Phục hồi ảnh - Đại Học BKHN

B GIO DC V O TOI HC NNG

TIU LUN MN HC

X L NH

TN TI:

KHI PHC NH

Hng dn khoa hc : TS. Ng Vn S

Hc vin thc hin : Ng Vn c

Phm Minh Hi

L Huy

L Anh Khoa

Lp : Cao hc KTT K25

Nin kha : 2012 - 2014

nng, thng 5 nm 2014

CNG NGH MNG RING O3

1 Gii thiu

X l hnh nh l mt hnh thc x l tn hiu m u vo l mt hnh nh,

chng hn nh mt bc nh hoc khung hnh video, u ra ca x l hnh nh c

th l mt hnh nh hoc mt tp hp cc c im hoc cc thng s lin quan n

hnh nh. Ti y, mt hnh nh c nh ngha l mt mng, hoc mt ma trn,

im nh vung c sp xp theo hng v ct. Hu ht cc k thut x l hnh nh

u lin quan n vic x l nh nh l mt tn hiu hai chiu v p dng cc k

thut x l tn hiu tiu chun cho n. X l hnh nh thng lin quan n x l

hnh nh k thut s. Lnh vc x l hnh nh k thut s dng x l hnh nh s

bng my tnh s. N bao gm nhiu k thut nh phn chia hnh nh, nhn dng

nh, chnh sa mu, khi phc nh,

2 K thut v phng php

2.1. Khi phc nh

Khi phc hnh nh l qu trnh ti to hnh nh gc t hnh nh c cht lng

suy gim do 1 s cc nhn t. Phc hi hnh nh k thut s l mt lnh vc k

thut nghin cu v cc phng php c s dng khi phc li nh gc t

nhng hnh nh b suy gim v quan st. K thut c s dng khi phc li

CNG NGH MNG RING O4

hnh nh nh lm gim m, nhiu v p dng cc b lc khc nhau c c nh

tng ng vi nh gc. C rt nhiu nguyn nhn gy ra s suy gim nh v v

khi phc nh l mt trong nhng lnh vc quan trng trong x l hnh nh. S suy

gim thng xy ra bao gm m, chuyn ng v nhiu. M c th do i tng

trong hnh nh b mt nt khi phi sng, trong khi chuyn ng m c th c gy

ra khi mt i tng di chuyn so vi my nh khi phi sng.

Mc ch ca phc hi hnh nh l " b" hoc "khi phc" sai hng m

lm suy gim hnh nh. Suy gim c nhiu hnh thc nh chuyn ng lm m,

nhiu, mt tiu c camera. Trong trng hp nh lm m chuyn ng, c th a

ra mt c lng rt tt so vi m thc t v "khi phc" m khi phc li hnh

nh gc. Trng hp nh b li bi nhiu, c th thc hin b nhiu.

Trong qu trnh khi phc, suy gim c th xem l mt hot ng khng gian

tuyn tnh bt bin trong , nu g(x, y) l nhiu t do, vic khi phc c th c

thc hin bng cch s dng chc nng chuyn nghch o ca h(u, v) l b lc

phc hi v (x, y) l nhiu. Cc k thut phc hi s dng nhiu loi b lc t

c hiu sut tt nht, nh b lc ngc, b lc Wiener, b lc Histogram

Adaptive Fuzzy, b lc Min-max Detector Based v b lc Centre Weighted Mean,

CNG NGH MNG RING O5

g(x, y)= h(x, y) * f(x, y) + (x, y)

2.2. Cc loi nhiu nh

Cc loi nhiu khc nhau c 1 s c tnh. Trong phim nh, nhiu thu c ch

yu l do cc ht bc kt ta trong qu trnh phi sng. Nhiu do cc ht bc, c

gi l nhiu ht phim. Nhiu ht phim khng thc hin bt k s tng quan thng

k v khong cch gia cc mu ln hn kch thc ht. Do nhiu ht phim l

nhiu trng 2 chiu x l ngu nhin. Trong my d nh in t, hai loi nhiu xut

hin: Nhiu nhit: ngun ca n l cc mch in t khc nhau v nhiu

Photoelectron: n c sinh ra bi bin ng ngu nhin ca s lng photon trn

b mt nhy cm nh sng ca my d.

