A Non-Parametric Blur Measure Based on Edge Analysis for Image Processing Applications

pancakesnightmuteAI and Robotics

Nov 5, 2013 (4 years and 7 days ago)

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A Non-Parametric Blur Measure Based on Edge
Analysis for Image Processing Applications

Yun-Chun
g C
hung
, Jung-
Ming Wang,
R
obert R. Bai
l
ey, Sei-Wang Chen
G
r
adu
a
te In
stitu
te of C
o
m
p
u
t
er Scien
ce an
d
Inform
atio
n
Eng
i
n
e
ering

N
a
tio
n
a
l Taiwan
N
o
rm
al
U
n
iv
ersity
88
, Ti
ng
-Ch
o
w
Rd,
Sect
i
o
n
4,

Taip
ei, Taiw
an, Repub
lic o
f
C
h
in
a
10
6

Tel:8
86
-2
-29
3
2
-
24
11#
108
. Fax
:
88
6-2
-
2
932-
237
8

sche
n@csi
e
.
n
t
n
u
.
e
d
u
.
t
w




Shyang-Li
h C
hang
Depa
rt
m
e
nt

of El
ect
roni
c En
g
i
neeri
n
g
St. Jo
hn
's & St
. Mary's Institu
te o
f

Tech
nol
ogy

499,
Sec.
4, Ta
m
King Roa
d

Tam
s
ui,
Taip
ei, Taiw
an, Repub
lic o
f
C
h
in
a
ali@
m
a
il.sj
s
m
i
t
.ed
u
.tw
Abstrac
t
— A
non-par
a
me
tr
ic image blur
me
asur
e
is
pr
e
s
e
n
te
d.
The
me
asur
e

is based on
edge analy
s
is and
is suitable
for
var
i
ous
image
pr
oc
e
ssing app
lications. Th
e proposed
mea
sure
for an
y

edge
point is obtaine
d by

c
o
mbining the
standar
d

deviation of the edge gradient
ma
gnitude
pr
ofile
and the
valu
e
of
the edge gradient magnitude
using a
w
e
ighte
d
ave
r
a
ge
.
The

standar
d
de
viation de
sc
ribe
s the

w
i
dth of the e
d
ge, and its
edge

gr
adie
nt magnitude
is also include
d to make the blur me
as
ur
e
more reliable.
Moreov
e
r, the
value of
the
weight is
related
to

image

c
o
ntr
a
st and c
a
n be
c
a
lc
ulate
d dire
c
t
ly
fr
om the image
.

Expe
r
i
me
nts on natur
a
l sc
ene
s
indic
ate that the
pr
opose
d

te
c
hnique
c
a
n
e
ffe
c
t
ive
l
y de
scr
i
be
the blur
rine
ss of image
s
in
image
pr
oc
e
ssing applic
ations.

Ke
y
w
ords—blur m
e
a
sure
; e
d
ge

analy
s
is; im
age c
o
ntrast
calculat
ion

I.

II.

I
NTRODUCT
I
ON


A m
easure of
t
h
e sha
r
p
n
ess
or
bl
u
rri
ne
ss
of e
dge
s i
n

an

im
age
can be useful for
a

num
b
er
of
a
ppl
i
cat
i
ons i
n
i
m
ag
e

processi
ng, s
u
ch as
chec
king
the
foc
u
s
of a cam
era lens,
h
e
lp
ing to
i
d
entify sh
ad
ow
s (w
ho
se edg
e
s are
o
f
ten
less sharp

th
an obj
ect edg
e
s), t
h
e sep
a
ratio
n

of
v
a
riatio
ns i
n
illu
m
i
n
a
tio
n

from
the reflectance of the
obj
ects in
an
im
age (known as

in
tr
in
sic im
ag
e
ex
tr
actio
n)
, and
in
-fo
cu
s ar
eas (
o
r
fo
r
e
gr
ound
)
vs.
o
u
t
-
of
-f
oc
u
s
(
o
r
bac
k
gr
ou
nd
) a
r
eas i
n
a
n

im
age.
In
t
h
i
s
pa
pe
r
we

pr
o
p
ose
a m
e
t
hod
t
o

det
e
rm
i
n
e t
h
e

bl
u
rri
ne
ss
o
f
e
dge
s i
n
a
c
o
l
o
r i
m
age.
T
h
e
m
e
t
hod
nee
d
s
n
o

user
-s
up
pl
i
e
d
param
e
t
e
rs l
i
k
e sha
p
es
an
d
p
o
si
t
i
ons
o
f

o
b
j
ect
s

o
r
inform
atio
n
abou
t ligh
t
sou
r
ces.

