Kekre’s hybrid wavelet transform technique with dct, walsh, hartley and kekre’s

INTERNATIONALComputer EngineeringCOMPUTER ENGINEERING
International Journal of JOURNAL OF and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME
& TECHNOLOGY (IJCET)
ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)
Volume 4, Issue 1, January- February (2013), pp. 195-202
IJCET
© IAEME: www.iaeme.com/ijcet.asp
Journal Impact Factor (2012): 3.9580 (Calculated by GISI) ©IAEME
www.jifactor.com

KEKRE’S HYBRID WAVELET TRANSFORM TECHNIQUE WITH
DCT, WALSH, HARTLEY AND KEKRE’S TRANSFORM FOR IMAGE
FUSION

Rachana Dhannawat1, Tanuja Sarode2, H. B. Kekre3
1
(Computer Science and Technology, UMIT, SNDT University, Juhu, Mumbai, India,
rachanadhannawat82@gmail.com)
2
(Computer engineering department, TSEC Mumbai University, Bandra, India,
tanuja_0123@yahoo.com)
3
(MPSTME, SVKM’S NMIMS university, Vile parle , India, hbkekre@yahoo.com)

ABSTRACT

Kekre’s hybrid wavelet transform is generated by using two input matrices so that
best qualities of both of the matrices can be incorporated into hybrid matrix. The matrix has
one major advantage that it can be used for images which are not integer power of 2. In this
paper hybrid matrices are generated using four matrices DCT, Walsh, Kekre’s transform and
Hartley transform. Image fusion combines two or more images of same object or scene so
that the final output image contains more information. In image fusion process the most
significant features in the input images are identified and transferred them without loss into
the fused image.

Keywords: Hartley transform, Kekre's hybrid wavelet transform, Kekre’s Transform, Pixel
level Image Fusion, Walsh Transform.

I. INTRODUCTION

The Kekre's hybrid transform is generated by combination of two basic matrices like
DCT, Walsh, Kekre’s transform and Hartley transform, etc. In wavelets of some orthogonal
transforms the global characteristics of the data are hauled out better and some orthogonal
transforms might give the local characteristics in better way. The idea of hybrid wavelet
transform [1] comes in to picture in view of combining the traits of two different orthogonal
transform wavelets to exploit the strengths of both the transform wavelets. The matrix has
one major advantage that it can be used for images which are not integer power of 2.

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International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-

The objective of image fusion [2] [3] is to obtain a better visual understanding of certain
phenomena, and to enhance intelligence and system control functions. The data gathered
from multiple sources of acquisition are delivered to preprocessing such as denoising and
image registration. The post-processing is applied to the fused image. Post-processing
includes classification, segmentation, and image enhancement.

Many image fusion techniques pixel level, feature level and decision level are
developed. Examples are like Averaging technique, PCA [4], pyramid transform, wavelet
transform [5], neural network, K-means clustering, etc. In this paper Kekre's hybrid wavelet
transform matrix is applied on both of the input images for transformation pixel by pixel so
this technique will be categorized as pixel level image fusion technique.

Several situations in image processing require high spatial and high spectral
resolution in a single image. For example, the traffic monitoring system [6], satellite image
system, and long range sensor fusion system, land surveying and mapping, geologic
surveying, agriculture evaluation, medical and weather forecasting all use image fusion.

Like these, applications motivating the image fusion are: Image Classification, Aerial
and Satellite Imaging, Medical imaging [7], Robot vision, Concealed weapon detection,
Multi-focus image fusion, Digital camera application, Battle field monitoring, etc.

II. KEKRE’S TRANSFORM

Kekre transform matrix [8] [9] is the generic version of Kekre’s LUV color space
matrix. Most of the other transform matrices have to be in powers of 2. This condition is not
required in Kekre transform. All upper diagonal and diagonal elements of Kekre’s transform
matrix are 1, while the lower diagonal part except the elements just below diagonal is zero.
Generalized NxN Kekre’s transform matrix can be given as,

 1 1 1 ... 1 1
 − N +1 1 1 ... 1 1
 
 0 -N+2 1 ... 1 1
 
. . . . ... . .
 . . . ... . .
 