Mt loi nhiu khc xut hin trong qu trnh truyn hnh nh l nhiu xung

Salt-Pepper. N xut hin nh xung nh en v/hoc trng. Ngun ca n thng l

nhn to hoc nhiu trong khng kh, xut hin nh l tp m xung. N c dng

sau: ni z (k , j) biu th xung v i(k , j ) biu th mt nh gc ti cc im nh

(k , j). Trong trng hp cc my nh CCD, dng chnh ca nhiu l nhiu do suy

hao truyn.

C rt nhiu loi nhiu trong qu trnh x l hnh nh v mt s trong s bao

gm:

Nhiu Gause: l mt loi nhiu xut pht bi phn b bin Gaussian. Phn

b xc sut Gauss c hm mt xc sut:

CNG NGH MNG RING O6

trong x l mc xm, l trung bnh, l lch chun v phng sai 2.

b. Nhiu Gamma: l nhiu c hm phn b xc sut

Vi gi tr trung bnh =b/a, phng sai 2= b/a2. a v b l cc s nguyn dng.

c. Nhiu nhn: l nhiu vi hm mt xc sut theo hm m ca:

Vi gi tr trung bnh =1/a v 2= 1/a2 vi a>0

CNG NGH MNG RING O7

d. Nhiu ng u: l nhiu vi hm mt xc sut

Vi gi tr trung bnh =a+b/2 v phng sai 2= (b-a)2/12

e. Nhiu xung: l nhiu vi mt hm mt xc sut

CNG NGH MNG RING O8

f. Nhiu Speckle

C th c m hnh bng cch nhn cc gi tr ngu nhin vi gi tr ca

cc pixel. Nhiu speckle l vn quan tm ch yu trong cc ng dng radar.

Trong matlab nh vi nhiu speckle c tnh ton: I *(1+N)

T= imnoise(image,speckle)

Nhiu N c phn phi chun vi gi tr trung bnh bng 0. C th cung caaos

thm thng s xc nh gi tr k vng ca N, gi tr mc nh ca n l 0.04.

3 Cc b lc

Loi b nhiu l mt trong nhng cng vic chnh c thc hin bng cch x

l nh v quan st trn my tnh. Nhng thng tin nhiu khng mong mun nh:

cht lng my nh v phc hi, iu kin thu nhn, nh cng sng, hiu chnh

v nh v hoc c th l mi trng cnh. B lc k thut s c s dng loi

b nhiu t cc hnh nh b suy gim, n l mt h thng ph quan trng ca bt k

h thng x l tn hiu no. Cc b lc c s dng nng cao hnh nh, v n

loi b cc thnh phn tn hiu khng mong mun. B lc c nhiu loi khc nhau

nh b lc tuyn tnh hoc b lc phi tuyn. Trong thi gian u, khi cc tn hiu x

l l tng t, b lc c s dng l b lc tng t . Ngy ny, cc b lc k

CNG NGH MNG RING O9

thut s dn dn tip qun cc h thng tng t v tnh linh hot ca n, chi ph

thp, kh nng lp trnh, tin cy,... Cc b lc s c thit k bao gm ba bc

c bn : (i) cc c im k thut ca cc thuc tnh mong mun ca h thng, (ii)

xp x ca cc c tnh s dng h thng thi gian ri rc nhn qu , v (iii) vic

thc hin ca h thng bng cch s dng thut ton hu hn chnh xc.

3.1. B lc trung bnh s hc -Arithmetic Mean filter:

f= mn1 ( )

yxtsg

,,

(31)

Gi tr ca nh c khi phc ti ta (x,y) n gin l trung bnh s hc

ca nhng pixel trong min Sxy .

B lc trn c thc hin trong IPT nh sau :

w = fspecial(average ,[m,n])

f = imfilter(g,w)

3.2. B lc trung bnh hnh hc ( Geometric Mean filter):

F= ( )

ysxtstsg

,,

,mn1

(32)

Mi gi tr pixel ca nh phc hi : l tch ca nhng pixel trong min S xy ,

sau ly ly tha 1/m/n. IPT khng h tr hm tnh ton trc tip b lc ny.

