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• " Ts < 0.75 H % # 8 #B 8 I ( " 0, 75 ≤Ts ≤ 0, 90 H % # 8 # B (

• N 4 H H (

;( 7 Π # H # H (

6( "K Π% +K % 0→ 1 1← 0(" G # % ( + (

:(;* ( " " , & " , &

:>

R # # % % # H ( - # H % 7% % # # K # 7 H H (

' # + B #( J :(6% # * % % 8(

:(6* < : ! Π

## 1

) ? + ! % #% # B ! K #O( 7 % # # + !

:5

% K H #( +*

!$9 ' I K% (

$2 !. ,:;- \ K + + (

T? (

, -

) K K 8 ! K % + K 8 + K % # +H #O(

• U;;V% K G(

• U4:V% G K ! (

' K # % % ! K % % + K ( # +? K% 8 *

4( B (u, v) I% B! K NUfBNUf % K *

IUnf(u, v) =I(u, v)−min

max−min, /:(:0

#% max min HB ! & K (u, v)(

( ' & IUnf + + U>V%U5V(

INor(u, v) = IUnf(u, v)+

0.5m∑

i=n

HT iBbrc(u, v)− 0.5

m∑i=n

HT iBprt(u, v)

/:(;0

;

*

HT iBbrc(u, v) = (IUnf − IUnf iB)(u, v) HT iB

prt(u, v) = (IUnf • iB −IUnf)(u, v) + 8 + % % # B # i QQQ•Q 8 + + K% (

) /40 K ! K /0 + K + K ( J :(= + K I + K(

:(=* < > " 3 I IUnf INor

./ ! 012

# B % ! !% %H + ( ' # ! + U5>V U44V( % K K %

;4

! / K ? 0 % + *

IMej(u, v) =∥∥∥IDFT2

‖DFT2 INor(u, v)‖k DFT2 INor(u, v)

∥∥∥ ,

/:(60 #* (u, v) ∈ SNB,NTR

ij % % SNB ,NTRij (i, j)

INor NBBNB NTR B% DFT2 IDFT2 + % k B # ‖•‖ (

U5>V k = 0, 6 U44V 8 k = 1, 4( ) H ! % % * K 8 H (

' + # / 0 & % #% # k % + ! HB % # HB ( HB + % K % # + # + B % # ! H B ! +( J :( NB = 32% NTR = 20 k = 1, 0(

#' 0

' 8 % K ? 7 U;;V% U:>V%U:5V% U5:V% P + 7 U4;V% U56V% ! + 7 8 % U4=V% U46V% U6V( ) ! G% & % P% # H 8 UV% U>>V% # UV

;

:(* & !(2+ "

+P U=V( . % P% G 8 % G # H (

• 7 !B (u, v) I G # + # K (u, v) B K / :(>0( ' 8 % ! % % # ( ' Θ % 7 K NF ilBNCol Θ(i, j) (i, j) I% #* NFil ≤ N I

F il NCol ≤ N ICol(

• 7 P K# + (" K B

;:

% P 1( % K ! 8% P 0% ? # 8 P 1% # 8 / 0 P 0(

:(>* = % ,"

( 3% &

TH H + ( ' #H H K G ( + U6V% U:V U>=V% U;>V% U6V U;V( *

8$($ < # Gx Gy% + B (

! $$ . % ! (

T? (

;;

8$($ < #

) Gx(u, v) Gy(u, v)( B + K +* H U:V% K + H U:V ( + K H % 7 " (

! $$

J K # U6V U;V U6V U5V(

) # B B % 7 Gp(u, v)% # # G ( H% # K % ?H # % # # 180o(

Gd(u, v) = (Gx(u, v) + jGy(u, v))2

Gd(u, v) = (G2x(u, v)−G2

y(u, v)) + j(2Gx(u, v)Gy(u, v)),

/:(=0

% K Skij Sk

ij% #H Gp(i, j)*

Gp(i, j) = 1N2

k

∑(u,v)∈Sk

ij

Gd(u, v)

