin l cc ta trong mt
phngnh: S bin thin hm s c biu din bng cc ohmring. S bin thin ca hm
nh biu din bng vector gradient;- Gradient ch hng bin thin tng cc i
ca hm nh;- i vi nh s, phi xc nh cc gradient ri rc405/22/2012251.2.
Cc kiu bin c bn Bin l tng:uxHnh 1: ng bin l tng61.2. Cc kiu bin c
bn Bin dc:uxHnh 2: ng bin dc71.2. Cc kiu bin c bn Bin khng
trn:uxHnh 1: ng bin khng trn81.3. Quy trnh pht hin bin Bc 1: Do nh
ghi c thng c nhiu, bc mt l phi lc nhiu theo cc phng php tm hiu cc
phn trc. Bc 2: Lm ni bin s dng cc ton t pht hin bin. Bc 3: nh v
bin. Ch rng k thut ni bin gy tc dng ph l gy nhiu lm mt s bin gi xut
hin do vy cn loi b bin gi. Bc 4: Lin kt v trch chn
bin.05/22/201239NI DUNG BI GING1. Khi nim bin2. Cc k thut pht hin
bin Pht hin bin trc tip Phng php GradientK thut Gradient+ Phng php
tm bin Roberts+ Phng php tm bin Sobel+Phng php tm bin PrewittK thut
la bn Phng php Laplace10CC K THUT PHT HIN BIN C 2 phng php pht hin
binPht hin bin trc tipLm ni ng bin da vo s bin thin v gi tr cp xm
ca cc im nh.K thut c dng ch yu y l k thut o hm: - Nu ly o hm bc nht
ca nh, ta c phng php Gradient- Nu ly o hm bc hai ta c k thut
Laplace.Pht hin bin gin tipPhn chia nh thnh cc vng ng phn cch gia
cc vng chnh l bin.11CC K THUT PHT HIN BIN So snh 2 phng php pht hin
bin Phng php trc tip: t ra hiu qu v t chu nh hng ca nhiu. Song nu s
bin thin sng khng t ngt, phng php ny t ra km hiu qu. Phng php gin
tip: tuy kh ci t nhng li p dng kh tt khi s bin thin sng nh.12NI
DUNG BI GING1. Khi nim bin2. Cc k thut pht hin bin Pht hin bin trc
tip Phng php GradientK thut Gradient+ Phng php tm bin Roberts+ Phng
php tm bin Sobel+Phng php tm bin PrewittK thut la bn Phng php
Laplace05/22/2012413PHNG PHP GRADIENT Phng php Gradient l phng php
d bin cc b da vo cc i ca o hm bc nht. Theo nh ngha, Gradient l mt
vct c cc thnh phn biu th tc thay i xm (mu) ca im nh theo hai hng x,
y. Cc thnh phn ca gradient c tnh bi:l ln ca vector Gradient ca
nh.(((
=(((((
=yGxGyy) f(x,xy) f(x,y) G(x,2y2xG G y) G(x, + =PHNG PHP
GRADIENTTheo nh ngha v Gradient, nu p dng n vo x l nh, vic tnh ton
s rt phc tp. n gin m khng mt tnh cht ca phng php Gradient, ngi ta s
dng k thut Gradient dng cp mt n H1, H2 trc giao (theo 2 hng
vunggc).Vic xp x o hm bc nht theo cc hng x v y c thc hin thng qua 2
mt n nhn chp tng ng s cho ta cc k thut pht hin bin khc
nhau.1415PHNG PHP GRADIENTF(x,y)FyxHnh 1: Gradient ca
nhG(x,y)Fxy16PHNG PHP GRADIENTi vi pht hin bin, ta c th tnh n gin
nh sau: tch bin bng phng php Gradient, ngi ta chia thnh hai k thut
(do dng hai ton t khc nhau), l: K thut Gradient v k thut la bn.
