Xử lý ảnh số - Nâng cao chất lượng ảnh part 1 pdf

Chu
.
o
.
ng 4
N
ˆ
ANG CAO CH
ˆ
A
´
TLU
.
O
.
.
NG A
˙’
NH
Nˆang cao chˆa
´
tlu
.
o
.
.
ng a
˙’
nh (image enhancement) l`a xu
.
˙’

l´y a
˙’
nh d¯ˆe
˙’
cho a
˙’
nh d¯ˆa
`
u ra th´ıch
ho
.
.
pho
.
n so v´o
.
ia
˙’
nh gˆo
´
c nhˇa
`
mmˆo
.
tsˆo
´
´u
.
ng du
.

ng d¯ˇa
.
cbiˆe
.
t. C´o hai c´ach tiˆe
´
pcˆa
.
nd¯ˆe
˙’
nˆang cao chˆa
´
tlu
.
o
.
.
ng a
˙’
nh l`a
(1) C´ac phu
.
o
.
ng ph´ap miˆe
`
n khˆong gian; v`a
(2) C´ac phu
.
o

.
ng ph´ap miˆe
`
ntˆa
`
nsˆo
´
.
Trong miˆe
`
n khˆong gian, nguyˆen tˇa
´
c chung l`a su
.
˙’
du
.
ng c´ac gi´a tri
.
x´am cu
˙’
a pixel
trong a
˙’
nh. Xu
.
˙’
l´y trong miˆe
`
ntˆa

`
nsˆo
´
du
.
.
a trˆen phu
.
o
.
ng ph´ap biˆe
´
nd¯ˆo
˙’
i Fourier cu
˙’
amˆo
.
t
a
˙’
nh. K˜y thuˆa
.
t nˆang cao chˆa
´
tlu
.
o
.
.

ng a
˙’
nh du
.
.
a trˆen co
.
so
.
˙’
kˆe
´
tho
.
.
p nhiˆe
`
uphu
.
o
.
ng ph´ap
cu
˙’
a hai miˆe
`
n khˆong gian v`a tˆa
`
nsˆo
´

.
4.1 Co
.
so
.
˙’
cu
˙’
anˆang cao chˆa
´
tlu
.
o
.
.
ng a
˙’
nh
C´ac phu
.
o
.
ng ph´ap nˆang cao chˆa
´
tlu
.
o
.
.
ng a

˙’
nh trong chu
.
o
.
ng n`ay du
.
.
a trˆen c´ac k˜y thuˆa
.
t
miˆe
`
n khˆong gian hoˇa
.
cmiˆe
`
ntˆa
`
nsˆo
´
.Mu
.
cd¯´ıch cu
˙’
a phˆa
`
n n`ay cung cˆa
´
pnh˜u

.
ng ´y tu
.
o
.
˙’
ng
co
.
ba
˙’
nv`amˆo
´
iliˆenhˆe
.
gi˜u
.
a hai c´ach tiˆe
´
pcˆa
.
n n`ay.
69
4.1.1 Phu
.
o
.
ng ph´ap miˆe
`
n khˆong gian

C´ac phu
.
o
.
ng ph´ap miˆe
`
n khˆong gian t´ac d¯ˆo
.
ng tru
.
.
ctiˆe
´
plˆen tˆa
.
p c´ac pixel trong a
˙’
nh. C´ac
h`am xu
.
˙’
l´y a
˙’
nh trong miˆe
`
n khˆong gian d¯u
.
o
.
.

cbiˆe
˙’
udiˆe
˜
nbo
.
˙’
i
g(x, y):=T [f(x, y)],
trong d¯´o f(x, y)l`aa
˙’
nh v`ao, g(x, y)l`aa
˙’
nh ra v`a T l`a to´an tu
.
˙’
t´ac d¯ˆo
.
ng lˆen h`am a
˙’
nh f.
To´an tu
.
˙’
T c´o thˆe
˙’
t´ac d¯ˆo
.
ng trˆen nhiˆe
`

ua
˙’
nh v`ao, chˇa
˙’
ng ha
.
nnhu
.
cˆo
.
ng c´ac gi´a tri
.
x´am
cu
˙’
a c´ac pixel trong tˆa
.
pa
˙’
nh v`ao d¯ˆe
˙’
gia
˙’
m nhiˆe
˜
u. Ta c˜ung c´o thˆe
˙’
t´ınh hiˆe
.
ucu

