functii biometrice

2
1 P k,I) + 26,y1 = ,1 &d$r, ,p*=pbttx+n) ,.2x" !tnx+n1 , =::r-- ,P*"fr=7H,x+t), ,2*= 2*= l('"'x+g' efirftz"la", A aai,'V"1,' po[o6;f;kteo co e perseah; inudrsto- Je 1{"(t ati, a{ '#z A ";"!a h 6s& a*i, respe&;v,frwt {a U d*- 6, oce*,L- +eulf. W&, fe0oir6 yre"eo{ul J, a"tuol'zure 5. . cor,6 f,< in viold h 6sc,L an; , " 0' p(+q6r), tE= H .o,rt. o ca& "^ ft tn vi# & Gt"l a,u: J(4qesi , L- V(+qcs) : (\ltcQ22 , @Care e fffi;hhk"eae fi+cwvri "( l+ d'u*i nx oGr:edua An{r< CS f 7o d. a4 i? (Prrerlz,dul oL o.il"(ieore & s), w, P(?r,65).2$4?o) = \--r *r--' pu'yt, ffirnfuL i,ntre'o{ "{ 1o ittrzistinew{c^ oL q,h: irrkrving c(J.'o,,; "le;s"r^!., = Et* Serninar : firro*,i A*raet'r,te - pe*ntt alud;n( fenorene(t de u;^l;/ de.ra tvt "oarl ai6urir;6r & f"ooclrr", F"Lbi0it4,j. v,"t{;* /, J..a, p(x,fr) * f .d["Ji4,'J"ieq. 4 vlFj"- (fo6.eae palscano- irr,lirs*a Je x o",i a;feinvrorfd hIanf , xs;). 2U,1) = p.o6"[if,&{eo ob de.? (f."b,eae Ferso,,nd 7atfrt'+b &. x o'- 'ad tu fu ;" v;"1; (" X ani , x "U)' 6) f,*"*," de aapravr'et,rirq: -r- M.e&' (* = mumi"ul -ne('n lu hJiv;t J'h#-e cod,ct;vilakt care vcrrf'' lnviaf; & * a,,i' {fo, Va&r;A A^; Q /*"'l -hkM ( rlta, dnexe i fA lt?, C,,,.&Xr"o o( 7r1&me) ' p(x,X)= * A, r/. I l. tC.) Y.ftrc{ ftt?d€ r -r% ^ bte,r^(""t *orlerlr.v- a ffirtk & q* F wo i'fitti qre oh {rAf e yerxaad t^$k4fr "4 xow. e*" !+ tr;EJon =!'r t(&r'*h'+") %, i" eqqln^tanr,'lrtr lrA * ,*"4 "4 ""rnn/"lrV ea$t" tnbri pen & r6,*t e[ oo aL a,wt -7 ,e*= t+ t(Qr,+ (*rr+,..n (,*) \ r taF tba 1 nP* = ptob. coe Pcrscctrt; e( zcwtti "6 f, tu *al"'7e'te Q ad 1o&r; ("'rh\,^h,el' x+i eni1, - {or^oLa y*hb;*kftt 'levi$;, I 1U,X)=f-7$,[), f*"\ Gt =912. E Aoftro{i", fi * oo(onhze wo#q *r*, i'i;' p"rtcvrne in u{.st; a. gr & arri , *i' egd = {r -h1Qt(,*) Perlr, prere^lr& of a"lrn(|zaft g a.rott ': err = !" h(as+rs) = 1,22+ ani . a l Aeehsi rezrft"fr ,v obil'v- ?' peirn precett^I /., a.*^(,"e"rq lO, ) ,

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Page 1: Functii biometrice

1

P k,I) + 26,y1 = ,1

&d$r, ,p*=pbttx+n),.2x" !tnx+n1 ,

=::r--

,P*"fr=7H,x+t),

,2*= 2*= l('"'x+g'

efirftz"la",

A aai,'V"1,' po[o6;f;kteo co eperseah; inudrsto- Je 1{"(t ati, a{'#z A ";"!a

h 6s& a*i, respe&;v,frwt

{a U d*- 6, oce*,L- +eulf.W&, fe0oir6 yre"eo{ul J, a"tuol'zure 5.. cor,6 f,< in viold h 6sc,L an; ,

" 0'p(+q6r), tE= H .o,rt.

o ca& "^ ft tn vi# & Gt"l a,u:

J(4qesi , L- V(+qcs) : (\ltcQ22 ,

@Care e fffi;hhk"eae fi+cwvri"( l+ d'u*i nx oGr:edua An{r< CS f 7od. a4 i? (Prrerlz,dul oL o.il"(ieore & s),

w, P(?r,65).2$4?o) =\--r *r--'pu'yt, ffirnfuL i,ntre'o{

"{ 1oittrzistinew{c^ oL q,h: irrkrving

c(J.'o,,; "le;s"r^!.,

= Et*

Serninar : firro*,i A*raet'r,te

- pe*ntt alud;n( fenorene(t de u;^l;/ de.ra tvt "oarl ai6urir;6r & f"ooclrr",F"Lbi0it4,j. v,"t{;* /, J..a,

p(x,fr) * f .d["Ji4,'J"ieq. 4 vlFj"-

(fo6.eae palscano- irr,lirs*a Je x o",i

a;feinvrorfd hIanf , xs;).2U,1) = p.o6"[if,&{eo ob de.?