Nor is inform
at
io
n
ab
ou
t

cam
e
ra ge
om
etry
nee
d
e
d
.
Marzilian
o

et
al.
[5
]

ha
ve
propose
d
a no-refe
r
e
n
ce
p
e
rcep
tu
al
b
l
ur m
e
tric (w
e
p
r
efer th
e term

mea
s
ure
rat
h
er
tha
n

m
e
tric
), wh
ich th
ey
d
e
fi
n
e
i
n
th
e
sp
atial
d
o
main
as th
e spread
of
t
h
e e
d
ges.
(
W
e
bri
e
fl
y

di
s
c
uss t
h
ei
r m
e
t
hod
i
n

sect
i
o
n
I
I
.
)
Room
s
et al.
[6
] h
a
v
e
pro
posed
a techn
i
que fo
r m
easu
r
ing
bl
u
r
usi
ng
wa
vel
e
t
s
. They
cal
culate the sharpness
of the
sh
arp
e
st ed
g
e
s in
th
e im
a
g
e b
y
co
m
p
u
tin
g
th
e Lipsch
itz
exponent
for e
dge
s as
a
sm
oothn
ess
m
easure.
The
Lipsc
h
itz
ex
pon
en
t (
a
lso
k
now
n
as
th
e
Hölder expone
nt) i
s
a

sm
oot
hness m
easure
fo
r a c
e
rt
ai
n
po
in
t.
It is actu
a
lly
th
e
resu
lt of ho
w man
y

ti
m
e
s
th
e
im
age can be di
ffe
rentiabl
e at a

poi
nt
.
T
h
i
s
m
easure
i
s
s
u
i
t
a
bl
e
fo
r
f
o
cu
s e
s
t
i
m
a
ti
on
wi
t
h
out

sp
atial do
m
a
in
pro
c
essing
t
o
avo
i
d no
ise effects.
Ho
w
e
v
e
r,
the estim
a
ted blur m
easure
for a
whole i
m
age m
a
y not
be
sui
t
a
bl
e f
o
r
ot
h
e
r a
ppl
i
cat
i
ons
.

Ou
r
p
r
o
p
ose
d

bl
u
r
m
easure
f
o
r
an
e
d
ge

poi
nt
i
s

o
b
t
a
i
n
e
d

by

com
b
i
n
i
ng t
h
e st
anda
rd
d
e
vi
at
i
on
of t
h
e ed
ge
gra
d
i
e
nt

m
a
gni
t
u
de
p
r
ofi
l
e
a
nd t
h
e
val
u
e
o
f
t
h
e ed
ge
gra
d
i
e
nt

m
a
gni
t
u
de usi
ng
a wei
g
ht
ed avera
g
e.

T
h
e st
anda
rd de
vi
at
i
o
n

descri
bes t
h
e

wi
dt
h
o
f
t
h
e
ed
ge, a
n
d t
h
e e
d
ge m
a
gni
t
ude

hel
p
s

m
a
ke
t
h
e
bl
ur
m
easure
m
o
re
rel
i
a
bl
e.
T
h
e
wei
g
ht

i
s

cal
cu
l
a
t
e
d
fr
om
t
h
e cont
rast
o
f
t
h
e i
n
put
im
age and needs no m
a
nual
in
pu
ts.
Ex
peri
m
e
nt
al
resul
t
s

co
ve
ri
ng
i
n
trin
sic i
m
ag
e extraction,
im
age foc
u
si
n
g
, a
n
d i
n
-
f
oc
us
vs.

out
-
o
f
-
f
oc
us a
r
eas
o
f
a
n

im
age are
di
sc
usse
d i
n
t
h
i
s

p
a
per
.

M
o
re
a
ppl
i
cat
i
o
n
s

of

t
h
e
pr
o
pose
d

bl
u
r

m
easure co
ul
d al
so
be investigated, s
u
c
h
as
sha
d
o
w
det
ect
i
o
n
an
d
rem
oval
,
a
n
d
be
nc
hm
arki
ng

of

t
h
e
q
u
a
lity of im
ag
e co
m
p
ression

alg
o
rith
m
s
.

Ou
r
p
r
o
p
o
se
d a
p
pr
oach

i
s
desc
ri
be
d
i
n
sect
i
o
n
2
.


Exp
e
rim
e
n
t
al
resu
lts are presen
ted i
n

sectio
n
3
,
and
concl
udi
ng
re
m
a
rks a
r
e i
n
se
ct
i
on
4.

