chapter 5 bilateral filtering fusion...
TRANSCRIPT
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CHAPTER 5
BILATERAL FILTERING FUSION METHOD
5.1 INTRODUCTION
Image enhancement plays fundamentally an important role in nearly all of
the vision and image processing systems. It aims at producing images with
improved brightness or contrast. An important preprocessing step in image fusion
is denoising an image corrupted by various noises. This chapter presents an
efficient way to the fusion of multisensor noisy images with the aid of bilateral
filter and CVT mechanisms.
To obtain strong edges, bilateral filter can smooth images while preserving
edges. Due to the simplicity of its formulation, dependency for only two
parameters, utilization in non-iterative fashion and synergistic speed, it is a
popular smoothing filter among different smooth filters such as anisotropic and
isotropic. Because of its nature of describing structures and preserving edges
without losing more details, it is more flexible in real time applications. It deviates
from the traditional filters by means of defining the nearness of two pixels by
considering both geometric and photometric distance.
5.2 DESIGNING BILATERAL FILTER
Bilateral filtering has proven to be a powerful tool for the purpose of
adaptive denoising. Unlike conventional filters, it defines the closeness of two
pixels not only based on geometric distance but also based on photometric (gray
level) distance.
A domain is nothing but a possible set of values that is arranged in a
specific order to represent the image details. The image transformation can be
performed in two ways either on pixel values directly or on pixel locations. If the
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operation is fixed directly on the pixels then it is considered as range domain. In
other way, in the spatial domain, the operation is fixed on pixels location. An
example of spatial domain is Gaussian filter in which the kernel is constructed by
its spatial details and the spatial distance is calculated in finding the distance
between two pixel locations.
Consider an image I represented as a two dimensional array of values, rows
and columns are represented the whole image. Suppose if the values are used by
the coordinate system, each x and y coordinates present a pixel value represented
image information and is denoted by yxi , . To calculate the distance between two
pixel locations, we choose Euclidean distance for 2D coordinate system as
2
21
2
21 yyxxd
Where 11, yx and 22 , yx indicates two locations and d is an integer value
given the distance value between the two locations. The popular traditional
Gaussian filtering mechanism derives the kernel by using this technique.
Statistically, the sample distribution having bell shaped, is presented by a formula
2
2
2
22
1,
yx
eyxf
This is acted as a kernel and is used to filter a signal by an operation called
convolution. If the distance value can properly be utilized, then some amazing
result can be obtained in the filtered images. The average values of the distance
would overcome the problem of over smoothing or blurring by means of reducing
weight of a desired pixel in the domain.
Weight can be calculated as
Ni
ieeweight
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Here, the sum of distance would be treated as a weight. Now the Gaussian
weight is calculated to replace the center pixel during the convolution by Gaussian
filter. It is achieved that each nearby pixel value of center pixel is multiplied with
the distance. An image is filtered by Gaussian is given by
i
N
i
i eeeweight1
Where N is a set containing nearby pixels, e is the center pixel and ei is the
nearby pixels. The result of the function is used to replace the center pixel and this
would continue for all the pixels. The second thing would have to be considered
here is setting parameter which describes the size of neighborhood denoted by .
i
N
i
i eeeSeh )()(1
Gaussian filtering is a process of replacing a center pixel value by the
average intensity of the neighborhood with the help of adjacent pixel distance over
decreasing weight. The weight is not determined by pixel value and by the spatial
distance between adjacent pixels. The outcome of this process results blurring
edges because the cross discontinuities are also considered to perform average.
5.3 BILATERAL FILTER
To preserve edges in a filtered image, a similar mechanism of Gaussian has
been generated with range domain. The weighted value is computed in spatial
domain for Gaussian filter. A new idea derived for smoothing an image is the
combination of range and spatial domain and is used to preserve edges while
convolving an image. This idea is originated by V. Aurich [AUR93], S. M. Smith
[SMI80], and L. S. Davis [DAV78] and is named as bilateral filter. In that, totally
three values are encountered to compute the average weight includes spatial
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distance between two locations, range distance between two pixel values and the
nearby pixel value.
The procedure of smoothing is one of the important steps in image
preprocessing. Gaussian filtering is the most demotic technique to denoise an
image. The concept behind the Gaussian filtering is that intensity values change
slowly over distances. When regarding edges in the image, this idea does not
operate well. To defeat this issue, bilateral filter was evolved [TOM98] by Tomasi
and Manduchi in 1998.
