KEKRE’S HYBRID WAVELET TRANSFORM TECHNIQUE WITH DCT_ WALSH_ HARTLEY AND KEKRE’S by iaemedu

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									  International Journal of JOURNAL OF and Technology (IJCET), ISSN 0976-
 INTERNATIONALComputer EngineeringCOMPUTER ENGINEERING
  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
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    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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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
    M            M            M    M        M           M         M   M          … M                  M            M   M
    0            0            … 0           0           0         … 0              a31                a32          … a3p
    M            M            M    M        M           M         M   M          … M                  M            M   M
    ap1          ap2          … app         0           0         … 0              0                  0            … 0
    0            0            … 0           ap1         ap2       … app            0                  0            … 0
    M            M            M    M        M           M         M   M          … M                  M            M   M
    0            0            … 0           0           0         … 0              ap1                ap2          … app

                                   Fig.1 Generation of Hybrid Transform Matrix
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International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME

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-
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6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME




                                   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



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International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME

   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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