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BO CO BI TP LN PHNG PHP TNH TON MM

Trng i hc Cng nghip H NiKhoa Cng ngh thng tin

BO CO BI TP LNPHNG PHP TNH TON MM

TI: TM HIU PHNG PHP PCANHN DNG KHUN MT.NG

DNG MATLAB

Ging vin: Ths. Trn Thanh HngThc hin: Nhm 10 Lp H KHMT2K3

1. Nguyn Thnh Trung(NT)2. Xun Toi

3. Nguyn Tun Dng4. Nguyn Huy Thin5. Nguyn Vn Tn6.H Vit Dng

Nhm 5 KHMT2K3 i hc Cng nghip H Ni1

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Mc Lc

1. Php bin i Karhunen-Love: ............................................................... 7

2. Thut ton PCA: ..................................................................................... 11

2.1. Gii thiu chung v thut ton : .......................................................... 11

2.2. Ni dung thut ton PCA: ................................................................... 13

3. p dng PCA trong bi ton nhn dng khun mt : .......................... 15

3.1. Gii thiu chung v cc phng php nhn dng mt ngi: ............15

3.2. Nhn dng khun mt da trn PCA: .................................................16

3.3 Cc hm hin th nh trong Matlab .................................................... 18

3.4 Cc hm khc c s dng trong ti ............................................. 20

4. Chng trnh Demo: ............................................................................... 22

Ti liu tham kho ...................................................................................... 27


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Bi Ton Nhn Dng Mt Ngi

-----oOo-----

2.1. Gii thiu

Trong th gii ngy nay vi s pht trin mnh m ca k thut s v mng toncu, vn m bo an ton v thng tin cng nh vt cht tr nn ngy cngquan trng v kh khn. Thnh thong chng ta li nghe ni n nhng v nh cpth tn dng, t nhp tri php vo cc h thng my tnh hay to nh ca c quannh nc, chnh ph. Hn 100 triu la l con s b tht thot M vo nm1998 do cc v gian ln v xm nhp ni trn (theo Reuters, 1999) [5]. Trong a scc v phm php ny, bn ti phm li dng nhng khe h c bn trong qu trnh

truy cp vo cc h thng thng tin v kim sot. Phn ln nhng h thng ny khngthc hin quyn truy cp ca ngi s dng da vo thng tin chng ta l ai m chda vo chng ta c g. Ni cch khc, thng tin m ngi s dng cung cp cho hthng khng c trng c cho bn thn h, m ch l nhng g h hin ang shu nh s chng minh nhn dn, cha kho, mt m, s th tn dng hoc h tn. Rrng nhng thng tin hay vt dng ny khng mang tnh c trng m ch mang tnhxc thc i vi ngi s dng, v nu chng b nh cp hay sao chp th k trmhon ton c quyn truy nhp, s dng d liu hay phng tin ca chng ta bt clc no h mun. Hin nay, nhng cng ngh hin i cho php vic xc thcda vo bn cht ca tng c nhn. Cng ngh ny da trn lnh vc c gi l

sinh trc hc. Kim sot bng sinh trc hc l nhng phng php t ng cho phpxc thc hay nhn dng mt c nhn da vo cc c trng sinh l hc ca ngi nh c im vn tay, gng mt, gen, hoc da trn nhng c im lin quann c trng hnh vi nh dng ch vit, cch g phm, ging niV nhng hthng nhn dng bng sinh trc hc s dng thng tin sinh hc ca con ngi nnkt qu chnh xc v c bit l rt kh b

gi mo.

Cc c trng sinh l hc l duy nht mi ngi v rt him khi thay i,

trong khi c trng hnh vi c th thay i bt thng do cc yu t tm l

nh cng thng, mt mi hay bnh tt. Chnh v l do ny, cc h thng nhn dng

da trn c trng sinh l t ra n nh hn cc h thng da vo c trng hnh

vi. Tuy nhin, nhn dng bng cc c trng hnh vi c u im l d s dng v

thun tin hn : thay v phi t mt trc mt my qut in t hay ly ra mt

git mu, ngi s dng s cm thy thoi mi hn khi c yu cu k tn hay ni


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vo mt micro.