3.3. B lc trung bnh hi ( Harmonic Mean filter)

F(x,y)= ( ) ySxts tsgmn

,, ,1

(33)

B lc ny lm vic tt vi nhiu Salt, nhng li khng hiu qu vi nhiu

Pepper.

CNG NGH MNG RING O10

4 Khi phc nh bng phng php cn bng Histogram

Histogram l mt trong nhng biu din c bn ca hnh nh trong vic tng

cng v phc hi hnh nh. Qu trnh Histogram l cch tt nht nng cao

tng phn. N cho thy cc chi tit ca hnh nh dng ri rc trn mt th.

Histogram hin th cc thng tin thng k ca hnh nh s.

tng phn o cht lng hnh nh ty thuc vo mu sc v sng ca

mt i tng m lm cho i tng trong mt hnh nh c phn bit r vi cc

i tng khc. Histogram trong th ch s lng im nh ti mi gi tr cng

khc nhau c tm thy trong hnh nh.

4.1.Biu din Histogram

Mt ca nh cy vi biu din Histogram c hin th di y:

Hnh. Biu din Histogram ca mt nh


Hnh. Biu hin Histogram m bn ca mt nh

Hnh trn cho thy cc biu din Histogram ca mt hnh nh v m bn ca n.

N cng cho thy rng mt trong nhng histogram hon ton tri ngc vi nh kia

cho thy phn mu en c gi tr ln trong khi phn mu trng c gi tr nh.

4.2.Cn bng Histogram

Trong biu din Histogram, mt tng phn nh khng c phn b tt. Do

, mt s iu chnh c thc hin trn hnh nh c nh tng phn tt

hn. Trong qu trnh cn bng Histogram, cc gi tr mt c phn b hiu qu.

iu ny gip cc vng trn hnh nh vi tng phn thp c tng phn tt

hn hoc cao hn.

Cn bng Histogram c thc hin bng cch s dng xc sut. Trong qu

trnh cn bng Histogram, cc gi tr pixel ca nh c lit k v vi cc gi tr

xy ra lp i lp li ca n. Sau khi lit k, gi tr xc sut ca cc pixel ti bt k

im nht nh u ra nh c tnh ton s dng phng php phn b xc sut

tch ly. Phng php ny s dng cc gi tr im nh ca hnh nh ban u v


phn b n trn tt c cc hnh nh u ra mong mun. N m t xc sut m mt

bin ngu nhin gi tr thc X vi mt phn b xc sut nht nh s c tm thy

ti mt gi tr nh hn hoc bng vi x. Ly gi tr v tnh ton hm phn b tch

ly hoc cdf theo cng thc sau:

V d cc gi tr pixel ca hnh nh c cho bi:

Bng 1. Gi tr pixel ca nh

Bng 2. Histogram ca nh

Hm phn b tch ly c tnh bng cng thc trn v c th c th hin nh

trong bng 3.


Bng 3. Hm phn b tch ly (cdf)

Sau khi tnh ton cdf gi tr ca n c th c d dng tnh ton cc gi tr

im nh u ra theo cng thc cn bng Histogram chung nh sau:

Trong cdf(v) l gi tr ti thi im c th, cdfmin l gi tr cdf ti thiu, L l

kch thc pixel chun ha ca ton b hnh nh v MXN l s pixel ca nh gc.

Cc gi tr ca cdfmin = 1, MxN = 16, L = 256 (i vi hnh nh y ) v cdf(v)

cc gi tr hin th trn bng 3 nh 1, 2, 3, 6 ... 16. t cc gi tr trong cng thc

trn s dn n gi tr pixel mi.

Bng 4. Gi tr pixel ca nh u ra

Di y l s khc bit trong nhng nh c th thy c khi s dng cn bng

Histogram.


Hnh. Biu din Histogram ca mt nh

Hnh. Cn bng Histogram


Nh hnh trn, cn bng histogram to ra nh c mt tng phn tt hn i

vi nh c. Ngoi ra n cho thy mt c phn b u trn s histogram.