 . . . ... . .
 0 0 0 ... 1 1
 
 0
 0 0 ... − N + ( N − 1) 1


Any term in the Kekre's transform matrix is generated by using equation 1:

1 : x ≤ y

Kxy =  − N + ( x − 1 ) : x = y +1 (1 )
0 : x > y +1


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III. GENERATION OF HYBRID WAVELET MATRIX

The idea of hybrid wavelet transform comes in to picture in view of combining the traits of two
different orthogonal transform wavelets to exploit the strengths of both the transform wavelets. The hybrid
wavelet transform matrix [10] [11] [12] of size NxN (say ‘TAB’) can be generated from two orthogonal
transform matrices (say A and B respectively) with sizes pxp and qxq, where N=p*q=pq as shown in figure
.Here first ‘q’ number of rows of the hybrid wavelet transform matrix are calculated as the product of each
element of first row of the orthogonal transform A with each of the columns of the orthogonal transform B. For
next ‘q’ number of rows of hybrid wavelet transform matrix the second row of the orthogonal transform matrix
A is shift rotated after being appended with zeros as shown in figure . Similarly the other rows of hybrid wavelet
transform matrix are generated (as set of q rows each time for each of the ‘p-1’ rows of orthogonal transform
matrix A starting from second row up to last row). Hybrid transform matrix is generated as shown in figure
given below.

b11 b12 ... b1q
a11 a12 .. a1p
. b21 b22 ... b2q
A= a21 a22 .. a2p B=
. M M ... M
M M .. M
.
ap1 ap2 .. app bq1 bq2 ... bqq
.

a11 * a12 * .. a1p * a11 * a12 * … a1p* b12 … a11 * b1q a12 * … a1p *
b11 b11 . b11 b12 b12 b1q b1q
b22 b2q
b21 b21 b21 b22 b22 M M b2q b2q
M bqq
M M M M bq2 M M
bq1
bq1 bq1 bq2 bq2 bqq bqq
a21 a22 … a2p 0 0 … 0 … 0 0 … 0
0 0 … 0 a21 a22 … a2p … 0 0 … 0
M M M M M M M M … M M M M
0 0 … 0 0 0 … 0 … a21 a22 … a2p
a31 a32 … a3p 0 0 … 0 0 0 … 0
0 0 … 0 a31 a32 … a3p 0 0 … 0
0 0 … 0 0 0 … 0 a31 a32 … a3p
ap1 ap2 … app 0 0 … 0 0 0 … 0
0 0 … 0 ap1 ap2 … app 0 0 … 0
0 0 … 0 0 0 … 0 ap1 ap2 … app

Fig.1 Generation of Hybrid Transform Matrix
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IV. PROPOSED METHOD

1. Take as input two images of same size and of same object or scene taken from two
different sensors like visible and infra red images or two images having different
focus.
2. If images are colored separate their RGB planes to perform 2D transforms.
3. Perform decomposition of images using different hybrid transforms like hybrid walsh-
DCT, hybrid DCT-Walsh, hybrid DCT-Hartley, hybrid Hartley-DCT, hybrid Kekre-
Hartley, hybrid Walsh-Hartley, etc.
4. Fuse two image components by taking average.
5. Resulting fused transform components are converted to image using inverse
transform.
6. For colored images combine their separated RGB planes.
7. Compare results of different methods of image fusion using various measures like
entropy, standard deviation, mean, mutual information, etc.