Gp(i, j) = (Γxx(i, j)− Γyy(i, j)) + j(2Γxy(i, j)), /:(0

*

Γxx(i, j) =1

N2k

∑(u,v)∈Sk

ij

G2x(u, v), /:(>0

Γyy(i, j) =1

N2k

∑(u,v)∈Sk

ij

G2y(u, v), /:(50

;6

Γxy(i, j) =1

N2k

∑(u,v)∈Sk

ij

Gx(u, v)Gy(u, v), /:(40

% # Φ(i, j) *

Φ(i, j) =1

2arctan

(2Γxy(i, j)

Γxx(i, j)− Γyy(i, j)

), /:(440

#* Φ(i, j) ∈ [−π/2, π/2] arctan (y/x) y/x x y(

) P H 7 *

Coh(i, j) =‖Gp(i, j)‖

1N2

k

∑(u,v)∈Sk

ij

‖Gd(u, v)‖ /:(40

/:(0 # Gd(u, v) % # + Φ(i, j) Coh(i, j)% B % Gd(u, v) G # Gd(u, v) #% # P( % 2 U6V 8 # + + H (

% Skij

Λr% #* Skij = Λ1 ∪ Λ2 ∪ . . . ∪ Λr ∪ . . . ∪ ΛM % Λr H

+ NΛ B(3 % Λr #H

P*

Gp(r) =1

NΛ

∑(m,n)∈Λr

Gd(m, n), /:(4:0

Coh(r) =‖Gp(r)‖

1NΛ

∑(m,n)∈Λr

‖Gd(m, n)‖ . /:(4;0

# % Sk

ij *

Gpn(i, j) =1

M

M∑r=1

w(r)Gp(r), /:(460

;=

7 *

w(r) =Coh(r)

‖Gp(r)‖ , /:(4=0

" /:(4=0 /:(460 *

Gpn(i, j) =1

M

M∑r=1

Coh(r)Gp(r)

‖Gp(r)‖ , /:(40

/:(4;0% /:(0 /:(=0 /:(40 *

Gpn(i, j) =1

M

M∑r=1

(Γxx(r)− Γyy(r)) + j(2Γxy(r))

Γxx(r) + Γyy(r). /:(4>0

% Φ(i, j) Coh(i, j)% 8*

Φ(i, j) =1

2arctan

(Im Gpn(i, j)Re Gpn(i, j)

)/:(450

Coh(i, j) =‖Gpn(i, j)‖1M

M∑r=1

Coh(r)

≈ ‖Gpn(i, j)‖ /:(0

) % % U5V% % # H Φ(i, j)( + Sk

ij 7 *

D1 = Ski−1,j−1 ∪ Sk

i−1,j ∪ Ski,j−1 ∪ Sk

i,j

D2 = Ski−1,j ∪ Sk

i−1,j+1 ∪ Ski,j ∪ Sk

i,j+1

D3 = Ski,j−1 ∪ Sk

i,j ∪ Ski+1,j−1 ∪ Sk

i+1,j

D4 = Ski,j ∪ Sk

i,j+1 ∪ Ski+1,j ∪ Sk

i+1,j+1

/:(40

#* Ski,j = D1 ∩ D2 ∩ D3 ∩ D4% Dr

Φr Cohr% 8 /:(440 /:(40%7 Φ(i, j) Sk

ij Φr # ? HB Cohr(' Φ% Θ(

K K Φ( K U6=V% % Φ / ? [cos(2Φ), sin(2Φ)]0 7 H wsv*

;

Υx(i, j) =∑

(m,n)∈Ssv

wsv(m, n) cos(2Φ(i + m, j + n)) /:(0

Υy(i, j) =∑

(m,n)∈Ssv

wsv(m, n) sin(2Φ(i + m, j + n)) /:(:0

Θ 8*

Φsv(i, j) =1

2arctg(

Υy(i, j)