Bilateral filtering denotes as a union of domain and range filtering, non
lineal, nonrecurring and local technique. It can conserve edges whereas smooth
out images, to express a non linear uniting of close pixel values [TOM98]. In this,
the pixel cost of a location yxp , is superseded by average of analogous and close
pixel values. It protects edges in a well fashion with the assistance of range filters
though smoothing an image. Resulting from its edge preserving properties, it is
broadly exploited in many applications [AUR93]. Though the behavior of bilateral
filter is identical as Gaussian filter, the weighted average is estimated by both
Euclidean length and range variance to attain the closed values which is used to
replace the center pixel value in the convolution process. The Euclidean length is
fixed through spatial domain and the range variance or intensity difference is set
through range domain.
The process of finding Euclidean distance is performed in the spatial
domain. Consider a vector consists of nearby pixels locations of center pixel. The
average weight is calculated to sum up the distance values performed from the
vector. The domain filter is given by the equation
dxcxh
k d
,f)(1
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Where, f and h are input and output images which indicates multiband in
nature. The center pixel x and nearby point in this filter represents the
geometric closeness of the signal. Geometric closeness refers to the value found
by Euclidean distance. The equation to preserving the DC component for low-pass
filtering is defined by
dxcxkd ,)(
where, dk is a normalization constant. The procedure xc , obtains the
geometric difference between the central and nearby pixel. Similarly the function
xf offers the range filter and is constructed by
dsxh
k r
xf,ff)(1
The pixel similarity between center and nearby pixels is computed by the
function xf,fs . The photometric similarity is calculated by performing the
sum of difference from center to nearby intensity values [TOM98]. Thus s is
operated by the range function and c is operated by the domain function. The
normalization constant is replaced by
dsxk rxf,f
Now both the domain and range filter is available to combine and is
described by
dsxcxk
xh xff,f)(
1
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The new value calculated by averaging similar and nearby pixel values
would have been placed at the location x . This is what happening while combining
the domain and range filters that can be used to achieve bilateral filter to present
securing edges while smooth out the image.
dsxcxk xff,
The above mathematical equation represents the convolution operation. The
bilateral filter associates low-pass filter and edge stopping function to acquire
which attenuates mask weights when it gets high variation among pixel values.
The parameters c and s contributes in fixing weights in spatial and range domains.
Both are under the control of standard deviations k and r computed in spatial and
range domains respectively.
5.4 ENHANCED BILATERAL FILTER
The drawback of bilateral filter is that the impulse noise will remain exist in
the filtered image. The reason behind the appearance of noise in the denoised
image after filtering is because of the photometry function of the bilateral filter.
Because, it cannot handle impulse value of the noise in a proper manner. It
produces the weight of the nearby pixels very small but the intensities where the
noises appear get large weights. To find the solution to this problem, the
photometric function has to be modified. It is possible to alter the function to gain
more performance. By doing in that way, the bilateral filter can be enhanced to
produce a noiseless image with preserving edges.
Bilateral filter uses both geometric and photometric functions to denoise the
noisy image. So, the two functions determine the performance of the filter. If both
are well designed then the level of performance will be increased. But, it is not
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easy to implement the well-designed functions and it will take more time. We used
an easily implemented photometric function in the proposed approach.
The photometric function involves an important role in order to determine
the performance of the bilateral filter. The main consideration in designing the
photometric function is the effect of the impulse noise because of the disadvantage
of the bilateral filter.
The given equation is used in photometric function.
1
1,
xd
xdxs
In the above equation, xd is the photometric difference between the
central and nearby intensity values. The value 1 added is for avoiding the divide-
by-zero error.
The same procedure will apply to every pixel of the whole image. In this
procedure, the geometric weight can be calculated using geometric function and
photometric weight can be calculated using photometric function. Then the mask
can be applied to the central pixel.
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5.5 PROPOSED BFFM METHOD
Proposed BFFM Technique
Step 1: Decompose the source noisy image as smoothed and residual
parts by new enhanced bilateral filter.
Step 2: Extract edge and texture from the residuals by processing it
by CVT.
Step3:Calculate weight from the deviation of smoothed and
processed-residual image.
Step 4: Fuse the residual images processed by CVT in step 2 using
weight obtained from step 3.
Step 5: Fuse the smoothed images using average fusion.
Step 6: Merge the smoothed-fusion and residual-fusion obtained from
step4 and step5 using averaging fusion rule.