T
HE PROP
OSED
NON
-
PARA
ME
T
R
IC BLUR
ME
AS
URE

Fig.
1 prese
n
ts
a flowcha
r
t for t
h
e propose
d bl
ur m
easure.
Gi
ve
n an
i
n
pu
t
im
age
I
(
x
,
y
), where
x
and

y
are the
row
and

colum
n
coordinates,
respecti
v
el
y, the
gra
d
ient at any
pixel

lo
catio
n
p
= (
x
,
y
) is
ca
lculated
by a
pplying t
h
e t
w
o-
di
m
e
nsi
onal
di
rect
i
onal

deri
v
a
t
i
v
e

(,
)
(,
)
(,
)
x
y
I x
y
G
x
I x
y
G
I x
y
y

 
 
 

 
 

 

 
 
 

 



T
h
is wor
k
is suppo
r
t
ed in par
t
b
y
the
National Science
Council,

T
a
iwan, Republic of China un
de
r
contr
act NSC
-
92-
221
3-
E
-
003-
004.

Proceedings of the 2004 IEEE
Conference on Cybernetics and Intelligent Systems
Singapore, 1-3 December, 2004��
0-7803-8643-4/04/$20.00 © 2004 IEEE
356

(a)

(b
)
Figur
e 2.
Gr
adient
m
a
gn
itude at an
edge point
p
= (
x
,
y
)

in the direction


of the gr
adient.
(
a
)
shar
p edge and (
b
)
blur
r
e
d edge
Input im
age
I
x
-gradient map,
G
x
x
-directional
derivative filter
y
-gradient map,
G
y
y
-
d
irectional
derivative f
i
lter
Calculate gradient
orientation of
pix
e
ls
Gradient orientation
ma
p,

(
x
,
y
)
Fit normal
distribu
tion
(
) on
pix
e
ls

Standard deviation
of pix
e
ls
Fusion
Blur metric,
(
x
,
y
)
C
a
lculate
im
age
con
t
ras
t
Weight
co
effic
i
en
t,
Calculate edge
magn
itude
Edge magnitu
de
ma
p,
em
(x,
y
)

Figur
e 1.
Flowchart of calculation of
the pr
oposed no
n-
p
a
r
a
m
e
tr
ic blur

m
e
asure
The
gra
d
i
e
nt

m
a
gni
t
ude
(a
n
d
t
w
o
fast
,
dec
r
easi
n
g acc
ura
c
y

app
r
oxi
m
a
t
i
ons) at

p

ca
n be o
b
t
a
i
n
ed

f
r
om

G
x
and
G
y
by


2 2
1
2
(,
)
ma
x
(
,
)
x y
x
y x
y
x
I x
y
G
G
G
G
G G
G G
 

 
 


 
y




Consi
d
er
a
n
e
dge

poi
nt
at

p
= (
x
,
y
)
de
fined as
a
local

m
a
xim
u
m
of t
h
e ed
ge
gra
d
i
e
nt
m
a
gni
t
ude,
and
wi
t
h
t
h
e


-ax
i
s
in
th
e
d
i
rection
of th
e grad
ien
t
. Th
e
o
r
ig
i
n
o
f
t
h
e

-a
xis is at
t
h
e
poi
nt

of
l
o
cal
m
a
xim
u
m
.
See
Fi
g
.
2
.

T
h
e e
d
ge
wi
dt
h

w
is
defi
ned as
the

distance
bet
w
e
e
n t
h
e
nea
r
est l
o
cal m
i
nim
a
(

=

m
l
and

=

m
r
) o
n
eac
h si
de
of t
h
e m
a
xim
u
m
,
i
.
e.,
w
= |
m
l

!

m
r
|.

For co
m
p
ariso
n
, Marziliano

et al.
[5]
calculated a
nd
avera
g
e
d
all the wi
dth
values
fr
om
t
h
e out
p
u
t
of a
ve
r
t
i
cal
ed
g
e
filter t
o

d
e
fi
n
e
th
ei
r
b
l
u
r
m
e
tric fo
r
th
e who
l
e im
a
g
e.
Thei
r m
e
t
hod i
s
q
u
i
c
k,
b
u
t
,
i
n
som
e
cases, can be
si
g
n
i
f
i
c
a
n
t
l
y

affected
by
noi
se, as
the
exam
ple
in Fi
g.
3 s
h
ows.
The c
o
rrect
edge
wi
dt
h i
s

w
, wh
ile th
e calcu
lated w
i
d
t
h
is
w

, th
e
di
ffe
re
nce
bei
n
g ca
use
d

by
n
o
i
s
e aro
u
n
d
t
h
e
edge
pi
xel
.


Figur
e 3.
I
llustr
a
tion of bad es
tim
a
tion of edge width
w as
w
’.

