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 ( ( (= = ( (