5 Khi phc nh bng bin i Wavelet

5.1. C s ton hc

5.1.1. Bin i wavelet lin tc

Bin i Wavelet lin tc (Continuous Wavelet Transform - CWT) ca mt

hm f ( t ) c bt u t mt hm Wavelet m (mother Wavelet) ( t ) . Hm

Wavelet m ( t ) c th l bt k mt hm s thc hoc phc lin tc no tho

mn cc tnh cht sau y: Tch phn suy rng trn ton b trc t ca hm ( t ) l

bng 0. Tc l:

(t)dt= 0 (2)

Tch phn nng lng ca hm trn ton b trc t l mt s hu hn, tc l:

( )

t2 dt (3)

iu kin (1.2) c ngha l hm ( t ) phi l mt hm bnh phng kh tch

ngha l hm ( t ) thuc khng gian L2 ( R ) cc hm bnh phng kh tch.

Sau khi hm Wavelet ( t ) c la chn, bin i Wavelet lin tc ca

mt hm bnh phng kh tch f ( t ) c tnh theo cng thc:

W(a,b)= ( )

atf 1

* ( abt

)dt (4)

Bin i ny l mt hm ca hai tham s thc a v b. Du * k hiu l lin

hip phc ca ( t ) . Nu chng ta nh ngha mt hm a ,b ( t ) theo biu thc:

a,b (t) = a

1

( abt

) (5)


Gi tr a1

l h s chun ho m bo rng tch phn nng lng ca hm

a ,b ( t ) s c lp vi a v b .

Vi mi gi tr ca a th a ,b ( t ) l mt bn sao ca a ,0 ( t ) c dch

i b n v trn trc thi gian. Do b c gi l tham s dch. t tham s dch b

= 0 ta thu c:

a,0 (t) = a

1

at

(6)

iu cho thy rng a l tham s t l.

5.1.2. Bin i Wavelet ri rc

Vic tnh ton cc h s Wavelet ti tt c cc t l l mt cng vic ht sc

phc tp. Nu tnh ton nh vy s to ra mt lng d liu khng l. gim

thiu cng vic tnh ton ngi ta ch chn ra mt tp nh cc gi tr t l v cc v

tr tin hnh tnh ton. Hn na nu vic tnh ton c tin hnh ti cc t l v

cc v tr trn c s lu tha c s 2 th kt qu thu c s hiu qu v chnh xc

hn rt nhiu. Qu trnh chn cc t l v cc v tr tnh ton nh trn to thnh

li nh t (dyadic). Mt phn tch nh trn hon ton c th thc hin c nh

bin i Wavelet ri rc (DWT). Do , vic tnh ton bin i DWT thc cht l

s ri rc ho bin i Wavelet lin tc (CWT); vic ri rc ho c thc hin vi

s la chn cc h s a v b nh sau:

a = 2m ; b= 2m n m,n (7)

Vic tnh ton h s ca bin i Wavelet c th d dng thc hin bng cc

bng lc s nhiu nhp a knh, mt l thuyt rt quen thuc trong x l tn hiu.

5.2.Tnh cht ca php bin i wavelet

5.2.1. Tnh cht sng

Hm wavelet phc (tng qut) 0 c nh x hon ton trong c hai

min: min khng gian v min t l (nghch o tn s) v ng thi phi tha mn


tnh cht sng, ngha l dao ng vi gi tr trung bnh ca hm wavelet bng khng

0

( )ydy= 0 (8)

Nh vy, wavelet l dng sng nh c khng gian tn ti hu hn v c gi

tr trung bnh bng khng. H qu t tnh cht sng ca hm wavelet dn n s c

lp ca php bin i wavelet i vi tt c cc hm c phn tch.

Lu rng khi s dng php bin i wavelet lin tc, phi chun ha phin

bn ca hm wavelet l 0 (xb ) trong mt vng khng gian gii hn c qui

nh bi kch thc ca s; bn ngoi vng gii hn hm wavelet trit tiu. Vy

php bin i wavelet lin tc cung cp nhng thng tin v s thay i cc b

vng ang kho st m chng ta khng cn quan tm n bin i ton cc ca hm

wavelet.

5.2.2. c trng v nng lng

Nng lng tng ca tn hiu f(x) c nh ngha bi biu thc sau:

(9)

Tn hiu c nng lng xc nh khi biu thc trn nhn gi tr xc nh.