˙’
a hai h`am
a
˙’
nh f( x, y)v`ah(x, y)
g(x, y):=f( x, y) −h(x, y)
nhˆa
.
nd¯u
.
o
.
.
cbˇa
`
ng c´ach t´ınh hiˆe
.
ugi˜u
.
atˆa
´
tca
˙’
c´ac cˇa
.
p pixel tu
.
o
.
ng ´u

.
ng cu
˙’
a f v`a h. Tr`u
.
a
˙’
nh c´o mˆo
.
tsˆo
´
´u
.
ng du
.
ng quan tro
.
ng trong phˆan d¯oa
.
na
˙’
nh v`a nˆang cao chˆa
´
tlu
.
o
.
.
ng a
˙’

nh.
C´ach tiˆe
´
pcˆa
.
nch´ınh d¯u
.
o
.
.
cd`ung trong lˆan cˆa
.
n (x´ac d¯i
.
nh tru
.
´o
.
c) cu
˙’
a(x, y) l`a su
.
˙’
du
.
ng mˆo
.
tv`ung a
˙’
nh con h`ınh ch˜u

.
nhˆa
.
t tˆam d¯ˇa
.
tta
.
i(x, y). Tˆam cu
˙’
aa
˙’
nh con n`ay d¯u
.
o
.
.
c
di chuyˆe
˙’
n theo c´ac pixel (x, y) (kho
.
˙’
id¯ˆa
`
ut`u
.
g´oc trˆen bˆen tr´ai) v`a ´ap du
.
ng to´an tu
.

˙’
T
lˆen d¯iˆe
˙’
m(x, y).
Da
.
ng d¯o
.
n gia
˙’
n nhˆa
´
tcu
˙’
a T khi lˆan cˆa
.
n c´o k´ıch thu
.
´o
.
c1× 1. Trong tru
.
`o
.
ng ho
.
.
p
n`ay, g ch ı

˙’
phu
.
thuˆo
.
c v`ao gi´a tri
.
cu
˙’
a f ta
.
i(x, y)v`aT tro
.
˙’
th`anh ph´ep biˆe
´
nd¯ˆo
˙’
im´u
.
c
x´am
s = T (r),
trong d¯´o k´y hiˆe
.
u r, s l`a c´ac gi´a tri
.
x´am cu
˙’
a f v`a g ta

.
ivi
.
tr´ı (x, y). V`ı nˆang cao chˆa
´
t
lu
.
o
.
.
ng a
˙’
nh ta
.
imˆo
.
td¯iˆe
˙’
m n`ao d¯´o trong a
˙’
nh chı
˙’
phu
.
thuˆo
.
cv`aom´u
.
c x´am ta

.
id¯iˆe
˙’
m d¯´o,
nˆen c´ach tiˆe
´
pcˆa
.
n n`ay d¯u
.
o
.
.
cgo
.
il`axu
.
˙’
l´y d¯iˆe
˙’
m.
V´ı d u
.
4.1.1 (i) T (r) trong H`ınh 4.1(a) c´o t´ac du
.
ng ta
.
omˆo
.
ta

˙’
nh c´o d¯ˆo
.
tu
.
o
.
ng pha
˙’
n
cao ho
.
na
˙’
nh gˆo
´
cbˇa
`
ng c´ach l`am d¯en c´ac m´u
.
c <m,v`a l`am s´ang lˆen c´ac m´u
.
c >mtrong
a
˙’
nh gˆo
´
c. K˜y thuˆa
.
t n`ay d¯u