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CVT Residual -ACurvelet
TransformCVT Residual -B
RESIDUAL PROCESS
Deviation
Weight
Intermediate Fusion for Residuals
Fused Image
Intermediate Fusion for Smooth
Input ARegistration
Input B
Smooth A Residual A Residual B Smooth B
BILATERAL DECOMPOSITION
Figure 5.1 Block Diagram of BFFM
Decomposition
Firstly, the input noisy images jiA , and jiB , captured from the two
different sensors are filtered by the enhanced bilateral method. Two forms of the
input image are acquired in this smoothing operation. One is denoised or coarse
forms another one is residual or approximation obtained by subtracting denoised
version from original. However, the noise-free images BA and BB are the
smoothed version of bilateral filter.
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11
1
11*,,
pppr
x
sB IIIgxxgxn
jiAjiA
11
1
11*,,
pppr
x
sB IIIgxxgxn
jiBjiB
In the above equation, the first part in the right side indicates the input
image and the second part indicates the filter to be smoothed the image. The
symbol * indicates the convolution operation carried to replace the center pixel in
the location ji, . The noise-removed images must effectively be demonstrated
because they persists various local qualities. Secondly, residual images of testing
images A and B are obtained and they are presented as rA for testing image A and
rB for testing image B. This can be accomplished by the following mathematical
models.
jiAjiAjiA Br ,,,
jiBjiBjiB Br ,,,
Where, A and B are original noisy signals, jiAB , and jiBB , are pixel
location of denoised signals and jiAr , and jiBr , are the pixel location of
residuals. Thus the two sub bands can be derived.
Residual Processing
The residuals derived from the above step contain a close combination of
noise and high frequency details. As the high frequency details give the
foreground information, residual has to be processed. This proposed algorithm
uses CVT to separate the high frequency details from noise in the residuals.
CVTjiAjiA rF *,,
CVTjiBjiB rF *,,
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The above expressions give the geometrical structures of the source images
without noise achieved by incorporating the curve preserving features of curvelet
with residuals of the source images. Where jiAF , and jiBF , are smoothed
version of residuals.
Computing Fusion Weight
Simply merging two images introduce contrast in the fused image. So,
weight value need to be assigned when the fusion take place. For the fusion of
background and foreground sub bands, two weights are required. One is assigned
for the denoised fusion and other for the restored residual fusion. For the fusion of
background images, average fusion is proposed. So the weight required is simple
constant value 0.5. On the other hand, the denoised residuals contained rich
textures require proper weight intensity because they have higher values and leads
to high contrast. To overcome by means of reducing higher contrast the weight
required for foreground fusion is computed to each pixel by:
j) (i, image residual restored
j) (i, image denoised - j) (i, imagenoisy j) (i,weight
According to the above eqn. weight required for both denoised residuals
jiAF , and jiBF , is computed by
jiA
jiAjiAjiW
F
Ba
,
,,,
is for source A.
jiB
jiBjiBjiW
F
Bb
,
,,,
is for source B.
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Fusion of Background and Residual Images
The weight, which needs to be computed by variances estimated in the
former step using the given formula. Next, the denoised images BA and
BB are
fused with a weight, constant value of 0.5, and this produces an intermediate fused
image yxf ,1 .
jiBjiAjif BB ,,*5.0,1
Similarly the restored residual images FA and
FB produce the second
intermediate image yxf ,2 by fusing them with the weights aW and bW .
jiBjiWjiAjiWjif FbFa ,*,,*,,2
Final Image Fusion
Finally, a simple average fusion can be applied over the intermediate
images to obtain the best complementary information.
jifjifjif ,,*5.0),( 21
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Pseudo Code of BFFM
for every source noisy images do
Decompose as smoothed and residual for each image
for i=1 to M do
for j= 1 to N do
/ / smoothed by bilateral
11
1
11*,,
pppr
x
sB IIIgxxgxn
jiXjiX
jiXjiXjiX Br ,,,
endfor
endfor
Apply CT decomposition to rX to obtain FX
end for
for the fused image do
for i=1 to M do i
for j= 1 to N do
jiX
jiXjiXW
F
BX
,
,,
n
BFX jiXjiXWn
jiF1
,,*1
,
endfor
endfor
end for
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5.6 EXPERIMENTAL RESULTS
To evaluate the proposed BFFM fusion algorithm using enhanced fast and
efficient bilateral filter against Laplacian and Wavelet, experiments were carried
out using the similar experimental setup and parameters discussed in the previous
chapter.