Nhn dng gng mt l mt trong s t cc phng php nhn dng da vo

c trng sinh l cho kt qu chnh xc cao ng thi rt thun tin khi s dng. Hn

na, trong s cc c trng sinh l hc, gng mt ca mi ngi l yu t u tinv quan trng nht cho vic nhn bit ln nhau cng nh biu t cm xc. Kh

nng nhn dng ni chung v kh nng nhn bit gng mt ngi ni ring ca

con ngi tht ng kinh ngc. Chng ta c kh nng nhn ra hng ngn gng mt

ca nhng ngi mnh gp, giao tip trong cuc sng ch bng mt ci nhn

thong qua, thm ch sau nhiu nm khng gp cng nh nhng s thay i trn

gng mt do tui tc, cm xc, trang phc, mu tc,Do , vic nghin cu cc

c tnh ca gng mt ngi thu ht rt nhiu nh trit hc, nh khoa hc quanhiu th k, trong c c Aristotle v Darwin [1].

Chnh v nhng l do trn, t nhng nm 1970, nhn dng mt ngi thu ht

s quan tm ca nhiu nh nghin cu trong cc lnh vc nh bo mt, tm l hc,

x l nh v th gic my tnh. Ngy nay cc chng trnh my tnh v nhn dng

mt ngi tm c nhng ng dng thc t nh [3] :

Nhn dng ti phm

Cc h thng nhn dng mt ngi c tch hp vo trong cc hthng kim sot sn bay v c s dng tm kim v nhn din

nhng tn khng b hay bn bun bn ma tu.

Kim sot truy cp vo cc h thng my tnh trong mi trng cng tc

Vic kim tra ng nhp vo cc h thng my PC c kt hp gia

thng tin mt m v / hoc nhn dng mt ngi. iu ny gip ngi

lm vic khng cm thy b ri bi trong cc th tc truy cp phc tp

ng thi vn m bo c tin cy i vi thng tin khch hng vcc b mt trong kinh doanh.

Gii php bo mt b sung cho cc giao dch rt tin t ng (ATM)

Vic truy cp vo cc my rt tin t ng v cc dch v khc ca

ngn hng c kim sot bi cc thng tin nh s tn dng (PIN),


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ging ni, trng mt kt hp vi nhn dng gng mt.

i snh nh cn cc trong hot ng ca ngnh lut php

Cc c quan lut php c th s dng cc h thng nhn dng mt ngi

i snh nhng m t ca cc nhn chng vi nhng tn ti phm clu tr trong c s d liu.

ng dng trong cc giao tip ngi my

Sau khi xc nh c ngi s dng v cm xc ca h ti thi im

, cc h thng my tnh c th c cc ng x thch hp.

Trong chng ny trc tin chng ta s im qua mt s phng php c

s dng trong lnh vc nhn dng mt ngi. Sau khi a ra mt m hnh tiu biu

cho mt h thng nhn dng mt ngi v bn lun v mt s kh khn cho tonb qu trnh nhn dng, chng ta s tp trung vo hai giai on rt trch c trng v

phn lp vi hai phng php : phn tch thnh phn chnh (Principle Components

Analysis PCA) v mng lng ho vector (Learning Vector Quantization Network

LVQ).


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1. Php bin i Karhunen-Love :

Cc php bin i Karhunen-Love (KL) c lin quan vi cc gii thch cu trc d

liu thng qua mt s tuyn tnh kt hp ca cc bin. Ging nh PCA, php bin i

KL cng l cch ti u cho d n d - chiu im gim im chiu sao cho sai s cad n (tc l tng ca khong cch bnh phng (SSD)) l ti thiu (Fukunaga, 1990).