Hm sng wavelet c c trng v nng lng c chun ha bng n v

cho mi t l s. Vy, tnh cht th hai ca hm wavelet l:

(10)

5.3. Mt s h bin i wavelet

5.3.1. Bin i Wavelet Haar

Bin i Wavelet Haar l bin i n gin nht trong cc php bin i


Wavelet. Hnh v di cho thy dng ca hm ( t ) vi bin i Haar. Do tnh

cht n gin ca bin i Haar m n c ng dng tng i nhiu trong nn

nh, khi p dng bin i ny nn nh th thut ton nn nh trn my tnh c

mt s im khc vi cng thc ton hc ca bin i Haar

Hnh 8: Hm Wavelet Harr

5.3.2. Bin i Wavelet Meyer

Yves Meyer l mt trong nhng nh khoa hc t nn mng cho php bin

i Wavelet. Php bin i Wavelet mang tn Meyer cng l mt php bin i

thng dng, bin i ny c kh nng phn tch tn hiu tt hn nhiu so vi bin

i Haar. Dng ca hm ( t ) vi bin i Meyer cho hnh v:

Hnh 9: Hm Wavelet Meyer

5.3.3. Bin i Wavelet Daubechies


Ging nh Meyer, Daubechies cng l mt nh khoa hc c cng lao to ln

trong vic nghin cu pht trin php bin i Wavelet. Bin i Daubechies l mt

trong nhng php bin i phc tp nht trong bin i Wavelet. H bin i ny

c ng dng ht sc rng ri, bin i Wavelet p dng trong JPEG2000 l mt

bin i trong h bin i Wavelet Daubechies. Di y l mt s hm ( t )

trong h bin i Wavelet Daubechies:

Hnh 10: Hm Wavelet Daubechies


Ph lc: code Matlab1.I = imread('board.tif');I = I(50+(1:256),2+(1:256),:);figure;imshow(I);title('Original Image');text(size(I,2),size(I,1)+15, ... 'Image courtesy of courtesy of Alexander V. Panasyuk, Ph.D.',

... 'FontSize',7,'HorizontalAlignment','right');text(size(I,2),size(I,1)+25, ... 'Harvard-Smithsonian Center for Astrophysics', ... 'FontSize',7,'HorizontalAlignment','right');PSF = fspecial('gaussian',5,5);Blurred = imfilter(I,PSF,'symmetric','conv');figure;imshow(Blurred);title('Blurred');V = .002;BlurredNoisy = imnoise(Blurred,'gaussian',0,V);figure;imshow(BlurredNoisy);title('Blurred & Noisy');luc1_cell = deconvlucy({BlurredNoisy},PSF,5);luc2_cell = deconvlucy(luc1_cell,PSF);luc2 = im2uint8(luc2_cell{2});figure;imshow(luc2);title('Restored Image, NUMIT = 15');DAMPAR = im2uint8(3*sqrt(V));luc3 = deconvlucy(BlurredNoisy,PSF,15,DAMPAR);figure;imshow(luc3);title('Restored Image with Damping, NUMIT = 15');

2.I = imread('eight.tif');imshow(I)J = imnoise(I,'salt & pepper',0.02);figure, imshow(J)I = im2double(imread('cameraman.tif'));imshow(I);


title('Original Image (courtesy of MIT)');noise_mean = 0;noise_var = 0.0001;blurred_noisy = imnoise(blurred, 'gaussian', ... noise_mean, noise_var);imshow(blurred_noisy)title('Simulate Blur and Noise')I = imread('cameraman.tif');class(I)LEN = 21;THETA = 11;PSF = fspecial('motion', LEN, THETA);blurred_quantized = imfilter(I, PSF, 'conv', 'circular');class(blurred_quantized)wnr4 = deconvwnr(blurred_quantized, PSF, 0);imshow(wnr4)title('Restoration of blurred, quantized image using NSR = 0');

I = im2double(imread('cameraman.tif'));imshow(I);title('Original Image (courtesy of MIT)');LEN = 21;THETA = 11;PSF = fspecial('motion', LEN, THETA);blurred = imfilter(I, PSF, 'conv', 'circular');imshow(blurred);title('Blurred Image');wnr1 = deconvwnr(blurred, PSF, 0);imshow(wnr1);title('Restored Image');I = imread('board.tif');I = I(50+(1:256),2+(1:256),:);figure;imshow(I);title('Original Image');


text(size(I,2),size(I,1)+15, ... 'Image courtesy of courtesy of Alexander V. Panasyuk, Ph.D.',