5.6.1 Performance Evaluation for Visual and IR Image Sets
To find out the grade of the proposed method, experiments have been
conducted on a couple of visual and IR image sets. A set of images for visual
effects and tables of values for metrics including MI, FABQ , WQ , EQ and OQ are
given.
i) Visual and Numerical Analysis for Uncamp Image Set
The proposed BFFM method is examined over a pair of Uncamp images
and the visual effects can be compared with the result images obtained by
Laplacian and Wavelet fusion methods.
a) Visual Analysis for Uncamp Images
The original versions of Uncamp Visual and IR are depicted in figure 5.2(a-
b). The corrupted image is shown in figure 5.2(c-d). Based on the proposed BFFM
fusion method, the residuals of visual and IR Uncamp images acquired by the
proposed enhanced bilateral filter are subjectively shown in figure 5.2(g-h).
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Figure 5.2 The Uncamp Source Images and Residuals
As per the algorithm, CVT executed a proper separation process of the
residuals. The denoised residuals of the Uncamp Visual and IR are depicted in
figure 5.3(a-b). The intermediate fused versions of Uncamp images are
subjectively demonstrated in figure 5.3(c-d). Finally, the visual performance of the
proposed BFFM, as shown in figure 5.3(g), is compared with Laplacian, as shown
in figure 5.3(e), and Wavelet, as shown in figure 5.3(f).
(a) Visual (b) IR
(c) Noisy Visual (d) Noisy IR
(e) Smoothed Visual (f) Smoothed IR
(g) Visual Residual (h) IR Residual
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Figure 5.3 Image Results of Uncamp and Fused Images of
various Fusion Algorithms
(a) Visual Processed by CVT (b) IR Processed by VCT
(c) Smoothed Fusion (d) Residual Fusion
(e) Laplacian (f) Wavelet
(g) BFFM
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b) Numerical Analysis for Uncamp Images
In this, the values of the tested image are produced for the proposed BFFM
fusion method with the comparison methods.
Table 5.1 Comparison Table for Uncamp Image Set
for Laplacian, Wavelet and BFFM
Metrics /
Methods MI
FABQ WQ EQ OQ
Laplacian 2.0228 0.4021 0.6023 0.4119 0.5876
Wavelet 2.0215 0.4284 0.6243 0.4347 0.5896
BFFM 2.0721 0.4424 0.7052 0.5020 0.6242
The Bilateral fusion algorithm achieves 2.0721 for MI, 0.4424 for FABQ ,
0.7052 for WQ , 0.5020 for EQ and 0.6242 for OQ . The Wavelet fusion yields the
second best result and the values are 2.0215, 0.4284, 0.6243, 0.4347 and 0.5896
respectively. And, Laplacian gives 2.0228, 0.4021, 0.6023, 0.4119 and 0.5876 for
the metrics. Therefore, the proposed algorithm performs well than the comparison
methods in terms of achieving better results.
From the figure 5.4, it assures that the proposed BFFM method earns higher
values for the five metrics MI, FABQ , WQ , EQ and OQ when compared with
Laplacian and Wavelet.
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Figure 5.4 Comparison Graph for the Fusion Performance of
Laplacian, Wavelet and BFFM
ii) Visual and Numerical Analysis for Gun Image Set
The visual effects of the proposed BFFM method and the comparison
methods for Gun images are given.
a) Visual Analysis for Gun Images
Both the visual and IR original images are depicted in the figure 5.5(a-b)..
The corrupted images of Gun’s visual and IR images are depicted in figure 5.5(c-
d). The residuals acquired from noisy images are visibly demonstrated in figure
5.4(g-h). The smoothed version s of noisy images by the proposed enhanced
bilateral filter is shown in figure 5.5(e-f).
0
0.5
1
1.5
2
2.5
MI QAB/F Qw QE Qo
Va
lues
Metrics
Laplacian
Wavelet
BFFM
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(a) Visual (b) IR
(c) Noisy Visual (d) Noisy IR
(e) Smoothed Visual (f) Smoothed IR
(g) Visual Residual (h) IR Residual
Figure 5.5 The Gun Source Images and Residuals
The primary goal of retrieving the geometrical structure from the noisy
environment is executed by processing the residuals with CVT and is visually
shown in figure 5.6(a). The intermediate fusion of smoothed and processed-
residuals can be shown in figure 5.6(b-c). The comparison images Laplacian and
wavelet are depicted in figure in figure 5.6(d-e).