ChoD {x1,x2, ...,xn} l mt tp d liu khng gian d chiu, v X l ng v ma trn

dxd, ngha l X= (xij)nxd vi xijl gi tr j thnh phn ca xi.

xi( i = 1,2, ,n) l vector d chiu. Chng c th hin th khng li bng php tnh tng

vector tuyn tnh c lp nh

Cc ma trn d d c s v chng ta bit thm c th cho rng nhng hng hnh

thc mt b trc giao, ngha l:


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V vy, Y ch n gin l mt bin i trc giao ca X. j c gi l vect th j tnhnng v yij l thnh phn th j ca mu xi trong khng gian tnh nng ny. gim bt

chiu, chng ta ch chn m(m

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2. Thut ton PCA:

2.1. Gii thiu chung v thut ton :

PCA (Principle Components Analysic) l mt thut ton c s dng to ra mt

nh mi t nh ban u. nh mi ny c kch thc nh hn nhiu so vi nh ban u

nhng vn mang nhng c trng c bn nht ca nh cn nhn dng.

PCA khng cn quan tm n vic tm ra cc c im c th ca thc th cn nhn

dng v mi quan h gia cc c im . Tt c cc chi tit u c th hin

nh mi c to ra t PCA.

V bn cht, PCA tm ra mt khng gian mi theo hng bin thin mnh nht ca

mt tp hp cc vector trong khng gian cho trc. Trong khng gian mi, ngi ta hi

vng rng vic phn loi s mang li kt qu tt hn so vi khng gian ban u.


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Khng gian mi (p1,p2) theo hng phn b mnh nht ca cc vector trong khng gian

(x1, x2) tm theo PCA

u im ca phng php PCA :

Tm c cc c tnh tiu biu ca i tng cn nhn dng m khng cn phixc nh cc thnh phn v mi quan h gia cc thnh phn .

Thut ton c th thc hin tt vi cc cnh c phn gii cao, do PCA s thu

gn nh thnh mt nh c kch thc nh hn.

PCA c th kt hp vi cc phng php khc nh mng Nron, Support Vector

Machinge mng li hiu qu nhn dng cao hn.

Nhc im ca PCA :

PCA phn loi theo chiu ln nht ca tp vector. Tuy nhin, chiu phn b ln

nht khng phi lc no cng mang li hiu qu tt nht cho bi ton nhn dng. y

l nhc im c bn ca PCA.


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PCA rt nhy vi nhiu.

2.2. Ni dung thut ton PCA:

Khng gian mi c to bi PCA c cu thnh t k vector n v c chiu l N.

Mi vector c gi l mt Eigenface.

Php bin i :

A= W = vi K

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Gi cc gi tr ring ca C l : 1, 2,, n sp xp theo th t gim dn, tng ng vi

N vector ring u1, u2,, uN. Cc vector ring ny trc giao tng i mt, Mi vector

ring ui c gi l mt eigenface. Tp hp cc vector ban u c biu din trong

khng gian to bi n eugenface theo m t :

x-xtb = w1u1+ w2u2++ wNuN=

Chn ly K vector ring u tng ng vi K gi tr ring ln nht, ta c :

x-xtb = w1u1+ w2u2++ wNuN= vi K

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Nhn c 2 v vi A, ta c :

A.AT.A.vi = i. A . vi

Ta thy A.vi chnh l vector ring ca C=A.A

T

ng vi gi tr ring i.

3. p dng PCA trong bi ton nhn dng khun mt :

3.1. Gii thiu chung v cc phng php nhn dng mt ngi:

a. Cc phng php nhn dng khun mt ngi :

Cc phng php nhn dng hin nay c 2 loi :

Nhn dng da trn cc c trng phn t trn khun mt (Feature based facerecognition).

Nhn dng da trn xt tng th khun mt (Apppearance base face recognition )

b. Nhn dng da trn mi quan h gia cc phn t :

y l phng php nhn dng khun mt da trn vic xc nh cc c trng hnh

hc ca cc chi tit trn khun mt ( nh v tr, din tch, hnh dng ca mt, mi,

ming..), v mi quan h gia chng (nh khong cch 2 mt, khong cch 2 lng

my)

u im ca phng php ny l n gn vi cch m con ngi s dng nhn bit

khung mt. Hn na, vi vic xc nh c tnh v mi quan h, phng php ny c

th cho kt qu tt trong cc trng hp nh c nhiu nhiu, b nghing, b xoay v

nh sng thay i.

