1. INTERNATIONAL JOURNAL OF COMPUTER ENGINEERING
International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1,(IJCET)
& TECHNOLOGY January- February (2013), © IAEME
ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)
Volume 4, Issue 1, January- February (2013), pp. 89-96
IJCET
© IAEME: www.iaeme.com/ijcet.asp
Journal Impact Factor (2012): 3.9580 (Calculated by GISI) ©IAEME
www.jifactor.com
NOVEL IMAGE FUSION TECHNIQUES USING GLOBAL AND
LOCAL KEKRE WAVELET TRANSFORMS
Dr. Sudeep D. Thepade
Professor, Department of Computer Engineering,
Pimpri Chinchwad College of Engineering, Pune
Mrs. Jyoti S.Kulkarni
Senior Lecturer,Department of Information Tech.,
Pimpri Chinchwad College of Engineering, Pune
ABSTRACT
Image Fusion is the process of combining the information from multiple
images such that the fused image gives or represents more information than that of
single image gives. Images for image fusion may be from single sensor with different
time slots or may be from multiple sensors. Image fusion is used in different
applications such as medical imaging, Military images, Multisensory images,
Multifocus images etc. Different transforms are used for image fusion. In this
proposed method, Kekre transform is used. Kekre transform is one of the orthogonal
transforms. Here Kekre transform along with Local Kekre Wavelet Transform and
Global Kekre Wavelet Transform are proposed to be used in novel image fusion
methods. For each of the proposed Image Fusion techniques , the Average , Minimum
and Maximum are considered for generation of fused image. Experimentation is
performed on ten sets of images to generate the fused images. Result has shown the
Local Kekre wavelet transform proves to be better for image fusion than Global Kekre
wavelet transform and Kekre Transform. Also the averaging based fusion is better
than minimum or maximum.
Keywords- Kekre Transform, Local Transform, Global Transform
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2. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
I. INTRODUCTION
Now a days, Image fusion is used in many fields. In this, the images from different
sensors or from same sensor with different time or season are fused together. After image
fusion, the resultant image generated will be more informative than source images. In fused
image, the relevant information from source images get used to find more information which
will be further processed.
There are increasing applications of image fusion in different fields. In topographic
mapping, the area that is not covered by one sensor might be available in another sensor. By
combining the information from these sensors, the area or map is updated. Similarly to get
the idea about natural hazards such as flood monitoring and snow monitoring. Image fusion is
also used in geology to get the information on soil geochemistry, vegetation, land use, soil
moisture and surface roughness.
Many image fusion methods are available such as Intensity Hue Saturation (IHS),
Principle Component Analysis (PCA), Brovey Transform (BT), High Pass Filtering (HPF) ,
High Pass Modulation (HPM) and Transform domain image fusion..
Here use of Kekre Transform is proposed along with Local Kekre Wavelet Transform
and Global Kekre Wavelet Transform for Image Fusion.
Section II describes the Kekre Transform and generation of Local Kekre Wavelet
Transform and Global Kekre Wavelet Transform. Section III describes the proposed Image
Fusion Method with block diagram. Section IV describes the experimentation on proposed
Image Fusion Method and Section V describes the results and discussion on the fused images
by using these methods.
II. USED TRANSFORMS
(a) Kekre Transform: In Kekre Transform, it is not essential that the matrices have to be in
powers of 2. The Kekre Transform is generated by using equation (1).
1 , x≤y
{
Kx,y = (-N+(x+1) , x=y+1
0 , x>y+1
(1)
Let the following matrix generated by this equation having PxP size.
1 2 … P
1 …
2 …
⁞ ⁞ ⁞ … ⁞ ⁞
P …
Figure 1: PxP Kekre Transform matrix
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3. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
(b) Local Kekre WaveletTransform : Generation of Local Kekre Wavelet Transform of size
P2xP2 from Kekre Transform of size PxP is shown in fig. 2.
… … … …
… … … …
⁞ ⁞ … ⁞ ⁞ ⁞ … ⁞ … ⁞ ⁞ … ⁞
… … … …
… 0 0 … 0 … 0 0 … 0
0 0 … 0 … … 0 0 … 0
⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞
0 0 … 0 0 0 … 0 … …
… … … …
… 0 0 … 0 … 0 0 … 0
0 0 … 0 … … 0 0 … 0
⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞
0 0 … 0 0 0 … 0 … …
Figure 2: P2xP2 matrix of Kekre Local Wavelet Transform
(c) Global Kekre Wavelet Transform: Generation of Global Kekre Wavelet Transform of size
P2xP2 from Kekre Transform of size PxP is shown in fig. 3.