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(a) Residual Processed by CVT
(b) Smoothed Fusion (c) Residual Fusion
(d) Laplacian (e) Wavelet
(f) BFFM
Figure 5.6 Image Results of Gun and Fused Images of
various Fusion Algorithms
b) Numerical Analysis for Gun images
The numerical results of the objective evaluation are tabulated in Table 5.2.
From this table, it can be found that BFFM method exceeds all other methods.
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Table 5.2 Comparison Table for Gun Image Set
for Laplacian, Wavelet and BFFM
Metrics/
Methods MI
FABQ WQ EQ OQ
Laplacian 2.1340 0.6549 0.8053 0.7012 0.7059
Wavelet 2.1357 0.6632 0.8246 0.7210 0.7294
BFFM 2.2843 0.6994 0.8713 0.7632 0.7512
In table 5.2, the proposed BFFM and Wavelet fusion methods affords better
result than Laplacian fusion where, the laplacian reaches 2.1340, 0.6549, 0.8053,
0.7012 and 0.7059 for the metrics and Wavelet gives 2.1357, 0.6632, 0.8246,
0.7210 and 0.7294 for the parameters MI, FABQ , WQ , EQ and OQ . Finally the
proposed BFFM approach benefits 2.2843, 0.6994, 0.8713, 0.7632 and 0.7512
which are high than other two approaches.
Figure 5.7 Comparison Graph for the Fusion Performance of Laplacian, Wavelet and
BFFM
0
0.5
1
1.5
2
2.5
MI QAB/F Qw QE Qo
Va
lues
Metrics
Laplacian
Wavelet
BFFM
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Figure 5.7 indicates that for the five metrics MI, FABQ , WQ , EQ and OQ of
Bilateral Filtering Fusion Method achieves higher positions for fusion when
compared with Laplacian and Wavelet.
5.6.2 Performance Evaluation for Medical Image Sets
The parameters MI, FABQ , WQ , EQ and OQ are calculated for MRI-T1 and
MRI-T2 image set.
i) Visual and Numerical Analysis for MRI Image Set
To show the effectiveness of the proposed method, two different MRI
bands are tested over a couple of MRI-T1 and MRI-T2 images. The various
images obtained during the process of BFFM are also shown in the forthcoming
sections. Finally, the visual effect of BFFM fused image is compared with the
result obtained by Laplacian and Wavelet fusion methods.
a) Visual Analysis for MRI Images
The original and corresponding noisy models are shown in 5.8(a-d). The
smoothed model obtained by the proposed enhance bilateral filter is shown in
figure 5.8(e-f) for both MRI images. The residuals embedded high frequency
details of both MRI-T1 and MRI-T2 are demonstrated in figure 5.8(g-h).
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Figure 5.8 The MRI Source Images and Residuals
The foreground and background details of the fused image are depicted in
figure 5.9(b-c). In this, the important high frequency information can be located
which is left out during the process of decomposing by enhanced bilateral filter.
As per the BFFM algorithm, curvelet provides a proper separation between noise
and the high frequency details. The output of this process is shown in figure
5.9(a). The final fused image obtained by merging the background and foreground
(a) MRI-T1 (b) MRI-T2
(c) Noisy MRI-T1 (d) Noisy MRI-T2
(e) Smoothed MRI-TI (f)Smoothed MRI-T2
(g) Residual MRI-T1 (h)Residual MRI-T2
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is shown in figure 5.9(f) and the fused images used by Laplacian and Wavelet are
also shown in figure 5.9(d-e).
Figure 5.9 Image Results of MRI and Fused Images of
various Fusion Algorithms
b) Numerical Analysis for MRI Images
In order to evaluate the ability of the BFFM algorithm, the numerical
assessment is made and is tabulated and plotted in the following sections. The
results of the comparison methods are compared with BFFM method numerically.
(a) Residuals Processed by CVT
(b) Smoothed fusion (c) Residual fusion
(d)Laplacian (e) Wavelet
(f) BFFM
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Table 5.3 Comparison Table for MRI Image Set
for Laplacian, Wavelet and BFFM
Metrics /
Methods MI
FABQ WQ EQ OQ
Laplacian 2.4174 0.5487 0.6009 0.4001 0.4262
Wavelet 2.4200 0.5678 0.6108 0.4350 0.4465
BFFM 2.4592 0.6382 0.6592 0.4812 0.5008
From the table 5.3, the result values of the five metrics for BFFM produce
highest when compared with traditional Laplacian and Wavelet fusion methods.