Nhc im ca phng php ny l ci t thut ton phc tp do vic xc nh mi

quan h gia cc c tnh i hi cc thut ton phc tp. Mt khc vi nh kch thc

b th cc c tnh s kh phn bit.

c. Nhn dng khun mt da trn xt ton din khun mt :


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Ni dung chnh ca hng tip cn ny l xem mi nh c kch thc RxC l mt

vector trong khng gian RxC chiu. Ta s xy dng mt khng gian mi c chiu nh

hn sao cho khi biu din trong khng gian cc c im chnh ca mt khun mt

khng b mt i. Trong khng gian , cc nh ca cng mt ngi s c tp trungli thnh mt nhm gn nhau v cch xa cc nhm khc.

Thut ton PCA ( Principle Components Analysis) thuc nhm ny.

3.2. Nhn dng khun mt da trn PCA:

Kohonen a ra phng php dng vector ring nhn dng khun mt, ng

dng mt mng neural n gin chng t kh nng ca phng php ny trn cc

nh c chun ha. Mng neural tnh mt m t ca khun mt bng cch xp xcc vector ring ca ma trn tng quan ca nh. Cc vector ring sau ny c bit

n vi ci tn Eigenface. Kirby v Sirovich chng t cc nh c cc khun mt c

th c m ha tuyn tnh bng mt s lng va phi cc nh c s. Tnh cht ny

da trn bin i Karhunen-Leve, m cn c gi di mt ci tn khc l PCA v

bin i Hotelling. tng ny c xem l ca Pearson trnh by u tin vo nm

1901v sau l Hotelling vo nm 1933. Cho mt tp cc nh hun luyn c kch

thc n x m c m t bi cc vector c kch thc m x m, cc vector c s cho mtkhng gian con ti u c xc nh thng qua li bnh phng trung bnh khi chiu

cc nh hun luyn vo khng gian con ny. Cc tc gi gi tp cc vector c s ti

u ny l nh ring sau gi cho n gin l vector ring ca ma trn hip phng

sai c tnh t cc nh khun mt vector ha trong tp hun luyn. Nu cho 100

nh, m mi khun mt c kch thc 91x50 th c th ch dng 50 nh ring, trong

khi vn duy tr c mt kh nng ging nhau hp l (gi c 95% tnh cht).

Turk v Pentland p dng PCA xc nh v nhn dng khun mt. Tng t,

dng PCA trn tp hun luyn nh cc khun mt sinh cc nh ring (cn gi l

eigenface) tm mt khng gian con (khng gian khun mt) trong khng gian nh.

Cc nh khun mt c chiu vo khng gian con ny v c gom nhm li. Tng

t cc nh khng c khun mt dng hun luyn cng c chiu vo cng khng


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gian con v gom nhm li. Cc nh khi chiu vo khng gian khun mt th khng b

thay i tnh cht c bn, trong khi chiu cc nh khng c khun mt th xut hin s

khc nhau cng khng t. Xc nh s c mt ca mt khun mt trong nh thng qua

tt c khong cch gia cc v tr trong nh v khng gian nh. Khong cch ny dng xem xt c hay khng c khun mt ngi, kt qu khi tnh ton cc khong cch

s cho ta mt bn v khun mt. C th xc nh c t cc tiu a phng ca

bn ny. C nhiu nghin cu v xc nh khun mt, nhn dng, v trch c

trng t tng vector ring, phn r, v gom nhm. Sau Kim pht trin cho nh

mu, bng cch phn on nh tm ng khng gian tm kim bt i.

Bc u tin trong nhn dng khun mt da trn PCA l trch chn vector c

tnh. Mt bc nh v khun mt c coi nh mt vector, nu bc nh c kch thc

l w*h pixels th khng gian cha vector ny c s chiu l N=w*h. Mi pixel s c

m ha bi mt thnh phn ca vector.

Khu quan trng nht trong bi ton nhn dng l trch chn vector c tnh. Cc

bc trch chn bao gm :

i. To mt tp X gm M nh (nh hc), mi nh c kch thc N, cc nh c chuyn

thnh vector N chiu.

X = {x1, x2, ,xM }

ii. Tnh trung bnh ca tp trn :

Xtb =

iii. Tnh sai lch ca nh u vo vi gi tr trung bnh trn:

i = xi - xtb


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iv. Tm mt tp M vector trc giao u biu din phn b mnh nht ca tp d liu X.