Υx(i, j)) /:(;0

Θ(i, j) =

Φsv(i, j) Φsv(i, j) ≥ 0

Φsv(i, j) + π Φsv(i, j) < 0/:(60

J :(5 :(4 P % # 8 H #% B U6V # + 8 H #% #% # (

:(5* Θ ( % % 6?@9 % 68A9

;>

:(4* Θ B ( % % 6?@9 % 68A9

#+ /

J 8 # # 8% K B !% % P 7 ( J % K +(

# 4 52 6

"" &

+P B ! & ( 7 +P # # HB / :(440(

B % Θ% ? *

• U6>V ! ( % 7% ! ! ! Θ /K

;5

:(44* !+

K Θ 8 % + 0( ' % +P 8 # HB (

• U64V Θ%# K +P H % # + 8 7 K (i, j) Θ( ! % 87 ! & ( ' % + +P 8 (

• U>4V # Θ # +P % ! ! & # (

• U=V H P / P # & P0 ! ( & P ! ! (

J K +P% % # +P

6

% H I ! (

6 / "

+P( ) I + ( ) /,'0% /330 /N30 P % # /M0 P % /'0 ( % H % ,'% 33% N3% M '(

! % U6=V% U4=V% U>V% U5=V( H U>;V% U>V( ) ! Θ % # 2 U6V K Θ ( + G U6V( ) *

6 / . 6 ! ( " % +P ! ( " +P(

6 / =! <> " 7 ! + K G K Θ( K K +P K K(

' ? (

6 / . 6

" C + Θ% ! PΘ,C 7 XB Θ C /T :(40% ?% 8 Θ C( ) ! PΘ,C (i, j) Θ *

64

4( "? Cr + # 7 #OP Θ% ! r W Cr H # NCrBNCr % #* NCr = 2r + 1 r > 0% r = 0% Cr H # 2B2( , H% :(4(

:(4* 1, ! & %

) Cr ( " # % # I ( % % (

( PΘ,C(i, j) + 8 ? Cr( " εx εy

x y Cr% # # (0, 0) % ! H *

PΘ,C(i, j) =

N2Cr

−1∑k=0

∆ij(k), /:(=0

*

6

∆ij(k) =

δij(k) |δij(k)| < π/2π + δij(k) δij(k) ≤ −π/2π − δij(k) outro caso

, /:(0

#*

δij(k) = Θ(i+ εx(k +1), j + εy(k +1))−Θ(i+ εx(k), j + εy(k)). /:(>0

PΘ,C(i, j) B 0o,±180o,±360o % (i, j) H * B 0o% B 180o B −180o% :(4:(

:(4:* 1B & % r = 1

:( ' PΘ,C Θ K # + ! ( # # ( ' % H /T :(4;0(

;( " % +P ! ( " +P% % # + ' H +PH + G(

6 / =! <>

' + G U6V '( ) H + G

6:

:(4;* ,% & % & % ,B - '

K G K (i, j) Θ( ) K B 0 K + ( ) H *

4( (i, j) Θ ! % K 8 qBq /q = 30 (i, j) Θi,j( , KΘi,j Π(

( K G Θi,j( K *

Σij =1

q − 1

q∑k=1

(Θkij − Uij)(Θ

kij − Uij)

T , /:(50

Θkij k K Θij Ui,j

K Θij (

6;

:( HB Σij ( ) + G (i, j) H HB & K G Σij % λij(

;( ) /40 /:0 # (i, j) Π% + G% K Ψ / 7 :(46(0(

6( Ψ K max(Ψ)/6 / max(Ψ) HB Ψ0% #% 6 + U44V( 3 % KK( . # +P H /7 :(46(0(

:(46* !+ : - ! , ' - B B ! , ' !+ :

66

6 / ! !?$"$ .< " !#!

