CHAPTER 5 BILATERAL FILTERING FUSION...

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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.


110

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


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


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


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


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


(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


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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