Trong , k thut Gradient dng ton t Gradient ly o hm theo hai hng, cn
k thut la bn ly o hm theo 8 hng chnh: Bc, Nam, ng, Ty, ng Bc, Ty
Bc, ng Nam v Ty Nam.y xG G y) G(x, + =05/22/2012517NI DUNG BI GING
Khi nim bin Cc k thut pht hin bin Pht hin bin trc tip Phng php
GradientK thut Gradient+ Phng php tm bin Roberts+ Phng php tm bin
Sobel+Phng php tm bin PrewittK thut la bn Phng php Laplace18K THUT
GRADIENT Cc ton t Gradient c m t bi cp mt n H1v H2trc giao (theo
hai hng vung gc). Nu nh ngha g1 v g2l Gradient tng ng theo hai hng
x v y, th bin ca Gradient (k hiu l g) ti im (m,n) c tnh theo cng
thc: Trong , g1v g2nhn c bng cch ln lt nhn chp nh vi cc mt n H1v
H2. Thng trng, phc tp khi tnh ton cng thc tnh ln Gradient c tnh gn
ng bi:n) (m, gn) (m, gtan n) (m,n) (m, g n) (m, g n) g(m,12 12221=+
=gn) (m, n) (m, n) g(m, g g2 1+ =19THUT TON LM NI BIN NH THEO
GRADIENT Input: nh xm I v mu Hx, Hy Output: nh Ikqc cc im bin vi mc
xm c tng cng. Procedure gradient;Bc 1: Tnh: Gx = Hx I vGy= Hy IBc
2: Tnh Ikq= Hx I+ Hy I20BIN V O HM TRN BINo hm cp 1Hm f(x)o hm cp
205/22/2012621PHNG PHP ROBERTS Ton t Roberts do Roberts xut vo nm
1965. N p dng trc tip ca cng thc o hm ti im (x, y).Mt n H1Mt n H2
Mt n ny c th nhn t mt n kia bng cch quay mt gc 900.0 1-1 0-1 00
122PHNG PHP ROBERTS0 1-1 0-1 00 1Mt n H1Mt n H2Gx= a2 a3Gy= -a1+ a4
ln ca Gradient l: Hoc:a1a2a3a4Tng qut2 2x yG G G = +x yG G G =
+23PHNG PHP ROBERTS V d: Xt mt nh I6x6vi cc mc xm: p dng ton t
Roberts:0 0 0 0 0 00 3 3 3 3 30 3 3 3 3 30 3 3 3 3 30 3 3 3 3 30 0
0 0 0 0I ( ( ( (=( ( ( ( (((((((
= 3 3 3 3 30 0 0 0 30 0 0 0 30 0 0 0 33 3 3 3 0HxI(((((((
= 3 3 3 3 00 0 0 0 30 0 0 0 30 0 0 0 33 3 3 3 3HyI(((((((
= + =0 0 0 0 30 0 0 0 60 0 0 0 60 0 0 0 60 0 0 0 3H H Iy x kqI
I24PHNG PHP ROBERTS L do chnh ngi ta s dng ton t Roberts l tc tnh
ton nhanh. Chng ch s dng 4 im nh tnh gi tr cp xm ca nh u ra. Ch c
php ton cng v tr c thc hin trong nh.05/22/2012725PHNG PHP ROBERTSa)
nh gcb) nh sau khi p dng ton t Robertsc) nh sau khi phn ngng nh b)a
b c26PHNG PHP ROBERTS1 1 2 6 7 71 2 2 7 7 62 2 2 6 7 62 2 3 7 7 62
3 1 7 7 63 1 4 6 7 5 Cho nh I, s dng phng php tm bin Roberts tm bin
nh sau:0 1-1 0-1 00 1271 1 2 6 7 71 2 2 7 7 62 2 2 6 7 62 2 3 7 7
62 3 1 7 7 63 1 4 6 7 5 Kt qu sau khi s dng ton t Roberts1 1 9 1 1
131 0 9 1 2 120 1 8 1 2 121 1 10 0 2 121 1 8 1 3 114 5 10 13 12
5PHNG PHP ROBERTS28PHNG PHP SOBEL Ton t sau do Sobel ngh dng tm bin
ca nh.Mt n H1 Mt n ny c th nhn t mt n kia bng cch quay mt gc 900.-1
0 1-2 0 2-1 0 1-1 -2 -10 0 01 2 1Mt n H205/22/2012829PHNG PHP
SOBELGx= a3+ 2a6+ a9- (a1+ 2a4+ a7)Gy= a1+ 2a2+ a3- (a7+ 2a8+ a9)
ln ca Gradient l: Hoc:2 2x yG G G = +x yG G G = +Mt n H1-1 0 1-2 0