(f."b,eae Ferso,,nd 7atfrt'+b &. x o'-'ad tu fu ;" v;"1; (" X

ani , x "U)'

6) f,*"*," de aapravr'et,rirq:

-r-M.e&' (* = mumi"ul -ne('n lu hJiv;t J'h#-e

cod,ct;vilakt care vcrrf'' lnviaf; & * a,,i'

{fo, Va&r;A A^; Q /*"'l -hkM( rlta, dnexe i fA lt?, C,,,.&Xr"o o( 7r1&me) '

p(x,X)= *

A, r/. I l.tC.) Y.ftrc{ ftt?d€ r

-r%^ bte,r^(""t *orlerlr.v- a ffirtk & q* F wo i'fittiqre oh {rAf e yerxaad t^$k4fr "4 xow.

e*" !+ tr;EJon =!'r t(&r'*h'+")%, i" eqqln^tanr,'lrtr lrA * ,*"4

"4 ""rnn/"lrVea$t" tnbri pen & r6,*t e[ oo aL a,wt -7

,e*= t+ t(Qr,+

(*rr+,..n (,*) \

r taF

tba

1 nP* = ptob. coe Pcrscctrt; e( zcwtti "6 f, tu *al"'7e'te

Q ad 1o&r; ("'rh\,^h,el' x+i eni1,

- {or^oLa y*hb;*kftt 'levi$;,

I 1U,X)=f-7$,[),

f*"\Gt =912. E

Aoftro{i", fi * oo(onhze wo#q *r*,i'i;' p"rtcvrne in u{.st; a. gr & arri ,

*i' egd = {r -h1Qt(,*)

Perlr, prere^lr& of a"lrn(|zaft g a.rott ':

err = !" h(as+rs) = 1,22+ ani .a

l Aeehsi rezrft"fr ,v obil'v- ?' peirnprecett^I /., a.*^(,"e"rq lO, ) ,

Page 2: Functii biometrice

1

/r[ore...n*o vraEer,i oi de Jau'-w-'

- ihu&e^z; {eno,rrennl Jt ^:;"F; "t ,6il0.- ?r&* y*{enbrdo* e cerrline,

q gW( in eo're ,u'"fr ewil

9) arce utferieare ( ;ndl"a' faelul dpersaano. rfir,,ilne ?n viala )

$ wt arc, i&"ier ( rnJrcd' f,aela!- 6perEeauA f,paolsazd in anal resyed;v)

Brgggt5" t#, (pn{'n a pet*aai 4 x a*aS

k*r 4,r, X*nQ 8,7+t "' (t+n-t-

(,

6{ ?e arc& ffilrere^, 2n+n

W- oorrtrn ,nkiQ f^r"$16 [iene*r,re

na /egsiT ,i^r^k "( A ol ani ^-a^4

a*r*a#ou+n64car & *rohb,({'al ;,l/

&r=0,$ , ?a1=a,* , fas=4s , E+-9\, ftr"92.c*e# ,n,4"br! J' qactto(ilak y"ntvx y6u$; u,t

tdrgb oup*hsi' lntve 8( d 8{ Je ani, '2lnarl (6,

= tom,6o/cda:

ztttitW==Ql€. B

&*(r,F]

- n*rrilru,(

f<rxcuila+da"dof" in#e

xnt t*4 ed.,

0rr,= 0-d*

q5' €fs ' t * o (cf,c< rott t( ove^ f Q

Fry72 (A,&ec,e)tg.,l(l

7reb6n","k. 5,6,+,8,3

ffi:RjPpreh&;&&"d. dot;, tn tau^p ee

p are.ul ir,fn;er o,smtrece Trihli(il"ho de de"q.

&&sis' 'i",AaW Jn*k {' "r,1F a wt6wo&(er ce

x ?,( 2r (^ 4, e?c

Er Q,3 ql 3

to aa = laoo 2,+7

8z 0,7 or3 g00o 2:loo l,€!

f3 o,{ o,e 6w 3tso lr4

8{ orh 8,6 3tso lEgo q9

E' or2 a,8 I2e0 too& orS

;{ef,eotft;:-t4-

@ Sf,- nln"h"e,4 &'&*r'.-.'&*n-.Ib) P*' Prrr' ...' Prt+n-r' 2x+n .

.6ofo,:[,i,

^)

@At",lt^;* orhreunlo W t"d(, olt p,Prt* e VrwnJ ,L Adru^ .* a yft.u,olt*r/^ inlre go n il ote aon;. GAsiJf e

=*oP((fftn)'*P^'

b) P"'P**,' .-' ?*n-i 2*rr, - ^Px

(l - h*n)=

=b('-W)= t"+n - (rrnn,

NdamnPuIx = Qno- Q:n*J

(*

teft pre$^b:Lt"ka ca c perca,a; o( /W ai Jt 4Jr/te inlrc t+n +; x+n+t ant),

?. ,l ele otaq . \icsit, ,82 r, .

= t*'txJn

'7drrti,