.
o
.
.
cgo
.
il`ad˜an d¯ˆo
.
tu
.
o
.
ng pha
˙’
n.
(ii) T (r) trong H`ınh 4.1(b) c´o t´ac du
.
ng ta
.
omˆo
.
ta
˙’
nh nhi
.
phˆan.
C´ac lˆan cˆa
.
nl´o
.

nho
.
nc˜ung thu
.
`o
.
ng d¯u
.
o
.
.
csu
.
˙’
du
.
ng nˆang cao chˆa
´
tlu
.
o
.
.
ng a
˙’
nh. Gi´a
tri
.
cu
˙’

a g ta
.
i(x, y)d¯u
.
o
.
.
c x´ac d¯i
.
nh thˆong qua c´ac gi´a tri
.
cu
˙’
a f trong lˆan cˆa
.
ncu
˙’
a(x, y).
Mˆo
.
t trong nh ˜u
.
ng nguyˆen tˇa
´
c d¯´o du
.
.
a trˆen co
.
so

.
˙’
cu
˙’
a mˇa
.
tna
.
(mask) (c`on go
.
il`acu
.
˙’
a
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s = T (r)
L −1
r
L − 1

m
(0, 0)
(b)

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s = T (r)
L − 1
r
L − 1
m
(0, 0)
(b)

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.
H`ınh 4.1: D
-
ˆo
`
thi
.
c´ac h`am biˆe
´
nd¯ˆo

˙’
im´u
.
c x´am d¯ˆe
˙’
nˆang cao d¯ˆo
.
tu
.
o
.
ng pha
˙’
n.
sˆo
˙’
(window) hoˇa
.
c lo
.
c (filter)). Vˆe
`
co
.
ba
˙’
n, mˆo
.
tmˇa
.

tna
.
l`a mˆo
.
tma
˙’
ng hai chiˆe
`
uc´ok´ıch
thu
.
´o
.
c nho
˙’
(chˇa
˙’
ng ha
.
n, k´ıch thu
.
´o
.
c3× 3), m`a c´ac hˆe
.
sˆo
´
d¯ u
.
o

.
.
ccho
.
nd¯ˆe
˙’
ph´at hiˆe
.
n c´ac
t´ınh chˆa
´
t d¯˜a cho cu
˙’
aa
˙’
nh. Chˇa
˙’
ng ha
.
n, gia
˙’
su
.
˙’
a
˙’
nh f c´o cu
.
`o
.

ng d¯ˆo
.
s´ang hˇa
`
ng ch´u
.
amˆo
.
t
d¯ i ˆe
˙’
m cˆo lˆa
.
p (cu
.
`o
.
ng d¯ˆo
.
s´ang ta
.
i d¯´o kh´ac nˆe
`
n). D
-
iˆe
˙’
m n`ay c´o thˆe
˙’
bi

.
x´oa bˇa
`
ng c´ach su
.
˙’
du
.
ng mˇa
.
tna
.
W :=



−1 −1 −1
−18−1
−1 −1 −1



.
Thuˆa
.
t to´an nhu
.
sau: Tˆam cu
˙’
amˇa

.
tna
.
(g´an nh˜an 8) d¯u
.
o
.
.
c di chuyˆe
˙’
n xung quanh a
˙’
nh.
Ta
.
imˆo
˜
ivi
.
tr´ı (x, y) trong a
˙’
nh, ta nhˆan mˆo
˜
i gi´a tri
.
x´am cu
˙’
a pixel d¯u
.
o

.
.
cch´u
.
a trong
v`ung mˇa
.
tna
.
v´o
.
i c´ac hˆe
.
sˆo
´
cu
˙’
amˇa
.
tna
.
;t´u
.
c l`a pixel tˆam cu
˙’
amˇa
.
tna
.
d¯ u

.
o
.
.
c nhˆan v´o
.
i8,
trong khi 8 pixel lˆan cˆa
.
nd¯u
.
o
.
.
c nhˆan v´o
.
i −1. D
-
´a p ´u
.
ng cu
˙’
amˇa
.
tna
.
ta
.
i(x, y)bˇa
`

ng tˆo
˙’
ng
c´ac t´ıch n`ay. Nˆe
´
utˆa
´
tca
˙’
c´ac pixel trong v`ung c´o c`ung gi´a tri
.
, d¯´ap ´u
.
ng bˇa
`
ng khˆong.
Mˇa
.
t kh´ac, nˆe
´
u tˆam cu
˙’
amˇa
.
tna
.
d¯ ˇa
.
tta
.