... 'FontSize',7,'HorizontalAlignment','right');text(size(I,2),size(I,1)+25, ... 'Harvard-Smithsonian Center for Astrophysics', ... 'FontSize',7,'HorizontalAlignment','right');PSF = fspecial('gaussian',5,5);Blurred = imfilter(I,PSF,'symmetric','conv');figure;imshow(Blurred);title('Blurred');V = .002;BlurredNoisy = imnoise(Blurred,'gaussian',0,V);figure;imshow(BlurredNoisy);title('Blurred & Noisy');luc1_cell = deconvlucy({BlurredNoisy},PSF,5);luc2_cell = deconvlucy(luc1_cell,PSF);luc2 = im2uint8(luc2_cell{2});figure;imshow(luc2);title('Restored Image, NUMIT = 15');DAMPAR = im2uint8(3*sqrt(V));luc3 = deconvlucy(BlurredNoisy,PSF,15,DAMPAR);figure;imshow(luc3);title('Restored Image with Damping, NUMIT = 15');RGB = imread('motion.png');I = rgb2gray(RGB);RGB = imread('motion.png');I = rgb2gray(RGB);J = imnoise(I,'gaussian',0,0.025);imshow(J)K = wiener2(J,[5 5]);figure, imshow(K)I = im2double(imread('cameraman.tif'));imshow(I);title('Original Image (courtesy of MIT)');LEN = 21;THETA = 11;


PSF = fspecial('motion', LEN, THETA);blurred = imfilter(I, PSF, 'conv', 'circular');imshow(blurred);title('Blurred Image');noise_mean = 0;noise_var = 0.0001;blurred_noisy = imnoise(blurred, 'gaussian', ... noise_mean, noise_var);imshow(blurred_noisy)title('Simulate Blur and Noise');wnr2 = deconvwnr(blurred_noisy, PSF, 0);imshow(wnr2)title('Restoration of Blurred, Noisy Image Using NSR = 0');signal_var = var(I(:));wnr3 = deconvwnr(blurred_noisy, PSF, noise_var / signal_var);imshow(wnr3)title('Restoration of Blurred, Noisy Image Using Estimated NSR');I = imread('tissue.png');I = I(125+(1:256),1:256,:);figure;imshow(I);title('Original Image');text(size(I,2),size(I,1)+15, ... 'Image courtesy of Alan Partin, Johns Hopkins University', ... 'FontSize',7,'HorizontalAlignment','right');PSF = fspecial('gaussian',11,5);Blurred = imfilter(I,PSF,'conv');figure;imshow(Blurred);title('Blurred');V = .02;BlurredNoisy = imnoise(Blurred,'gaussian',0,V);%adding gause noise%figure;imshow(BlurredNoisy);title('Blurred & Noisy');NP = V*numel(I); % noise power[reg1, LAGRA] = deconvreg(BlurredNoisy,PSF,NP);


figure,imshow(reg1),title('Restored with NP');reg2 = deconvreg(BlurredNoisy,PSF,NP*1.3);figure;imshow(reg2);title('Restored with larger NP');reg3 = deconvreg(BlurredNoisy,PSF,NP/1.3);figure;imshow(reg3);title('Restored with smaller NP');Edged = edgetaper(BlurredNoisy,PSF);reg4 = deconvreg(Edged,PSF,NP/1.3);figure;imshow(reg4);title('Edgetaper effect');reg5 = deconvreg(Edged,PSF,[],LAGRA);figure;imshow(reg5);title('Restored with LAGRA');reg7 = deconvreg(Edged,PSF,[],LAGRA/100);figure;imshow(reg7);title('Restored with small LAGRA');REGOP = [1 -2 1];reg8 = deconvreg(BlurredNoisy,PSF,[],LAGRA,REGOP);figure;imshow(reg8);title('Constrained by 1D Laplacian');

MC LC1 Gii thiu2 K thut v phng php3 Cc b lc4 Khi phc nh bng phng php cn bng Histogram5 Khi phc nh bng bin i Wavelet

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