In

ou
r
p
r
o
p
ose
d
m
e
t
hod
,
l
o
ca
l
m
a
xim
u
m
poi
nt
s,

p

=
(
x

,
y

),
of t
h
e
gra
d
i
e
nt

m
a
gni
t
ude
o
f
e
dge
s are
use
d
t
o

den
o
t
e
t
h
e e
d
ge
lo
catio
n
s
.
The grad
ien
t

o
r
ien
t
atio
n (d
irectio
n
o
f
th
e

-a
x
i
s)
indicates the
direction of th
e norm
al to the edge at
p


w
ith
respect t
o
the
x
-a
xi
s an
d
i
s
defi
ned
as

(,
)
a
t
a
n
2
(
,
)
y
x
x
y
G
G




,
w
h
er
e
w
e

ha
v
e
u
s
ed

th
e
a
t
a
n
2
fu
nct
i
o
n f
o
un
d i
n
m
o
st
pr
og
ram
m
i
ng l
a
ng
ua
ges si
nce
t
h
e

resu
lt is in th
e in
terv
al


to +

.

W
e
treat
the e
d
ge
gradient
m
a
gni
t
u
de

(acr
oss
t
h
e
ed
ge
)
bet
w
ee
n


=
m
l
and


=
m
r
as a

d
i
screte p
r
ob
ab
ility
d
i
strib
u
t
io
n
,
w
ith

th
e mean

at
po
in
t

p

,

corres
ponding to

=

0
.
L
e
t

m
r
b
e

o
n
th
e
po
sitiv
e

-
ax
is
,
a
n
d
m
l
be o
n

ne
gat
i
v
e

-
a
x
is, i.e
.,
m
r
> 0 a
n
d
m
l
< 0.
Refe
r to
Fig
.

4
.

Fo
r th
is
d
i
stribu
tio
n,
w
e
calcu
l
ate th
e (sp
a
tial) v
a
rian
ce as
357

2 2
1
( )
(
)
.
r
l
m
m
r l
p I
m m

 







 



(W
h
ile th
is m
a
y a scaled
v
e
rsi
on
of the
va
riance, it does not

m
a
t
t
e
r, si
nce i
n
t
h
e ne
xt
eq
u
a
t
i
on,
we di
vi
d
e
by
a no
rm
al
izi
ng
term
.) The bl
ur m
easure

(
p

) f
o
r a
n
e
d
ge p
o
int
p


is ob
tain
ed
by
com
put
i
n
g
t
h
e wei
ght
e
d
a
v
era
g
e
of t
h
e s
t
anda
rd
de
vi
at
i
o
n


a
n
d
t
h
e e
d
ge
m
a
gni
t
ude
( )
I
p




ma
x
ma
x
( )
( )
( )
(
1
)
( )
I p
p
p
I p



 






 






whe
r
e

ma
x
and

(
)
I
p


ma
x
are norm
alization term
s
den
o
t
i
n
g t
h
e

m
a
xim
u
m
val
u
es f
o
r al
l
st
a
n
d
a
rd
de
vi
at
i
ons

and

for all edg
e

grad
ien
t
m
a
g
n
itu
des.
The weight


i
s
rel
a
t
e
d t
o
i
m
age c
ont
rast
an
d i
s

gi
ve
n
by


(,
)
(,
)
1
lo
g
(
,
)
i
MSR
x y
i
i
R
x y
B
C I




x
y



whe
r
e
B
i
s
t
h
e
num
ber
o
f

pi
xe
l
s
i
n
i
m
age
I
(
x
,
y
) and

C
is t
h
e
num
ber
of
c
o
l
o
r
ban
d
s.

Si
nce
we
are
p
r
oces
si
ng
RGB i
m
ages,

we
use

C
=
3
,

but
i
t
c
oul
d
be

di
ffe
re
nt

fo
r
an
ot
he
r c
o
l
o
r
s
p
a
ce;
for e
x
am
ple, for t
h
e CMYK
color s
p
ace,
C

= 4.
I
i
(
x
,
y
) is
the
i
th
color ba
nd of im
age
I
(
x
,
y
), a
nd
R
MSRi
is th
e
i
th
col
o
r
com
pone
nt
of the

out
put

of the
M
u
ltiscale Retinex
(M
SR)
alg
o
rith
m
[3
], w
h
ich
is th
e co
m
b
in
ed
weig
h
t
ed

su
m
o
f

N

Single
-
scale R
e
tinex
(SSR) output
s (disc
u
ss
ed below) [4]. The

M
S
R o
u
t
p
ut
i
n
di
cat
es t
h
e
am
ou
nt

of
e
nha
nc
em
ent
nee
d
ed

fo
r
edge
co
nt
rast
.