id¯iˆe
˙’
m cˆo lˆa
.
p, d¯´ap ´u
.
ng s˜e kh´ac khˆong. Nˆe
´
ud¯iˆe
˙’
m
cˆo lˆa
.
pd¯ˇa
.
tgˆa
`
n (nhu
.
ng kh´ac) tˆam, d¯´ap ´u
.
ng c˜ung kh´ac khˆong, nhu
.
ng gi´a tri
.
tuyˆe
.
td¯ˆo
´
i

cu
˙’
a d¯´ap ´u
.
ng s˜e yˆe
´
uho
.
n. C´ac d¯´ap ´u
.
ng yˆe
´
uho
.
n n`ay s˜e bi
.
khu
.
˙’
bˇa
`
ng c´ach so s´anh v´o
.
i
ngu
.
˜o
.
ng n`ao d¯´o.
Nhu

.
trong H`ınh 4.2, nˆe
´
u w
1
,w
2
, ,w
9
l`a c´ac hˆe
.
sˆo
´
cu
˙’
amˇa
.
tna
.
v`a kha
˙’
o s´at 8−lˆan
cˆa
.
ncu
˙’
a(x, y), ta c´o thˆe
˙’
tˆo
˙’

ng qu´at ho´a thuˆa
.
t to´an trˆen nhu
.
viˆe
.
c thu
.
.
chiˆe
.
n ph´ep to´an
71
.
.
.
z
1
z
2
z
3
··· z
4
z
5
z
6
···
z

7
z
8
z
9
.
.
.
(a)
w
1
w
2
w
3
w
4
w
5
w
6
w
7
w
8
w
9
(b)
H`ınh 4.2:
sau:

T [f(x, y)] := w
1
f( x −1,y− 1) + w
2
f( x −1,y)+w
3
f( x −1,y+ 1)+
w
4
f( x, y − 1) + w
5
f( x, y)+w
6
f( x, y + 1)+
w
7
f( x +1,y−1) + w
8
f( x +1,y)+w
9
f( x +1,y+1)
(4.1)
trˆen lˆan cˆa
.
n3×3cu
˙’
a(x, y). C´ac mˇa
.
tna
.

k´ıch thu
.
´o
.
cl´o
.
nho
.
nd¯u
.
o
.
.
c ´ap du
.
ng tu
.
o
.
ng tu
.
.
.
Ch´u´yrˇa
`
ng, trong biˆe
˙’
uth´u
.
c (4.1) viˆe

.
c thay d¯ˆo
˙’
i c´ac hˆe
.
sˆo
´
cu
˙’
amˇa
.
tna
.
s˜e thay d¯ˆo
˙’
i
ch´u
.
c nˇang cu
˙’
amˇa
.
tna
.
. C´ac phu
.
o
.
ng ph´ap nˆang cao chˆa
´

tlu
.
o
.
.
ng a
˙’
nh du
.
.
a v`ao mˇa
.
tna
.
thu
.
`o
.
ng go
.
il`axu
.
˙’
l´y mˇa
.
tna
.
hoˇa
.
c lo

.
c. Trong c´ac phˆa
`
n sau ta s˜e x´et c´ac mˇa
.
tna
.
nhˇa
`
m
phu
.
chˆo
`
ia
˙’
nh, phˆan d¯oa
.
na
˙’
nh
4.1.2 Phu
.
o
.
ng ph´ap miˆe
`
ntˆa
`
nsˆo

´
Co
.
so
.
˙’
cu
˙’
a c´ac phu
.
o
.
ng ph´ap xu
.
˙’
l´y a
˙’
nh trong miˆe
`
ntˆa
`
nsˆo
´
du
.
.
a trˆen d¯i
.
nh l´y t´ıch chˆa
.

