Enhancement of feature extraction for low-quality fingerprint images suing stochastic resonance.pptx
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Enhancement of feature extraction for low-quality fingerprint images using stochastic resonance
Choonwoo Ryu,Seong G,Kong,Hakil Kim
Reporter ： Chih-Hui Chang
O UTLINE
Introduction Fingerprint feature extraction Stochastic resonance Enhancing feature extraction with stochastic resonance Experiment results Conclusion
2
I NTRODUCTION
Histogram equalization is a well-known contrast enhancement technique due to its strong performance on all types of image.
Generally,histogram equalization can be categorized into two main processes:global histogram equalization(GHE) and local histogram equalization(LHE).
3
I NTRODUCTION
In GHE ,the histogram of the whole input image is used to compute a histogram transformation function.
As result ,the dynamic range of the image histogram is flattened and stretched ,and the overall contrast is improved.
The major drawbacks of GHE are that it cannot adapt the local information of the image and preserve the brightness of the original image.
4
I NTRODUCTION
In contrast ,LHE uses a sliding window method ,in which local histograms are computed from the windowed neighborhood to produce a local intensities remapping for each pixel.
LHE is capable of producing great contrast results but is sometimes thought to over-enhance images.
It also requires more computation than other methods because a local histogram must be built and processed for every image pixel.
5
I NTRODUCTION
Therefore ,we propose a new method Bi-Histogram Equalization with Neighborhood Metrics(BHENM) that not only preserves brightness but also improves the local contrast of the original image.
6
RELATED WORK
Global Histogram Equalization
h
(
i
)
n i
, for
i
0 , 1 ,...,
L
1 .
p i
n i
i L
1 0
n i
n i and L
1
p i N i
0 1 (1) (2)
P i
L i
1 0
p i
(3)
7
RELATED WORK
GHE maps the original image into the resultant image using the intensity transformation function:
g
(
x
,
y
)
T
(
f
(
x
,
y
)) (4) which maps the original image into the entire dynamic 0
I L
1
I
{ 0 ,
L
1 }
T
(
I
)
I
0 (
I L
1
I i
)
P i
(5)
8
RELATED WORK
Bi-histogram Equalization
Let
I m I m
{ 0 ,
L
1 }.
Based on ,the image is separated into two sub-
m
images and
i f j
as
f
f i
f j
(6) where
f i
{
f
(
x
,
y
) |
f
(
x
,
y
)
I m
,
f
(
x
,
y
)
f
} (7) and
f j
{
f
(
x
,
y
) |
f
(
x
,
y
)
I m
,
f
(
x
,
y
)
f
} (8)
9
RELATED WORK
Next,define the respective probability density functions
f i f j p i
(
I k
)
n i k n i
(9) and
p j
(
I k
)
n k j n j
(10)
10
RELATED WORK
The respective CDFs are then defined as
P i
(
I k
)
k I m
0
p i
(
I k
) and
P j
(
I k
)
k I L I
1
m
1
p j
(
I k
) (11) (12)
11
RELATED WORK
Let us similarly define the following transformation functions exploiting the CDFs
T i
(
I k
)
I
0 (
I m
I
0 )
P i
(
I k
) (13) and
T j
(
I k
)
I m
1 (
I L
1
I m
1 )
P j
(
I k
) (14)
12
RELATED WORK
Then the resultant image of the histogram can be expressed as
g
(
x
,
y
)
T
(
f
(
x
,
y
)) in which (15)
T
(
I
)
I
0
I
m
1 (
I m
(
I L
1
I
0 )
I P i m
1 (
I k
) ), if
P j
(
I k I k
I m
),
else
(16)
13
RELATED WORK
Histogram Equalization with Neighborhood Metric
(
r
)
n r i
, for
r
0 , 1 , ,
R
1
p r
n i r
r R
1 0
n i r
n i r and R
1
pr N
r 0 1 (17) (18)
P r P r
R r
0 1
p r
(19)
14
RELATED WORK
GHE maps the original image into the resultant image using the intensity transformation function:
g
(
x
,
y
)
T F
(
f
(
x
,
y
)) (20) which maps the original image into the entire sub-bin’s [
S
,
S
]
S
{ 0 ,
R
1 }
T F
T S
(
L
/
R
), (21) here
T S
(
S
)
S
0 (
S R
1
S r
)
P r
(22)
15
PROPOSED METHOD
Neighborhood Metrics
In previous work, we proposed two new neighborhood metrics: the contrast difference and distinction metric.
The distinction metric is used in this study because it proved to be more succesful than other metrics in improving image local contrast and histogram flatness in our previous work.
16
PROPOSED METHOD
The distinction metric not only preserves the main ideas of the voting and contrast difference metrics but can divide one bin of a histogram into more sub-bins than those methods. When using the voting metric, one bin of a histogram is divided into nine sub-bins.
The contrast difference metric can divide one bin of a histogram into 27 sub-bins.
17
PROPOSED METHOD
Figure 1.Dividing
one sub bin into sub bins of a histogram with voti ng metric.
18
PROPOSED METHOD
Figure 2.Dividing
one sub bin into further sub bins with the contrast difference metric(thr eshold 10)
19
PROPOSED METHOD
The proposed distinction metric can divide one bin into 2040 sub-bins.