BFFM for the five metrics of MI, FABQ , WQ , EQ and OQ yields values of 2.4592,
0.6382, 0.6592, 0.4812 and 0.5008. For the Wavelet fusion method, it gives values
of 2.4200, 0.5678, 0.6108, 0.4350 and 0.4465 which are better than Laplacian
fusion where it reaches 2.4174, 0.5487, 0.6009, 0.4001 and 0.4262.
Figure 5.10 Comparison Graph for the Fusion Performance of
Laplacian, Wavelet and BFFM
0
0.5
1
1.5
2
2.5
3
MI QAB/F Qw QE Qo
Va
lues
Metrics
Laplacian
Wavelet
BFFM
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Figure 5.10 point out that the values acquired for the five metrics MI,
FABQ , WQ , EQ and OQ of Laplacian, Wavelet and BFFM fusion methods.
Among them the BFFM reaches higher place for fusion when compared with
Laplacian and Wavelet.
ii) Visual and Numerical Analysis for CT and MRI Image Set
To show the impact of the proposed method, it is tested over a couple of
MRI-T1 and MRI-T2 images. And the results are tested and compared with the
result images obtained by Laplacian and Wavelet fusion methods.
a) Visual Analysis for CT and MRI Images
The original CT and MRI images of medical image set and the noisy
images of the source images are shown in figure 5.11(a-d) respectively. The
smoothed version of noisy CT and MRI is shown in figure 5.11(e-f). It shows that
the noise is removed but it lost some important details which are implanted in
residual as shown in figure 5.11(g-h).
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Figure 5.11 The CT and MRI Source Images and Residuals
The loss of details in CT image is strong edges which is retrieved back
from noisy residual and is shown in figure 5.12(a) for both CT and MRI. The
fusion of smoothed CT and MRI gives the background of the fused image.
(a) CT (b) MRI
(c) Noisy CT (d) Noisy MRI
(e) Smoothed CT (f) Smoothed MRI
(g) Residual CT (h) Residual MRI
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Similarly, combining the processed-residuals provide the foreground details of the
fused image.
Figure 5.12 Image Results of CT and MRI and Fused Images of
various Fusion Algorithms
(a) Residulas Processed by CVT
(b) Smoothed Fusion (c) Residual Fusion
(d) Laplacian (e) Wavelet
(f) BFFM
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The final fusion of CT and MRI images from medical image set is shown in
figure 5.12(f) obtained from the intermediate fused images of CT and MRI as
shown in figure 5.12(b-c). Previously, the fusion Laplacian and Wavelet is shown
in figure 5.12(d-e).
b) Numerical Analysis for CT and MRI Images
To show the efficiency of the proposed method, the CT and MRI images
are examined for numerical analysis using fusion evaluation metrics.
Table 5.4 Comparison Table for CT and MRI Image Set
for Laplacian, Wavelet and BFFM
Metrics /
Methods
MI FABQ WQ
EQ OQ
Laplacian 2.2174 0.6008 0.5790 0.4120 0.4720
Wavelet 2.2255 0.6024 0.5876 0 .4428 0.5835
BFFM 2.2612 0.6876 0.6884 0.4976 0.6407
From the table 5.4, the Laplacian fusion method for five metrics gives
lower values of 2.2174, 0.6008, 0.5790, 0.4120 and 0.4720. Next, the Wavelet
yields 2.2255, 0.6024, 0.5876, 0.4428 and 0.5835 which are higher than Laplacian.
For the proposed BFFM fusion method, it produces higher rate of 2.2612, 0.6876,
0.6884, 0.4976 and 0.6407 which are better than Laplacian and Wavelet fusion
methods.
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Figure 5.13 Comparison Graph for the Fusion Performance of Laplacian,
Wavelet and BFFM
Figure 5.13 directs that for the five metrics MI, FABQ , WQ , EQ and OQ of
BFFM attains higher values for fusion when compared with Laplacian and
Wavelet.
5.7 SUMMARY
This chapter provides the comprehensible discussion of the second
proposed methodology that uses modified Bilateral filter method to decompose the
source noisy images. The fusion can be done with the standard curvelet transform.
The performance of the BFFM has been evaluated against the state-of-the–art
image fusion methods including Laplacian Pyramid and Wavelet Transform for
the Visual, IR, CT, MRI-T1 and MRI-T2 images. It is found that the performance
of the proposed method is better than the methods Laplacian and Wavelet in terms
of securing the edges, textures and mutual information.
0
0.5
1
1.5
2
2.5
MI QAB/F Qw QE Qo
Va
lues
Metrics
Laplacian
Wavelet
BFFM
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