' 7 # ?7 K% # ! 7# ( ' % H ! B % B H +P 8 '% # +P 8 H ! # H ! # 7 +P '( % # ? + # +P ## % # ( ' B # # % # QI ! Q(

B + 8 XB 8 + +P( % :(4=% # XB +P # % 0o% XB + ( % # +P P #K 0o( U>4V +P # K ! # +P H K Θ ? #K ?0o( . + B +P / +P H #K 0o0 7 +P '( % 8 H Θ I ! #K % # #K 8 K 0o ? K % H (

[ Θ #K Q / ?% ! Q 8 π/Q 0 K Θ0% Θ1% · · · % ΘQ−1*

6=

:(4=* ," !+

Θ(i, j) =

Q−1∑k=0

kπ

QΘk(i, j), /:(:0

#*

Θk(i, j) =

1 k =

⌊Θ(i, j)Q

π

⌋0 caso contrario

, /:(:40

* • B (. Θk H 1

# Θ # kπ/Q% K # Θk k / #K 0 ( H I ! H K Θk / ! H0 # ! Θ ? ( # ! Θ +P 7 *

ΘBd (i, j) = Θm(i, j) + Θn(i, j), /:(:0

#* m = mod (−d, Q) n = mod (Q−1−d, Q)% % d G # 7 ! H ( #ΘB

d H / :(40% 8 mπ/Q nπ/Q 1% # 8 7 8 + ΘB

d 7 /:(:0( 8 ,'% N3% 33% M ,3 +P

H # ? H K

6

:(4* I Θ ( " 32 &, ΘB0 Θ

B1 Θ

B2 !Θ

B3

ΘBd / :(4>( :(4>(+0 '

+P H 7 ? H ΘB

d / :(4>(0 % & # ΘB

d % ! +P% +P 7 ( K U4V 7 *

ΘCd (i, j) =

Q−1∑r=0

Q−1∑k=0

wd(k, r)Θ mod (k−d,Q)(i, j), /:(::0

wd(k, r) = exp

(− 1

2σ2(k − mod(r − d, Q))2

). /:(:;0

)% wd + Θk% # # 8 mπ/Q nπ/Q ! % K K + # 8 ΘC

d % ! G # # 8mπ/Q nπ/Q / :(450(

+ 8 I ! ΘBd ΘC

d % # +P

6>

:(4>* ΘBd & : :

< C = ( d = 1 Q = 16

:(45* ΘCd d = 0 d = 1 d = 2 d = 3

( ) *

4( [K 8 Θ Q

65

0, π/Q, · · · , (Q− 1)π/Q(( ! #

K P Coh 8 Π( % I Π% # NPri% I Coh # + tQ% # NCoh( 7 [Qc(tQ) = NCoh/NPri% % H # Qc(tQ) H 1% #% tQ 7 Qc(tQ) /& # tQ B 1 8 7 #0(

:( d = 0, 1, · · · , Q/8− 1% K*

• " Qc(tQ) # 0.8% ΘBd % H

ΘCd ( J # ΘC

d ? % + % K 8 mπ/Q nπ/Q% # H H ΘB

d (

• $ ΘBd Π

Θ (

• K Bm ΘBd (

ΘBd ? 1

# ( , #* Bm(i, j) = 1 (i, j) ?H ( / :(0

• 7K Pe K Bm(' Bm 7 N K I K U;V% # 8 7K H 7/ Bm 70% 7K # ? H ΘB

d ( , 8 K 7K Pe = (ip1, jp1), (ip2, jp2), · · · (• NK 7 Pe # 8 # H ΘB

d ( % # ? W % # ? ? 1 # 2W %

=

:(* " B % Bm D 1 ΘB

d "