Separating the bins into many sub-bins results in a very flat histogram for the resultant image, constituting a more ideal form of GHE.
This metric is defined by distinction between the intensity of the current pixel and its neighborhood pixels whose intensities are less than that of the current pixel.
20
PROPOSED METHOD
Distinction Metric
Let be the function that extends an image function surrounded by a “background” of zero intensity: (
x
,
y
)
g
(
x
,
y
), (
x
,
y
) [ 0 ,
N
1 ] [ 0 ,
M
1 ] 0 ,
otherwise
(23) The distinction metric is expressed by the following formula:
d m
(
x
,
y
) (
x
,'
y
' )
R m t
( (
x
,
x
,
y
)
y
,
x
' ,
y
' ) (24)
21
PROPOSED METHOD
which requires the following distinction function:
t
(
x
,
y
,
x
' ,
x
' ) (
x
,
y
) (
x
' ,
y
' ), (
x
,
y
) (
x
' ,
y
' ) 0 ,
otherwise
(25) Hence,we can easily compute the minimum and maximun values.
22
PROPOSED METHOD
Bi-histogram Equalization with Neighborhood Metrics
z
z
{ 0 ,
B
1 }.
f U
and as
V f
f U
f V
, (26) where
f U
{
f
(
x
,
y
) |
f
(
x
,
y
) ,
f
(
x
,
y
)
f
} (27) and
f V
{
f
(
x
,
y
) |
f
(
x
,
y
) ,
f
(
x
,
y
)
f
} (28)
23
PROPOSED METHOD
Next,define the respective probability density functions of sub-images and as
U f V p U
(
z
)
n u z n u
(29) and
p V
(
z
)
n v z n v
.
(30)
24
PROPOSED METHOD
n u
u z z
0
n u z n v
B z
1 1
n v z
, and
n n u n v
repective CDFs are defined as
P U
(
z
)
z
z
0
p U
(
z
) and
P V
(
z
)
z
1
B
z
1
p V
(
z
) (31) (32)
25
PROPOSED METHOD
Let us similarly define the following transformation functions exploiting the CDFs:
T U
(
z
) 0 (
z
z
)
P U
(
z
) (33) and
T V
(
z
) (
z
1 ) (
B
1
z
)
P V
(
z
) (34) Then the resultant image of the histogram can be expressed as
g
(
x
,
y
)
T F
(
f
(
x
,
y
))
26
PROPOSED METHOD
which maps the original image into the entire sub-bin’s range,z,using CDF:
T F
T S
(
L
/
z
) (35) where
T S
(
z
)
T U T V
(
z
), if
f
(
z
), else if (
x
, (
P V y
) (
z
)
z
P
& (
P U V
(
z
(
z
1 )) )
P U
(
z
2 /(
B
1 )) 2 /
z
z
) (36)
27
EXPERIMENTAL RESULT
Three quality measurements were used: flatness ( ) ,contrast-per-pixel (C),and average absolute mean brightness error (AAMBE) To measure the flatness of a histogram
h,
we compute the variance of the bin sizes: 0
D
1 (|
h i
|
h
) 2
D
(37)
28
EXPERIMENTAL RESULT
Contrast-per-pixel measures the average intensity difference between a pixel and its adjacent pixels.
C
N i
0
M j
0 (
m
,
n
)
R
( 3
i
,
j
) | (
i
,
j
) (
m
,
n
) |)
M
*
N
* 8 Average absolute mean brightness error:
AAM
BE 1 S
n S
1 ~
X
Y
~ (38) (39)
29
EXPERIMENTAL RESULT
TABLE I HISTOGRAM FLATNESS VALUES OBTAINED FROM THREE SAMPLE IMAGES(x10 5 )
30
EXPERIMENTAL RESULT
31
Figure 3.Results
of Image I : a)Original sample image I with its histogram, b)GHE ed image with its histogram, c)BBHE ed image with its histogram, d)DSIHE ed image with its histogram, e)MMBEBHE ed image with its histogram and f) Proposed BHENM ed image with its histogram.
EXPERIMENTAL RESULT
TABLE II CONTRAST PER PIXEL VALUES OBTAINED FROM THREE SAMPLE IMAGES
32
EXPERIMENTAL RESULT
33
Figure 4.Results
of Image II : a)Original sample image II with its histogram, b)GHE ed image with its histogram, c)BBHE ed image with its histogram, d)DSIHE ed image with its histogram, e)MMBEBHE ed image with its histogram and f) Proposed BHENM ed image with its histogram.
EXPERIMENTAL RESULT
34
Figure 5.Results
of Image III : a)Original sample image III with its histogram, b)GHE ed image with its histogram, c)BBHE ed image with its histogram, d)DSIHE ed image with its histogram, e)MMBEBHE ed image with its histogram and f) Proposed BHENM ed image with its histogram.
EXPERIMENTAL RESULT
TABLE III AAMBE OBTAINED FROM THREE SAMPLE
35
EXPERIMENTAL RESULT
TABLE IV AVERAGE EXECUTION TIME OBTAINED FROM THREE SAMPLE IMAGES
36
CONCLUSION
We proposed a new method of histogram equalization extension , in which image contrast and histogram flatness are simultaneously improved while image brightness is preserved.
37
PERSONAL REMARK
Because the distinction metric can divide one bin into 2040 sub-bins ,so it’s computation may higher than LHE.
38