p.
X´et to´an tu
.
˙’
bˆa
´
tbiˆe
´
nvi
.
tr´ı, tuyˆe
´
n t´ınh Φtu
.
o
.
ng ´u
.
ng v´o
.
i h`am phˆan t´an d¯iˆe
˙’
m h
Φ
(x, y)
t´ac d¯ˆo
.
ng trˆen a
˙’
nh f. Khi d¯´o a

˙’
nh d¯ˆa
`
ura
g(x, y) := [Φ(f)](x, y)=h
Φ
(x, y) ∗ f(x, y).
Do d¯´o, theo d¯i
.
nh l´y t´ıch chˆa
.
p:
G(u, v)=H( u, v)F (u, v),
trong d¯´o G, H, F l`a c´ac biˆe
´
nd¯ˆo
˙’
i Fourier cu
˙’
a g,h
Φ
,f tu
.
o
.
ng ´u
.
ng.
Vˆa
´

nd¯ˆe
`
l`a v´o
.
i h`am a
˙’
nh f d¯˜a cho, mu
.
c tiˆeu l`a cho
.
n H d¯ ˆe
˙’
d¯ u
.
o
.
.
ca
˙’
nh mong muˆo
´
n
g(x, y)=F
−1
[H(u, v)F (u, v)]. (4.2)
72

.
.









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f( x, y) g(x, y)h(x, y)
(a)
.


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F (u, v) G(u, v)H(u, v)
(b)
H`ınh 4.3: Thao t´ac cu
˙’
ahˆe
.

thˆo
´
ng tuyˆe
´
n t´ınh. Trong (a) t´ın hiˆe
.
u ra l`a t´ıch chˆa
.
pcu
˙’
a
h(x, y)v´o
.
it´ınhiˆe
.
u v`ao. Trong (b) t´ınh hiˆe
.
u ra l`a t´ıch cu
˙’
a H(u, v)v´o
.
it´ınhiˆe
.
u v`ao.
V´ıdu
.
c´ac d¯u
.
`o
.

ng biˆen trong a
˙’
nh f(x, y)d¯u
.
o
.
.
c l`am nˆo
˙’
ibˇa
`
ng c´ach d`ung h`am H(u, v)
l`am nˆo
˙’
i c´ac th`anh phˆa
`
n c´o tˆa
`
nsˆo
´
cao cu
˙’
a F(u, v).
Trong H`ınh 4.3(a), h`am h(x, y)d¯ˇa
.
c tru
.
ng cho hˆe
.
thˆo

´
ng m`a ch´u
.
c nˇang cu
˙’
a n´o l`a
ta
.
o ra t´ın hiˆe
.
u g(x, y)t`u
.
t´ın hiˆe
.
u v`ao f(x, y). Hˆe
.
thˆo
´
ng thu
.
.
chiˆe
.
n t´ıch chˆa
.
pcu
˙’
a h(x, y)
v´o
.

ia
˙’
nh v`ao f(x, y) v`a xuˆa
´
trakˆe
´
t qua
˙’
. Theo d¯i
.
nh l´y t´ıch chˆa
.
p, c´o thˆe
˙’
thu
.
.
chiˆe
.
ntiˆe
´
n
tr`ınh n`ay theo c´ach kh´ac: nhˆan F (u, v)v´o
.
i H(u, v)d¯ˆe
˙’
c´o G(u, v) v`a sau d¯´o biˆe
´
nd¯ˆo
˙’

i
Fourier ngu
.
o
.
.
c.
Gia
˙’
su
.
˙’
rˇa
`
ng h`am h(x, y)chu
.
abiˆe
´
tv`ach´ung ta ´ap du
.
ng mˆo
.
t h`am xung d¯o
.
nvi
.
(t ´u
.
cl`amˆo
.