2-1 0 1-1 -2 -10 0 01 2 1Mt n H2a1a2a3a4a5a6a7a8a91/41/430PHNG PHP
SOBEL V d: Xt mt nh I6x6vi cc mc xm: p dng ton t Sobel:0 0 0 0 0 00
3 3 3 3 30 3 3 3 3 30 3 3 3 3 30 3 3 3 3 30 0 0 0 0 0I ( ( ( (=( (
( ( (((((
= 0 0 0 90 0 0 120 0 0 120 0 0 9Hx I(((((
= 12 12 12 90 0 0 00 0 0 012 12 12 9Hy I(((((
= + =12 12 12 00 0 0 120 0 0 1212 12 12 18H H I y x kq I I31PHNG
PHP SOBELa) nh gcb) nh sau khi p dng ton t Sobela b32PHNG PHP
SOBEL1 1 2 6 7 71 2 2 7 7 62 2 2 6 7 62 2 3 7 7 62 3 1 7 7 63 1 4 7
7 5 Cho nh I, s dng phng php tm bin Sobel tm bin nh sau:-1 0 1-2 0
2-1 0 11 2 10 0 0-1 -2 -105/22/20129331 1 2 6 7 71 2 2 7 7 62 2 2 6
7 62 2 3 7 7 62 3 1 7 7 63 1 4 7 7 5 Kt qu sau khi s dng ton t
Sobel4 6 16 24 16 408 4 30 34 14 3010 6 30 32 14 2814 2 32 32 14
2810 8 30 34 16 3012 10 26 34 30 40PHNG PHP SOBEL34PHNG PHP PREWITT
Ton t Prewitt c dng nh sau:Mt n H1 Mt n ny c th nhn t mt n kia bng
cch quay mt gc 900.-1 0 1-1 0 1-1 0 1-1 -1 -10 0 01 1 1Mt n
H235PHNG PHP PREWITTGx= a3+ a6+ a9- (a1+ a4+ a7)Gy= -(a1+ a2+ a3) +
(a7+ a8+ a9) ln ca Gradient l: Hoc:2 2x yG G G = +x yG G G = +Mt n
H1-1 0 1-1 0 1-1 0 1-1 -1 -10 0 01 1 1Mt n
H2a1a2a3a4a5a6a7a8a9131336PHNG PHP PREWITT V d: Xt mt nh I6x6vi cc
mc xm: p dng ton t Prewitt:0 0 0 0 0 00 3 3 3 3 30 3 3 3 3 30 3 3 3
3 30 3 3 3 3 30 0 0 0 0 0I ( ( ( (=( ( ( ( x6 0 0 09 0 0 0H 9 0 0
06 0 0 0I ( ( ( = ( ( (((((
= 9 9 9 60 0 0 00 0 0 09 9 9 6HyI(((((
= + =9 9 9 00 0 0 90 0 0 99 9 9 12H H Iy x kqI
I05/22/20121037PHNG PHP PREWITTa) nh gcb) nh sau khi p dng ton t
Prewittab38PHNG PHP PREWITT1 1 2 6 7 71 2 2 7 7 62 2 2 6 7 62 2 3 7
7 62 3 1 7 7 63 1 4 7 7 5 Cho nh I, s dng phng php tm bin Prewitt
tm bin nh sau:-1 0 1-1 0 1-1 0 1-1 -1 -10 0 01 1 1391 1 2 6 7 71 2
2 7 7 62 2 2 6 7 62 2 3 7 7 62 3 1 7 7 63 1 4 7 7 5 Kt qu sau khi s
dng ton t Prewitt6 7 21 26 20 277 4 15 15 1 227 4 15 15 2 218 0 14
15 3 216 2 15 13 2 229 6 20 24 22 27PHNG PHP PREWITT40PHNG PHP
ROBERTS2 7 6 1 1 142 2 4 6 0 132 1 0 5 6 122 3 3 3 7 60 0 7 6 7 71
1 1 6 6 72 2 2 1 7 60 2 1 2 1 605/22/20121141NI DUNG BI GING Khi
nim bin Cc k thut pht hin bin Pht hin bin trc tip Phng php
GradientK thut Gradient+ Phng php tm bin Roberts+ Phng php tm bin
Sobel+Phng php tm bin PrewittK thut la bn Phng php Laplace42K THUT
LA BN Vi mc ch nghin cu cc mt n cho kt qu tt hn, ngi ta ngh n vic
xem xt cc ln cn theo cc hng (c 8 hng chnh). chnh l phng php Kirsh v
gi l ton t Kirsh (hay ton t la bn). Ton t la bn o gardient theo tm
hng chn. Mi hng cch nhau 450theo chiu ngc chiu kim ng
h.NNESESSWNW43K THUT LA BN Nu k hiu Gk(m,n) l Gradient theo hng k=
/2 + k/4, k=0,1,2,...,7, khi Gradient ti im (m,n) c xc nh:vi Gk
(m,n)=Hk *x Vi Hxc th l cc ton t Robert, Kirsh, Prewitt, Sobel...