V. RESULTS AND ANALYSIS

At present, the image fusion evaluation methods can mainly be divided into two
categories, namely, subjective evaluation methods and objective evaluation methods.
Subjective evaluation method is, directly from the testing of the image quality evaluation,
a simple and intuitive, but in man-made evaluation of the quality there will be a lot of
subjective factors affecting evaluation results. An objective evaluation methods
commonly used are: mean, variance, standard deviation [13], average gradient,
information entropy, mutual information [14] and so on.
Above mentioned techniques are tried on pair of four color RGB images and six gray
images as shown in fig. 1 and results are compared based on measures like entropy, mean,
standard deviation and mutual information. Fig.2 shows image fusion by different
techniques for hill images with different focus. Fig. 3 shows Image fusion by different
techniques for gray brain images with different focus. Performance evaluation based on
above mentioned four measures for color hill image is given in table 1. Table 2 presents
performance evaluation for gray brain images.
From table 1 it is observed that for hill images mean is maximum using DCT Walsh
hybrid wavelet technique, while standard deviation is maximum using DCT Hartley
hybrid wavelet technique. Entropy is maximum using DCT Hartley hybrid wavelet
technique and Kekre Hartley hybrid wavelet technique. Maximum mutual information is
obtained by using Kekre Hartley hybrid wavelet technique and Walsh Hartley hybrid
wavelet technique. From table 2 it is observed that for brain images mean and SD is
maximum using hybrid Walsh DCT technique. Entropy is maximum using hybrid Kekre
Hartley wavelet technique and Maximum mutual information is obtained by
using Kekre Hartley hybrid wavelet technique and Walsh Hartley hybrid wavelet
technique.

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International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 0976-
January

Fig. 2 Sample images

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a) Hybrid Kekre Hartley b)Hybrid DCT Walsh fused c) Hybrid Walsh DCT fused
fused image image image

d) Hybrid DCT Hartley e) Hybrid Hartley DCT fused f) Hybrid Walsh Hartley
fused image image fused image
Fig. 3 Image fusion by different hybrid wavelet techniques for hill images with different
focus

a) Hybrid Kekre Hartley b)Hybrid DCT Walsh fused c) Hybrid Walsh DCT fused
fused image image image

d) Hybrid DCT Hartley e) Hybrid Hartley DCT f) Hybrid Walsh Hartley
fused image fused image fused image
Fig.4 Image fusion by different hybrid wavelet techniques for brain images

200


Table 1 Performance evaluation for color hill images using hybrid wavelet techniques
Transform Techniques MeanStandard Entropy Mutual
deviation Information
Hybrid DCT Walsh wavelet 134.3489 90.3206 7.2643 0.4819
Hybrid Walsh DCT 134.3347 90.3436 7.2656 0.4834
wavelet
Hybrid DCT Hartley 134.2882 90.3581 7.2664 0.4842
wavelet
Hybrid Hartley DCT 134.3206 90.3328 7.2651 0.4831
wavelet
Hybrid Walsh Hartley 134.2821 90.3551 7.2662 0.4845
wavelet
Hybrid Kekre Hartley 134.2818 90.3539 7.2664 0.4845
wavelet

Table 2 Performance evaluation for brain images using hybrid wavelet techniques
Transform Techniques Mean Standard Entropy Mutual
deviation Information
Hybrid DCT Walsh wavelet 49.5156 50.8400 5.2075 0.3961
Hybrid Walsh DCT wavelet 49.5244 50.8511 5.2101 0.3972
Hybrid DCT Hartley 49.4237 50.7309 5.2197 0.3987
wavelet
Hybrid Hartley DCT 49.5103 50.8382 5.2103 0.3967
wavelet
Hybrid Walsh Hartley 49.4143 50.7211 5.2199 0.3991
wavelet
Hybrid Kekre Hartley 49.4143 50.7211 5.2202 0.3991
wavelet

VI. CONCLUSION

In this project six hybrid pixel level image fusion techniques like hybrid Walsh-DCT,
DCT-Walsh, DCT –Hartley, Hartley-DCT, Walsh-Hartley and Kekre Hartley are
implemented and results are compared. It is observed that these new techniques gives better
results as compared to basic techniques for image fusion with added advantage that these
techniques can be used for images which are not necessarily integer power of 2.

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