td¯iˆe
˙’
m s´ang) lˆen hˆe
.
thˆo
´
ng. Biˆe
´
nd¯ˆo
˙’
i Fourier cu
˙’
a xung d¯o
.
nvi
.
bˇa
`
ng 1 nˆen
G(u, v)=H(u, v). Do d¯´o biˆe
´
nd¯ˆo
˙’
i ngu
.
o
.
.
ccu
˙’

a G(u, v)l`ah(x, y). D
-
ˆay l`a mˆo
.
tkˆe
´
t qua
˙’
d¯˜a biˆe
´
t trong l´y thuyˆe
´
thˆe
.
thˆo
´
ng tuyˆe
´
n t´ınh: Mˆo
.
thˆe
.
thˆo
´
ng tuyˆe
´
n t´ınh bˆa
´
tbiˆe
´

nvi
.
tr´ı
ho`an to`an d¯u
.
o
.
.
c x´ac d¯i
.
nh bo
.
˙’
i d¯´ap ´u
.
ng xung cu
˙’
ahˆe
.
thˆo
´
ng d¯ˆo
´
iv´o
.
imˆo
.
t xung. T´u
.
c l`a,

biˆe
´
nd¯ˆo
˙’
i Fourier cu
˙’
a h`am xung d¯o
.
nvi
.
´ap du
.
ng d¯ˆo
´
iv´o
.
ihˆe
.
thˆo
´
ng tuyˆe
´
n t´ınh bˆa
´
tbiˆe
´
n
vi
.
tr´ı ch´ınh l`a h`am H( u, v). Ta c˜ung c´o thˆe

˙’
t´ac d¯ˆo
.
ng xung tru
.
.
ctiˆe
´
pd¯ˆe
˙’
c´o t´ın hiˆe
.
u
ra h(x, y). V`ı l´y do n`ay trong l´y thuyˆe
´
thˆe
.
thˆo
´
ng tuyˆe
´
n t´ınh, biˆe
´
nd¯ˆo
˙’
i ngu
.
o
.
.

c h(x, y)
cu
˙’
a h`am chuyˆe
˙’
nd¯ˆo
˙’
ihˆe
.
thˆo
´
ng go
.
il`ad¯´ap ´u
.
ng xung. Trong quang ho
.
c, biˆe
´
nd¯ˆo
˙’
i ngu
.
o
.
.
c
h(x, y)cu
˙’
a h`am biˆe

´
nd¯ˆo
˙’
i quang ho
.
cgo
.
il`ah`am phˆan t´an d¯iˆe
˙’
m. Viˆe
.
cd¯ˇa
.
t tˆen du
.
.
a trˆen
a
˙’
nh hu
.
o
.
˙’
ng quang ho
.
co
.
˙’
d¯´o xung tu

.
o
.
ng ´u
.
ng v´o
.
id¯iˆe
˙’
m s´ang v`a hˆe
.
thˆo
´
ng quang ho
.
c
pha
˙’
n´u
.
ng l`am nho`e (phˆan t´an) d¯iˆe
˙’
m; m´u
.
cd¯ˆo
.
nho`e x´ac d¯i
.
nh bo
.

˙’
i c´ac th`anh phˆa
`
n quang
ho
.
c. Do vˆa
.
y h`am biˆe
´
nd¯ˆo
˙’
i quang ho
.
c v`a h`am phˆan t´an d¯iˆe
˙’
m l`a c´ac biˆe
´
nd¯ˆo
˙’
i Fourier
cu
˙’
a nhau. Mˆo
´
i quan hˆe
.
n`ay s˜e d¯u
.
o

.
.
c kha
˙’
o s´at trong Phˆa
`
n 4.3.
Ch´u´yrˇa
`
ng, biˆe
˙’
uth´u
.
c (4.2) ch´ınh l`a xu
.
˙’
l´y miˆe
`
n khˆong gian tu
.
o
.
ng tu
.
.
viˆe
.
csu
.
˙’

du
.
ng c´ac mˇa
.
tna
.
x´et trong phˆa
`
n tru
.
´o
.
c. V`ı l´y do n`ay, c´ac mˇa
.
tna
.
khˆong gian thu
.
`o
.
ng
73