Tp cc vector u c gi l eigenface ca tp d liu hc.

v. Xy dng cc nh mi vi theo M vector u :

vi = uit i

=[v1, v2, ,vM]T

Trong , vi = uit i l vector c tnh ca nh th I trong khng gian mi. y l

tp cc eigenface, cc thnh phn c bn cho bc nh cn nhn dng.

Sau khi trch chn c cc vector c tnh, cn i chiu vector ny vi c s d liu,

t a ra kt qu nhn dng. Trong bi ton, kt qu nhn dng s l nhn bit c

hoc cha nhn bit c.

thc hin phn loi c rt nhiu phng php nh khong cch Euclid, mng

Noron trong khong cch Euclid l phng php n gin nht. N cho kt qu

tt i vi trng hp i tng c to thnh cc nhm cch xa nhau. Vector c

tnh ca i tng c to thnh cc nhm cch xa nhau.

Vector c tnh ca i tng cn nhn dng s c so snh ln lt vi vector c

tnh ca tng nh mu trong tp cc nh hc. Cc khong cch ngn nht s c lu

li:

k= ||- k|| vi k=1,..,M

y kl vector ca khun mt th k trong CSDL. Nu knh hn mt s c xc

nh trc th bc nh c nhn dng l khun mt th k trong CSDL.

3.3 Cc hm hin th nh trong Matlab

hin th nh, Matlab cung cp 2 hm c bn l image v imagesc. Ngoi ra, trong

Image Processing Toolboxcng c hai hm hin th khc l imview v imshow


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- Hm image(x,y,c) hin th hnh nh biu din bi ma trn c kch thc mxn ln h

trc ta . x,y l cc vct xc nh v tr ca cc im c(1,1) v c(m,n).

- Hm imagesc c chc nng tng t hm image, ngoi tr vic d liu nh s c

co gin s dng ton b bn mu hin hnh.- Hm imview cho php hin th nh trn ca s ring nn Java, gi l Image Viewer.

- Hm imshow cho php hin th nh trn mt Figure v t ng thit lp gi tr cc

i tng image, axes, figure hin th hnh nh.

Cc hm chuyn i loi nh v kiu d liu nhdither To nh nh phn hay nh RGBgray2ind Chuyn nh trng en thnh nh indexed

grayslice Chuyn nh trng en thnh nh indexed bng ly ngngim2bw Chuyn nh thnh nh kiu d liu nh phnim2double Chuyn nh thnh nh kiu d liu doubleim2uint16 Chuyn nh thnh nh kiu d liu uint16im2uint8 Chuyn nh thnh nh kiu d liu uint8imapprox Xp x nh indexed bng cch gim s muind2gray Chuyn nh indexed thnh nh gray scaleind2rgb Chuyn nh indexed thnh nh RBGmat2gray To nh gray scale t ma trnrgb2ind Chuyn nh RBG thnh nh indexed

rgb2gray Chuyn nh RBG thnh nh gray scaleCc hm truy xut d liu nh

imfinfo Truy xut thng tin nhimread c nh t file v xut ra ma trn nhimwrite Lu ma trn nh thnh file nh

Cc hm bin i hnh hccp2tform nh ngha php bin i hnh hc tng cp tng ngimcrop Trch xut mt phn nhimresize Thay i kch thc nhimrotate Thc hin php quay nh

imtranform Thc hin php bin i hnh hc tng qutmaketform nh ngha php bin i hnh hc tng qut

Bng 3.3 Cc hm x l hnh nh c bn trong Matlab


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3.4 Cc hm khc c s dng trong ti

[filename,pathname]=uigetfile(filterspec,title): hin th hp thoi chn ng

dn file. Gi tr tr v tn file, v ng dn.

T=strcat(s1,s2,s3): ghp cc chui li vi nhau, tr v chui ni tip s1s2s3 strcmp(s1,s2): hm so snh, tr v 1 nu s1 ging s2, ngc li tr v 0

T=dir(pathname): Ly thng tin ca mt Folder bao gm: s file cha trong

folder, tn file, ngy to, kch thc file

S=int2str(x): Chuyn i s kiu integer thnh chui k t

N=num2str(x): Chuyn i cc s(bt k c th s nguyn hoc thc) thnh chui

k t.

