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INTERNATIONAL JOURNAL OF COMPUTER ENGINEERINGg 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) © I A E M E www.jifactor.com KEKRE’S HYBRID WAVELET TRANSFORM TECHNIQUE WITH DCT, WALSH, HARTLEYAND KEKRE’S TRANSFORM FOR IMAGE FUSION 1 2 3 Rachana Dhannawat , Tanuja Sarode , H. B. Kekre 1(Computer Science and Technology, UMIT, SNDT University, Juhu, Mumbai, India, 2 firstname.lastname@example.org) (Computer engineering department, TSEC Mumbai University, Bandra, India, email@example.com) (MPSTME, SVKM’S NMIMS university, Vile parle , India, firstname.lastname@example.org) 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  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. 195 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 objective of image fusion   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 , pyramid transform, wavelet transform , 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 , 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 , Robot vision, Concealed weapon detection, Multi-focus image fusion, Digital camera application, Battle field monitoring, etc. II. KEKRE’STRANSFORM Kekre transform matrix   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 + 1 196 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. GENERATION OF HYBRID WAVELETMATRIX 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    of size NxN (say AB ’) 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 . a 11 * a 12 * .. a1p * a11 * a12 * … a 1p*b12 … a 11 * 1q a12 * … a 1p * b 11 b 11 . b11 b12 b12 b1q b1q b22 b 2q b 21 b 21 b21 b22 b22 M M b2q b2q M bqq M M M M bq2 M M b q1 b q1 bq1 bq2 bq2 bqq bqq a 21 a 22 … a 2p 0 0 … 0 … 0 0 … 0 0 0 … 0 a21 a22 … a 2p … 0 0 … 0 … M M M M M M M M M M M M 0 0 … 0 0 0 … 0 … a a … a 21 22 2p a 31 a 32 … a 3p 0 0 … 0 0 0 … 0 0 0 … 0 a31 a32 … a 3p 0 0 … 0 … M M M M M M M M M M M M 0 0 … 0 0 0 … 0 a31 a32 … a 3p … M M M M M M M M M M M M a p1 a p2 … a pp 0 0 … 0 0 0 … 0 0 0 … 0 ap1 ap2 … a pp 0 0 … 0 M M M M M M M M … M M M M 0 0 … 0 0 0 … 0 ap1 ap2 … a pp Fig.1 Generation of Hybrid Transform Matrix 197 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 , average gradient, information entropy, mutual information  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. 198 InternatonalllJournallof CCompputer Enngineerng aand TTechnooogy ((JCEET)),,SSSN 00976- 6367(Print), ISSN 0976 6375(Onnlne)Vooumme 4,Isuee1,Januaary-February (2013),© IAEMMEE Fig. 2 Sample images 199 International Journal of Computer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME 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 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 Mean Standard 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. REFERENCES  Dr. H. B. Kekre, Archana Athawale, Dipali Sadavarti, Algorithm to Generate Kekre’s Wavelet Transform from Kekre’s Transform, International Journal of Engineering Science and Technology, 2(5), 2010, 756-767. 201 International Journal of Computer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME  MA. Mohamed and R.M EI-Den, Implementation of Image Fusion Techniques for Multi-Focus Images Using FPGA, Proc. 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