… … … …
… … … …
⁞ ⁞ … ⁞ ⁞ ⁞ … ⁞ … ⁞ ⁞ … ⁞
… … … …
… 0 0 0 0 0 0 0 0 0
⁞ ⁞ … ⁞ 0 0 0 0 0 0 0 0 0
… 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 ⁞ ⁞ … ⁞ 0 0 0 0 0
0 0 0 0 … 0 0 0 0 0
0 0 0 0 0 0 0 0 ⁞ 0 0 0 0
0 0 0 0 0 0 0 0 0 …
0 0 0 0 0 0 0 0 0 ⁞ ⁞ … ⁞
0 0 0 0 0 0 0 0 0 …
Figure 3: P2xP2 matrix of Kekre Global Wavelet Transform
The normalization of these wavelet transforms done before the use in processing.
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4. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
III. PROPOSED IMAGE FUSION METHOD
The proposed image fusion method using Kekre wavelet transform is given in fig.4.
Apply Local /
Transformed
Image 1 Global Kekre Fusion using
Image
Transform Minimum/M Inverse
Fused
aximum/Ave Transform
Image
rage
Apply Local / Method
Image 2 Global Kekre Transformed
Transform Image
Figure 4: Basic Block Diagram of proposed Image Fusion Method
In the proposed Image Fusion Method, normalized local or global transform is applied to two
blurred images separately. Three coefficients are available after this transformation. The
inverse transform is applied to find fused image. The coefficients are compared to find better
fused image.
IV. IMPLEMENTATION / EXPERIMENTATION
For experimentation, set of six images are considered to fused using proposed image
fusion method as shown in fig 5.
Set1: Tulip Set2: Moon
Set3: Animal Set4: Apple
Set5: Wool Set6: Scene
Figure 5: Test bed of set of images to be fused
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5. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
V. RESULTS AND DISCUSSION
The Kekre Transform, Local Kekre Wavelet Transform and Global Kekre Wavelet
Transform is applied on the images given in fig.5. Then the fused image is compared with
original image to find the mean square error. Result generated shows that local transform is
better than orthogonal transform as well as global transform.
Table1. Comparison of Kekre Transform, Kekre Local Wavelet transform and Kekre Global
Transform
Kekre Wavelet
Kekre Wavelet Kekre
Local
Global Transform transform
Transform
Tulip 271.7474 275.9028 17176
Moon 91.3706 91.1495 24568
Animal 122.5144 122.5086 13581
Apple 363.9339 363.9184 18797
Wool 385.4935 397.9610 15315
Scene 191.2848 190.5862 15438
Average 237.72 240.34 17479.17
Comparison of KT, LKWT,GKWT
30000
25000
Kekre transform
MSE VAlue
20000
15000
Kekre Wavelet
10000 Global
Transform
5000
Kekre Wavelet
0 Local
Transform
Figure 6: Graphical representation of comparison between transforms.
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6. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
By considering the Kekre Local wavelet Transform, the minimum, maximum and
average values are compared. After comparison it shows that average value is better than
other two values.
Table2. Comparison of Average, Minimum and Maximum values in Local KekreWavelet
transform
Average Minimum Maximum
Tulip 271.7474 326.2178 327.652
Moon 91.3706 102.0376 105.223
Animal 122.5144 143.7189 148.514
Apple 363.9339 413.4674 440.807
Wool 385.4935 474.4746 479.406
Scene 191.2848 217.3164 230.101
500
400
MSE value
300
Average
200
Minimum
Maximum
100
0
Tulip Moon Animal Apple Wool Scene
Images
Figure 7: Graphical representation of comparison between values of Kekre Local Wavelet
transforms.
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7. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
The output images after the application of these three transforms is given in figure 8.
(a)Original (b) Blurred (c) Blurred
Image Image Image
(d) Average (e) (f) Maximum
Minimum
Kekre Local Wavelet Transform
(g) Average (h) Minimum (i) Maximum
Kekre Transform
(j) Average (k) Minimum (l) Maximum
Kekre Global Wavelet Transform
Figure 8: Input and Output Images of all the Transforms.
Figure 8 represents the input and output images of Kekre Transform, Kekre Local wavelet
transform and Kekre Global Wavelet Transform. In figure, first row are the original image
and blurred images respectively. Second row represents outputs of Kekre Local Wavelet
Transform with Minimum, Maximum and Average values respectively. Third row represents
outputs of Kekre Transform with Minimum, Maximum and Average values respectively. And
last row represents, outputs of Kekre Global Wavelet Transform with Minimum, Maximum
and Average values respectively. From this, the Kekre Local Wavelet transform gives better
result than remaining two methods.
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8. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
CONCLUSIONS
Image Transform based fusion is gaining momentum in imaging research. Here novel
Image Fusion methods are proposed using Kekre Transform, Local Kekre Wavelet Transform
and Global Kekre Wavelet Transform .Experimentation has shown that the Kekre Wavelet
Transform based fusion is outperforming. In all Local Kekre Wavelet Transform with
averaging gives better performance for image fusion.
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