The
i
th
com
ponent of t
h
e MSR
is gi
ven by
Figur
e 5.
T
h
e differ
e
nce of

(
c
ontin
uous line)
,


(
dott
e
d line)
and
per
cent err
o
r
(
d
ash
e
d line)
of Sobel oper
a
tor
s
.


(a)

(b
)
Figur
e 4.
I
llustr
a
tion of the blur

m
easur
e for
an edge point
p’
(
x
,
y
),
(a
) th
e
edge point location, (b) f
itting
em
(

)

by
norm
a
l distr
i
bution

(

).
 
1
1
(,
)
l
o
g
(
(,
)
)
l
o
g
(
(,
)
*
(,
)
)
i
N
MSR
i
n
i
n
R
x
y
I x
y
F
x
y
I x
y
N

 


whe
r
e t
h
e sy
m
bol
* i
ndi
ca
t
e
s con
vol
ut
i
o
n.
F
n
(
x
,
y
) is
a
G
a
ussian sm
o
o
t
h
i
n
g
filter and is calcu
lated as
.
Param
e
ter
c
2 2
2
(
)
/
(,
)
n
x y
c
n
F x
y
K
e
 

n
is th
e scale con
s
tan
t

fo
r the

n
th
scale, and
K
is a no
rm
aliz
in
g

co
nstan
t
su
ch
th
at
F
n
(
x
,
y
)
s
u
m
s
t
o
1.

(Val
ues
of

c
n
are
gi
ve
n i
n

t
h
e ne
xt
sect
i
o
n.
)

II
I.

E
XPERI
M
EN
TA
L
R
ES
U
L
T
S

Sob
e
l op
erators are co
mm
o
n
l
y u
s
ed
as th
e filter to
d
e
tect
horizontal and vertical edges
in
d
i
g
ital i
m
a
g
es.
Du
e t
o
th
e
discrete c
o
ordinate syste
m

us
ed
, th
e grad
ien
t

d
i
rectio
ns


calcu
lated
from
So
b
e
l filters

requ
ire a subp
ix
el lev
e
l
correction to
decrease

the
e
r
ror in t
h
e cal
culated a
n
gles
[1].

To c
o
rrect

, it is first redu
ced
to
th
e o
c
tan
t
[0,

/4).
W
h
en



is in
th
e ran
g
e

tan
-1
(1/
3
) t
o


/4
, t
h
e co
rrection
is
[1
]


 
 
1
2
1 1
2
(,
)
i
f
0
t
a
n
1
3
(,
)
7
t
an
6
t
an
1
ta
n
i
f

ta
n
1
3
4
.
9t
a
n
2
2
t
a
n
1
x y
x y
 

 
 
 

 

 



 

 
 
 

 

 



Th
en
t
h
e angle is resto
r
ed to its
p
r
op
er
o
c
tan
t
.
The

diffe
re
nce bet
w
een


a
nd


and the
pe
rc
ent differe
n
ce
are
sh
ow
n i
n
Fi
g.
5.

The
m
a
xim
u
m
error
wi
t
h
o
u
t
c
o
r
r
ect
i
o
n i
s

abo
u
t
4.
3%.
358
Jobson
et al.

[3
] and
Star
ck

et al.
[7]
rec
o
m
m
e
nded t
h
at

t
h
e
num
ber o
f
S
S
R
scal
es of t
h
e
M
S
R be t
h
ree
,
an
d so
we
us
ed
N

=
3
.

Si
nce
t
h
i
s

val
u
e ga
ve go
o
d
res
u
l
t
s
, we di
d
not

b
o
t
her

expe
ri
m
e
nt
i
ng
wi
t
h
ot
her va
l
u
es.
In
a
d
di
t
i
on,

t
h
e Ga
uss
i
an
scale pa
ram
e
te
rs
c
n
, (
n
=
1,

2
,

3)
i
n
[
3
]
are

su
ggest
e
d
t
o
t
a
ke
on

t
h
e val
u
e
s
1
5
, 8
0
,
a
n
d 25
0.

Fi
g.
6 s
h
ow
s
an e
x
am
pl
e i
m
age o
f
t
h
e
p
r
o
p
o
se
d
bl
ur

measu
r
e.
Ap
p
l
yin
g
v
e
rtical
an
d
ho
rizo
n
t
al deriv
a
tiv
e filters
to
t
h
e i
n
p
u
t
i
m
ag
e Fi
g.
6(a
)
p
r
o
duce
s
t
h
e ed
ge

m
a
gni
t
ude i
m
ag
e

Fi
g.
6
(
b),

whe
r
e
bl
ue
i
n
di
cat
es t
h
e

vert
i
cal
ed
ge
m
a
gni
t
u
d
e

an
d
g
r
een
,
th
e horizon
tal edg
e
m
a
g
n
itud
e
.
Fro
m
(5), weig
ht



i
s
0.
5
7
7
2
.