D=size(a): Tr v gi tr l ma trn c dng [x,y] l kch thc ca ma trn a T=reshape(X,M,N): Tr v ma trn c kch thc MxN vi cc phn t l cc

phn t nm trong ma trn X.

mean(X): Ma trn X c kch thc MxN, hm tr v ma trn c kch thc 1xN

mi phn t l trung bnh tng ct trong ma trn X

mean(X,dim): vi dim l chiu ly trung bnh, nu dim bng 1 ly trung bnh theo

ct, nu dim bng 2 ly trung bnh theo hng. Khng c tham s dim th mc nh dim

bng 1. double(X): Chuyn i gp i chnh xc gi tr ma trn X .

E=eig(X): Tr v mt vector cha cc gi tr ring ca ma trn vung X.

[V, D] = eig(X): to ra mt ma trn ng cho D ca cc gi tr ring v mt ma trn

V c cc ct tng ng l cc vector ring, do : X * V = V * D

diag(V,K): Trong V l mt vector vi cc thnh phn N l mt ma trn vung

kiu N+ABS(K) vi cc phn t ca V trn ng cho th K. K = 0 l ng chochnh, K> 0 l pha trn ng cho chnh v K

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i vi cc vector, Sort(X) sp xp cc phn t ca X th t tng dn.

i vi ma trn, Sort(X) cc loi mi ct ca X th t tng dn.

Khi X l mt mng di ng ca chui, Sort(X) sp xp cc k t theo th t bng m

ASCII.

Norm(X): Chun ha ma trn v vector X.

Min(X): Tr v v tr ca phn t nh nht ca ma trn X.


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4. Chng trnh Demo:

Hnh 4.0: S khi tng qut ca chng trnh

Chng trnh m phng nhn dng khun mt s dng phng php PCA c vit

trn matlab v thit k trn giao din ngi dng GUI. m chng trnh bn khi

ng chng trnh Matlab. Ta ch ng dn Nhom5\ChuongTrinh\DemoGUI sau

m file BTLTTM.fig ch GUI, Run Figure. Nh hnh di y:


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Hnh 4.1: M chng trnh trn Matlab

Hnh 4.2: Giao din chng trnh chnh


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y chnh l giao din chnh ca chng trnh gm hai khung hin th hnh nh v hai

nt nhn Browse v Search. bt u tm kim ta cn load nh khun mt ngi

cn kim tra bng cch nhn vo phm Browse. Hp thoi m file xut hin, bn chn

file nh bn mun kim tra. y ta ly v d nh kim tra l nh 4.jpg nh hnh v:

Hnh 4.3: Chn nh cn kim tra

nh cn kim tra s c a ra giao din chng trnh chnh nh hnh:

Hnh 4.4: nh cn kim tra


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kim tra xem khun mt ngi trong nh cn kim tra chng ta nhn nt Search

chng trnh s chy v tm trong CSDL bc nh c khun mt ging vi khun mt

ngi trong nh cn kim tra. Hin th ra giao din chng trnh chnh.

Hnh 4.5: nh trung bnh

Hnh 4.6: Hnh chiu nh ln khng gian nh


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Hnh 4.7: nh cn tm

Chng trnh s tm ra khun mt gn ging nht vi khun mt cn kim tra. V

y kt qu tm c l hnh c tn 7.jpg.

Th mc TestDatabase cha tp kim tra

Th mc TrainDatabase (tp hun luyn)


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Ti liu tham kho

1. Nhp mn x l nh Nguyn Thanh Thy, Lng Mnh B

2. Face recognition using Principle Component Analysis - Kyungnam Kim

3. Tng quan cc phng php xc nh khun mt ngi Phm Th Bo


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4. A tutorial on Principle Component Analysis - Lindsay I Smith, 2002

5. http://www.mathworks.com
http://www.mathworks.com/http://www.mathworks.com/http://www.mathworks.com/

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