Th Hk c to bi php quay b lc Hxmt gc bng mt s nguyn ln.{ }==70( , )
( , )kkG m n Max Gm n444K THUT LA BN C nhiu ton t la bn khc nhau,
sau y l mt s ton t m mt n hng bc c nh ngha bi:((((
=((((
=((((
=((((
=((((
=((((
=((((
=((((
=3 3 33 0 53 5 53 3 53 0 53 3 53 5 53 0 53 3 35 5 53 0 33 3 35 5
35 0 33 3 35 3 35 0 35 3 33 3 35 0 35 5 33 3 33 0 35 5 58 76 5 43 2
1H HH H HH H H05/22/20121245THUT TON LM NI BIN NH DA VO K THUT LA
BN Input: nh I xm v mu H1, H2,H3,,H8 Output: nh Ikqc cc im bin vi
mc xm c tng cng. Procedure Kirsh;Bc 1: tnh: Hi I i = 1,2,...,8Bc 2:
Tnh Ikq= I =81 iiH46NI DUNG BI GING Khi nim bin Cc k thut pht hin
bin Pht hin bin trc tip Phng php GradientK thut Gradient+ Phng php
tm bin Roberts+ Phng php tm bin Sobel+Phng php tm bin PrewittK thut
la bn Phng php Laplace47PHNG PHP LAPLACE Cc phng php Gradient trn
lm vic kh tt khi m sng thay i r nt. Nhng khi mc xm thay i chm, min
chuyn tip tri rng, phng php s dng o hm bc hai li cho kt qu tt hn, m
trong phn trn gi l phng php Laplace. Ton t Laplace c nh ngha nh
sau: Trong :T ta a ra c mt n nhn chp ca phng php o hm bc hai:
|||
\|+ ||
\|=+= yfy xfx yfxff22222) 1 , ( ) 1 , ( ) , ( 2) , 1 ( ) , 1 ( )
, ( 22222+ =+ =y x f y x f y x fyfy x f y x f y x fxf) 1 , ( ) , 1
( ) 1 , ( ) , 1 ( ) , ( 42+ + = y x f y x f y x f y x f y x f
f((((
=0 1 01 4 10 1 01H 48PHNG PHP LAPLACE Thc t, ngi ta dng mt s kiu
mt n khc nhau tnh gn ng o hm ring bc hai. Cc dng mt n theo ton t
Laplace bc 3x3 hay dng: ((((
=((((
=((((
=1 2 11 5 21 2 11 1 11 8 11 1 10 1 01 4 10 1 03 2 1H H
H05/22/20121349Thut ton lm ni bin nh da vo k thut Laplace: Input:
mt nh I xm v mu H- (chn mt trong ba mu trn) Output: mt nh Ikqc cc
im bin vi mc xm c tng cng. Procedure Laplace;Bc 1: tnh: H I Bc 2:
Ikq= H I50PHNG PHP LAPLACE V d: Xt mt nh I6x6vi cc mc xm: p dng ton
t Laplace vi mt n H1, H2:0 0 0 0 0 00 3 3 3 3 30 3 3 3 3 30 3 3 3 3
30 3 3 3 3 30 0 0 0 0 0I ( ( ( (=( ( ( ( kq 16 3 3 33 0 0 0I H3 0 0
06 3 3 3I ( ( (= = ( ( kq 215 9 9 99 0 0 0I H9 0 0 015 9 9 9I ( (
(= = ( (