The
bl
ur
m
easure


(
x
,
y
)
fo
r an

edg
e

po
in
t
p

is
obt
ai
ne
d
by
av
eragi
ng t
h
e st
a
nda
r
d
de
vi
at
i
o
n

a
n
d t
h
e e
dge

mag
n
itu
d
e

(
)
I
p



from
(3). The
blur m
easure is
shown i
n

Fig
.
6
(
c),
w
h
ere sh
arp
e
r edg
e
s co
rresp
o
nd
to
h
i
g
h
er in
ten
s
ities

in
th
e im
ag
e.
Th
e co
m
p
u
t
atio
n of

(
x
,
y
) t
o
ok
less th
an

o
n
e
seco
nd
o
n
a
Pe
nt
i
u
m
based
P
C
.



(a)

(b
)

(c)



(d
)
(e)


(f
)
(g
)
Figur
e 6.
A blur

m
easur
e exa
m
ple i
m
age.
(
a
)
input im
ag
e,
(
b
) edge
m
a
gnitude im
age,
blue is ver
tical
e
dge,
gr
een is
hor
izontal edge,
(c)
blur

m
e
asur
e of edges; shar
per
edge has hi
gher intensity in t
h
e i
m
age,
(d)
the
i
m
p
r
oved ref
l
ectan
ce i
m
age,
(e
) the o
r
iginal ref
l
ectance

i
m
age,
(f
) the
i
m
p
r
oved illu
m
i
na
tion i
m
age, and
(g)
the original illu
m
i
nation i
m
age.


(a)

(b
)


(c)

(d
)


(e)

(f
)
Figur
e 7.
Another

exam
p
l
e of blur

m
easur
e.

(
a
) in-
f
ocus im
age, (
b
)

edge
m
a
gnitude im
age; blue is ver
tical edge,
gr
een is horizontal edge,

(
c
)
blur

m
e
asur
e of edges; shar
pe
r
ed
ges have higher
values,
(
d
)
out-
of-
f
oc
us im
age,
(e) edge
m
a
gnitude
i
m
a
g
e of
(d),
and (f
) an exa
m
pl
e
m
o
re o
u
t
-o
f
-
f
o
cu
s th
an
(d
).
Th
ere are m
a
n
y
po
ten
tial ap
p
licatio
ns of th
e
p
r
op
osed
measure.

One
is for the
ext
r
ac
tio
n of i
n
trin
sic im
ag
es (i.e.,
reflectan
ce an
d illu
m
i
n
a
tio
n
imag
es) fro
m
a sin
g
le im
ag
e. Th
e
blur m
easure
provides im
portan
t inform
ation about the
s
cene
illu
m
i
n
a
tio
n

because e
d
ges
of sha
d
ows trend to be
bl
urre
d
com
p
ared to object e
d
ges.
W
i
t
h
t
h
e
p
r
o
p
o
se
d bl
ur m
easure
,

th
e resu
lts
o
f

o
u
r
prev
i
o
u
s
st
u
d
y
of t
h
e ex
tractio
n

o
f
in
tri
n
sic

i
m
ag
es [2
] can
b
e
im
p
r
o
v
e
d
.

Fig
.

6(d) is th
e resu
ltin
g
im
proved re
fl
ectance im
age, c
o
m
p
arin
g w
ith

t
h
e origin
al

reflectance
image, Fig.
6(e
)

[2
], th
e
d
e
tails of t
h
e
recov
e
red
reflectance image is obvi
ously
b
e
tter an
d th
is d
e
m
o
n
s
trates
th
at th
e
p
r
op
osed b
l
u
r
m
easu
r
e
is effective, e.g., th
e
u
tilit
y

pole i
n
the le
ft u
ppe
r c
o
r
n
er
is better
recove
red i
n
(
d
) tha
n

(e).

Fig
.

6(f) is t
h
e i
m
p
r
ov
ed
illumin
a
tio
n
im
ag
e, and th
e
origin
al

illu
m
i
n
a
tio
n
imag
e is show
n in
Fi
g
.

6(g)
[2].
Anothe
r exam
ple t
h
at is
applicable t
o
ca
mera foc
u
sing is

sh
ow
n i
n
Fi
g.
7.