# # + ΘBd /

ip ≥ Nfil/1.6 0W # % B K 3B3 ΘB

d (ip, jp) ?H + + 0% 2% (

;( 7 H BT % # ΘBd %

?% BT = ΘB0 ∪ ΘB

1 ∪ · · · ∪ΘBQ/8−1% BT

% # K * K H BTp = (BT ∩ Π) ∪ (BT ∩ Π) % • % H BTp BT ? H ? # BTp(

6( H Pe% B BT % ? 1 # % /6 0 Pe( ,% B ? 1

=4

/ # # BT

?H 0(

=( " I H Pe # 0 I BT 1% % H Pe # BT + / # +PH # 0(3 % +P H / # +P + 0(

( " I H Pe 0 I BT 1% 7 +P Π(

>( " I H Pe 0 I BT 1% # + '% +P I BT % H BT # ( % % BT ? 1 # ? % ? 1 # BT % ? 1W % BT /;0W % I BT W # % # 7 +P # 1(

5( " +P /=0 />0 H % +P Π% H % +P /=0 K K P% Coh% B H ( B! K Coh +P% 11B11 7 +P K # P(

J :(4 #OP % #K Θ 32 / :(4(0% H

=

ΘBd #

? H ΘBd

K /7 :(4(0W :(4(+ H BT # % ! +P + W :(4( H +P K Coh :(4( +P 7 K(

:(4* Θ ( " 32 &, ΘB0 Θ

B1 Θ

B2 Θ

B3 !BT

B !+ " " Coh !+

#. /

J ! + B K 8 ! G # ? 7 / :(0% 8 # # H + % # + +P # K 8 + (

J 7 % # K + % + (

=:

:(* :(

%

'

. .'"<" +P% K 7 *

• 1A + %

• kK B

• / !0(

' 7 + + .'"<" B 7 U4V( ' 7 1A + kK B + + B ! % # 7 + H + / ?% % 8 +P ?H 7 K +0( ' % .'"<" + 7 % B + # 7 (

) . ! 8% 7 ! % % B ! G ( " % K%

! ,

=;

=6

? ! ! 7 % 7% 7 ! K ( J I ! (

' (*

K ! 7 ! /J % K B 0( K ! 7 % # 7 # ( . ?H % # .'"<"% # K 7 *

5 . ' Θ # % 9(

( !$ . 9 # H ( K H /.'0% # % 7 ! 4(

$ ) 7 K +8 Di% # ( ) ! 4 7 HB + U6V(

' ? (

( 7 !""

' U4V% U4:V% U4V U5V K Θ% ?*

v(i, j) = β(i, j)[

cos(Θreg(i, j)) sin(Θreg(i, j))], /;(40

% Θreg(i, j) β 7 7( 7 # K

==

/180o ↔ 0o0 ? ( 7K *

β(i, j) = 1, /;(0

#% Θ G( ) 9 7 v( J ;(4 #OP 9% Θ +P% Θreg / ;(4(0% % Θreg % v / ;(4(0 7 v% 9 / ;(4(0(

;(4* < E Θ= Θ Θreg v

( 8 "

" Θ 64B64 K 7 Θ 8192 /Y64B64B20% # I H% 7 7 ( % # H K ( K .'"<" .'(

=

8$ !" "$ @ A

" # ? 8 + Θ* 91, · · · , 9p m H% ? K # 4 n H% #% n < m( ) 7 K + B # ? 9 4 K # B

4 = BT9,E[9] = 0. /;(:0

)% E[•] (' .' U6:V + K

K K G ? K ( ' K G ? 8 ? 8 K *

Σz =1

p− 1

p∑j=1

9j9Tj , /;(;0

Σx =1

p− 1

p∑j=1

4j4Tj , /;(60

% p I 8( " # E[9j ] = 0 E[4j ] = 0( Σz #7 8 ! H ? % H G # H B G # ( . ? K % H K # ! G & H( . H + B% #% K Σx( .' K # Σz K Σx% B B (

Σz< = λ<. /;(=0

) λ ≥ 0 < ∈ Rm − 0 Σz( ' /;(=0% 7 Σz % *

> ,

=>

= CT ΣzC, /;(0

C < Σz λ Σz( ' /;(:0 /;(60*

Σx =1

p− 1BT ΣzB. /;(>0

. /;(0 /;(>0% # Σx H KH B K C(

' .' G(

4( . 8 91, · · · , 9p K 8 D ∈ RmpW D = [91, 92, · · · , 9p] / ;((0(

( . D% K ( ∈ Rm1W ( =1pD p1% p1 ∈ Rp1 1 /

;((0(

:( "! ( D% K E ∈ RmpWE = D− ( 1p% 1p ∈ R1p 1(

;( K G Σz ∈ RmmW Σz =1

p−1EET W 1

p−1(EET )C =

C( ' K C ∈ Rmm% <1,<2, · · ·<m Σz K ∈ Rmm% m λ1, λ2, · · ·λm Σz(

6( N C + Σz(

=( " n C 7 K + B * B = [<1,<2, · · · ,<n] / ;((0(

( ? 8 K 7 K + BW 4 =BT (9− () / ;((0(

" m > p /I H # I 80 K /;0% J % EET ∈ Rmm% K ETE ∈ Rpp% ?*

=5

1

p− 1ETEC = C, /;(50

/;(50 E% *

1

p− 1(EET )(EC) = (EC). /;(40

% EC p EET % m−p K 7 ( 'K EC % % H k EC

√pλk.

