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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
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MC LC
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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
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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,
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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:
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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
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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
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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
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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.
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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
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CNG NGH MNG RING O11
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
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CNG NGH MNG RING O12
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.
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CNG NGH MNG RING O13
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.
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CNG NGH MNG RING O14
Hnh. Biu din Histogram ca mt nh
Hnh. Cn bng Histogram
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CNG NGH MNG RING O15
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)
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CNG NGH MNG RING O16
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
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CNG NGH MNG RING O17
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
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CNG NGH MNG RING O18
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
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CNG NGH MNG RING O19
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
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CNG NGH MNG RING O20
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);
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CNG NGH MNG RING O21
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');
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CNG NGH MNG RING O22
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;
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CNG NGH MNG RING O23
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);
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CNG NGH MNG RING O24
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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