An
i
n
-
f
o
cus
im
age i
s
s
h
o
w
n i
n
Fi
g.
7(a
)
,

and

359
i
t
s
edge m
a
gni
t
ude i
m
age i
n
Fi
g. 7
(
b
)
. F
r
om
(5
),


is 0
.
651
4.
The
bl
u
r
m
easure
i
m
age i
s
sho
w
n i
n
Fi
g.
7(c
)
.

An
o
u
t
-
of
-
fo
cu
s is sho
w
n in Fig.
7
(
d), an
d its ed
g
e
m
a
g
n
itud
e
im
ag
e in
Fig.
7(e). A si
m
p
le way of ca
lculating a m
easure
of
foc
u
s
F
is

(,
)
(,
)
(,
)
.
| (
,
)
|
x y
x y
L
x y
F
I
x y

 
 
 

 



 



[2]

Y.
C.

C
L
i
s
a
n
o
rm
al
izi
n
g
co
nst
a
nt
,
whe
r
e
f
o
r
a

25
6 l
e
vel

gra
d
i
e
n
t

im
age |


I
(
x
,
y
) |
,

L
=
25
5 a
n
d, si
nce 0



(
x
,
y
)

1, we h
a
ve
m
a
de t
h
e m
easure
o
f

foc
u
s
0


F


1.
If th
e im
ag
e is no
t
correctly
fo
cu
sed on th
e targ
et, th
e b
l
ur
measure
can provide use
f
ul
i
n
fo
rm
ation to
evaluate the i
m
age

q
u
a
lity. Fo
r the i
m
ag
es shown
in Fig.
7
(
a) an
d (c)
w
ith
co
rrect
foc
u
s,
F
is 0.56
4, Fig.7 (d
)
an
d

(
e
) ar
e
o
u
t
o
f

f
o
cu
s, and

F
is
0.
45
9.

A
m
o
re bl
ur
red
ve
rsi
o
n
of
t
h
e
i
m
age i
s
sh
o
w
n
i
n
Fi
g.
7

(f
) f
o
r
whic
h
F
is 0.434
.
Fi
g.
8
prese
n
t
s
anot
her e
x
am
pl
e, wi
t
h
t
h
e i
n
p
u
t
i
m
age i
n

Fi
g.
8
(
a)
a
n
d t
h
e e
d
ge
m
a
gni
t
ude
i
m
age i
n

Fi
g.
8
(
b).

F
r
o
m


(5
),



i
s

0.
62
05
.
T
h
e
bl
ur

m
easure
o
f
t
h
e
ed
ges
i
s

sh
o
w
n i
n

Fi
g.
8(c
)
. T
h
i
s
exam
pl
e dem
onst
r
at
es t
h
at
fore
gr
o
u
n
d

(
i
n-
foc
u
s
)
a
n
d
ba
ckg
r
ou
n
d
(
o
ut
-o
f-
foc
u
s
)
ca
n
be
di
st
i
n
gui
s
h
ed

usi
n
g t
h
e
bl
u
r
m
easure.
I
n
t
h
is ex
am
p
l
e, th
e
b
i
rd
s in

th
e
foreground
(near the
cam
era)
h
a
v
e
sh
arp edg
e
s, wh
ile th
e
back
g
r
o
u
nd
fl
owe
r
s a
n
d
pl
ant
s

(fart
h
er from

the cam
era) are

bl
u
rre
d.


(a)

(b
)

(c)
Figur
e 8.
Another

blur

m
e
tric sa
m
p
le im
age.
(
a
)
the inp
u
t im
age, (
b
)
the
edge
m
a
gnitude im
age,
bl
ue: ver
tical
edge,
gr
een:
hor
izontal edge,
(
c
) the
blur

m
e
tric of edges,
shar
per
edge
has
higher intensity in
the i
m
age
.

M
o
re
ap
pl
i
cat
i
o
n
s

of
t
h
e

pr
o
p
o
s
ed

bl
ur
m
e
asure
c
o
ul
d
be

i
nvest
i
g
at
e
d
, s
u
ch a
s
s
h
ad
o
w
det
ect
i
o
n a
nd
rem
o
val
,

and

b
e
n
c
h
m
ark
i
ng

o
f
t
h
e
q
u
a
lity of im
ag
e co
m
p
ressio
n
algo
rithm
s
,

etc.

IV
.