;(* " , , % = , D- " !

( ""+

J K # 7 % 7 1A + % kK B /kJJ0 7

/$3 ) "0 ! /JJ " !&0% 7 ! .'% ? ! 4( . 7 +8 # 7 H HB ( ' K B 7 K % *

• L* I W L = 4, 5 / 4 /L = 40 8 7 N3% M% 33% ,''% 5 /L = 50 8 7 N3% M% 33% ,' '0%

• Ωi* i %

• P (Ωi)* Ωi%

• P (Ωi)* P (Ωi)%

• n* ! / K 0%

• 4W ! /! .'0%

• 4(i)j * i ! j %

• (i* Ωi%

• (i* (i%

• Σi* K G Ωi%

• Σi* Σi%

• d (4,F) = (4−F)T (4−F)* G 4 FW 4% F ∈ Rn%

• Di(4)* i + W 1 ≤ i ≤ L% 4 ∈ Rn(

$ EF ! =" !$ @$ !$A

7 H 1A + H Ωi( % HI 7 % # *

• p(4)* + 4 ∈ S ⊆ Rn% %∫S

p(4)d4 = P (4 ∈ S)%

4

• p(4|Ωi)* + 4 ∈ S ⊆ Rn # Ωi% %

∫S

p(4|Ωi)d4 = P (4 ∈ S|Ωi)%

• P (Ωi|4)* 4 % P (Ωi|4) =P (4 Ωi)(

) 7 1A # # K % 7 # 7 K 7 K 1( J % 7 1A 7 4 & Ωi # P (Ωi|4) ( 1A*

P (Ωi|4) =P (Ωi)p(4|Ωi)

p(4). /;(440

) 7 7 4 & Ωi P (Ωi|4) HB( 7 J Ωi # + *

p(4|Ωi) =1

(2π)n2 |Σi|

12

exp

(−1

2(4− (i)

T Σ−1i (4− (i)

), /;(40

% |Σi| Σi( J H (i Σi % ?* (i Σi( " /;(40 /;(440 8 (i Σi P (Ωi|4)( 7 + 7 % Di(4)% P (Ωi|4)*

Di(4) = ln(P (Ωi))− 1

2ln(

∣∣∣Σi

∣∣∣)− 1

2(4− (i)

T Σ−1i (4− (i), /;(4:0

/40 # + Ωi # BK P (Ωi|4) (2π)−

n2 (

& 4 HB + U6V(

c = arg maxi=1,2,··· ,L

Di(4) , /;(4;0

% c ! ! 4 arg max ! HB + (

$ kG<92 ! "H4!

) H K B E U:;V( 7 B ( J % +8 % P K +8 ( % B E + % 4% k B 4( # ? (. E U=V + U:;V% 1K B k = 1 / 1JJ% BF0% kK B /kJJ0( J ? B 1A( % B kJJ & B 1A% I 7 % 7 *

P ∗ ≤ P ≤ P ∗(

2− c

c− 1P ∗

), /;(460

% P ∗ B 1A P B kJJ% 7 c / ;(:0(

;(:* 0 k->> c = F 6GH9

:

' 7 1K B B %# ? 7 4% # ? % K B 4 ? ( "? 41NN K B 4% # 41NN Ωc% 4 Ωc(

' 7 + 1JJ *

Di(4) = − minj=1,2,··· ,Li

d2

(4,4(i)

j

), /;(4=0

1JJ 7 /;(4;0( R # K B 4 +K 7 + ? ( B 1JJ 7 kK B % kJJ% # kK B 4 ? P 4 & k K ( ' 7 + kJJ *

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