C
ONCLUS
I
ON

A technique
for a
non-para
m
et
ri
c bl
ur m
easure
ba
sed
on

edge
anal
y
s
i
s

was
pre
s
ent
e
d.
T
h
e
pr
o
pose
d
bl
u
r
m
easure

(
x
,
y
) f
o
r a
n
y
edg
e
poi
nt

p

=
(
x

,
y

) is
obtained by a wei
g
hted
avera
g
e
of the standard
de
viation of t
h
e
edge m
a
gnitude

pr
ofi
l
e
ar
o
u
n
d

p


a
n
d t
h
e
val
u
e of t
h
e ed
ge
g
r
adi
e
nt
m
a
gni
t
ude

usi
n
g a
wei
g
h
t
ed ave
r
a
g
e.

The st
a
nda
r
d

devi
at
i
o
n
pl
ay
s an

im
port
a
nt

rol
e

i
n
ef
fect
i
v
el
y
d
e
scri
bi
n
g
t
h
e e
d
ge
wi
dt
h a
r
ou
nd

p

, and its ed
ge m
a
g
n
itu
d
e
is also in
cl
ud
ed to m
a
k
e
th
e
b
l
ur
measure m
o
re
reliable. M
o
reove
r, t
h
e
value
of t
h
e
weight,

whi
c
h i
s

base
d
on
i
m
age cont
rast
i
n
fo
rm
at
i
o
n, i
s
com
p
ut
ed

directly from
the im
age.
Th
e propo
sed b
l
ur w
a
s
also tried
w
ith
so
m
e

app
licatio
n
s
,
in
clu
d
i
n
g
th
e ex
traction

o
f
in
t
r
in
sic im
ages,
ca
m
e
ra focus,
and

foregro
u
nd
/b
ack
g
ro
und
classificatio
n
.
In ad
d
ition
,
mo
re
appl
i
cat
i
o
n
s

of t
h
e
pr
op
ose
d
bl
ur m
easure
co
ul
d
be

i
nvest
i
g
at
e
d
, s
u
ch a
s
s
h
ad
o
w
det
ect
i
o
n a
nd
rem
o
val
and

b
e
n
c
h
m
ark
i
ng th
e qu
ality o
f
i
m
ag
e co
m
p
ressio
n
algo
rithm
s
,

etc.

R
EFER
ENCES

[1]

D.
H. Ballar
d

and C.
M.
B
r
own,

Computer V
i
sion
,
Pr
entice Hall,
1982.

h
u
n
g
,
J.
M. W
a
ng,
R.
R
.
Bailey
,

S.W
.
Chen,
S.
L
.
Chang,
and S.

Cherng, “
P
hysics-based Extraction
of
Intrinsic I
m
age
s
f
r
o
m
a Single

I
m
age
,

17th International C
onf
erence on Pattern Recognition
,
Cam
b
r
i
dge,
United
Kingdo
m
,
Vol.
4,
pp.
693-
69
6,
Aug 2004.

[3]

D.J. Jobson, Z. Rah
m
an, and G.A.
Woodell, “
A

m
u
ltiscale retinex for
br
idging the
gap
between color
im
ages and the h
u
m
a
n obser
vation
of

scenes,”
IE
EE
Tra
n
sactions on I
m
ag
e P
r
ocessing
, Vol.6 , Issue:7, Jul
y

1997,
pp.
96
5-
976.

[4]

D.
J.
Jobson,
Z.
Rah
m
an,
and
G.
A.

W
oodell,
“Pr
oper
t
ies and per
f
orm
a
n
c
e
of a center
/
sur
r
ound r
e
tinex,


IE
E
E

Transactio
ns on I
m
age P
r
ocessing
,
Vol.
6,
I
ssue:3,

Mar
c
h 1997,
pp.
451-
462.

[5]

P.
Mar
z
iliano,
F.

Dufaux,
S.
W
i
nkler
,

and T
.

E
b
r
a
him
i
, “A no-
r
e
fer
e
n
ce
per
ceptual blur

m
e
tr
ic,


2002 I
n
ternational Co
nference on I
m
age

Processing
,
Vol.
3,
24-
28,
June 2002,
pp.
I
I
I
-
57 -

I
I
I-
60.
[6]

F.
Roo
m
s,
A.
Pizur
i
ca,
and
W
.
Philips,
“E
stim
ating im
age blur
in the

wavelet do
m
a
in,”

Proceedings of the Fifth Asian Conference on
Computer V
i
sion
(
ACCV
2002)
,
pp.
210-
215.

[7]

J.
L
.

Star
ck, F. Mu
r
t
agh,
E.
J.
Cande
s
,
and D.L
.
Donoho,
“Gr
a
y and color

i
m
age
contrast
enhance
m
ent b
y
the
curvelet
t
r
ansf
or
m
,


IE
EE

Transactio
ns on I
m
age P
r
ocessing
,
Vol.
12,
I
ssue: 6,
J
une 200
3,
pp.
706

– 717.


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