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Discrete Cosine Transform Based Image Fusion Techniques VPS Naidu MSDF Lab, FMCD, National Aerospace Laboratories, Bangalore, INDIA E.Mail: [email protected]

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Discrete Cosine Transform Based Image Fusion Techniques VPS Naidu MSDF Lab, FMCD, National Aerospace Laboratories, Bangalore, INDIA E.Mail: Vpsnaidu@Gmail.Com View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by NAL-IR Journal of Communication, Navigation and Signal Processing (January 2012) Vol. 1, No. 1, pp. 35-45 Discrete Cosine Transform based Image Fusion Techniques VPS Naidu MSDF Lab, FMCD, National Aerospace Laboratories, Bangalore, INDIA E.mail: [email protected] Abstract: Six different types of image fusion algorithms based on 1 discrete cosine transform (DCT) were developed and their , k 1 0 performance was evaluated. Fusion performance is not good while N Where (k ) 1 and using the algorithms with block size less than 8x8 and also the block 1 2 size equivalent to the image size itself. DCTe and DCTmx based , 1 k 1 N 1 1 image fusion algorithms performed well. These algorithms are very N 1 simple and might be suitable for real time applications. 1 , k 0 Keywords: DCT, Contrast measure, Image fusion 2 N 2 (k 1 ) I. INTRODUCTION 2 , 1 k 2 N 2 1 Off late, different image fusion algorithms have been developed N 2 to merge the multiple images into a single image that contain all useful information. Pixel averaging of the source images k 1 & k 2 discrete frequency variables (n1 , n 2 ) pixel index (the images to be fused) is the simplest image fusion technique and it often produces undesirable side effects in the fused image Similarly, the 2D inverse discrete cosine transform is defined including reduced contrast. To overcome this side effects many as: researchers have developed multi resolution [1-3], multi scale [4,5] and statistical signal processing [6,7] based image fusion x(n1 , n 2 ) (k 1 ) (k 2 ) N 1 N 1 techniques. 1 2 (2n1 1)k 1 In similar line, contrast based image fusion algorithm in (k 1 ) (k 2 ) X (k 1 , k 2 ) cos k 0 k 0 2 N DCT domain has been presented [8] to fuse the out of focus 1 2 1 images. Local contrast is measured by 8x8 blocks. However, (2n 1)k 0 n1 N 1 1 there is no discussion on the fusion performance by choosing cos 2 2 , 2 N 0 n N 1 different block sizes. The present paper presents six different 2 2 2 (2) DCT based image fusion techniques and studies their performance. III. CONTRAST MEASURE II. DISCRETE COSINE TRANSFORM DCT decomposes the image/block into a series of waveforms, Discrete cosine transform (DCT) is an important transform each with a particular frequency. DCT coefficients are extensively used in digital image processing. Large DCT segregated into 21N different frequency bands for image or coefficients are concentrated in the low frequency region; th block of size NxN . The m band is composed of the hence, it is known to have excellent energy compactness properties [9-11]. The 2D discrete cosine transform coefficients with m k12 k . The contrast measure at each X (k 1 , k 2 ) of an image or 2D signal x(n1 , n 2 ) of size coefficient in the band is computed as [15-17]: N xN is defined as [12-14]: 1 2 X ( k , k ) C ( k , k ) 12 12 m 1 X (k 1 , k 2 ) (k 1 ) (k 2 ) E j N 1 1 N 2 1 j 0 (2n1 1)k 1 (3) x(n1 , n 2 ) cos 2 N (1) n1 0 n 2 0 1 X ( p,t ) 0 k N 1 Where j t p and j1 j N (2n 2 1)k 2 1 1 E j Y cos , Y 2( N 1 ) j 1 j N 2 N 2 0 k 2 N 2 1 (4) th E j is the average amplitude over a j spectral band. The DCT output for image or block size of 8x8 is shown in Fig-1. It also illustrates the 1st and 5th bands (enclosed with rectangles). VPS Naidu DCT av: In this fusion rule, all DCT coefficients from both E image blocks are averaged to get fused DCT coefficients. It is E1 5 X(,)X(,)X(,)X(,)X(,)X(,)X(,)X(,)00 01 02 03 04 05 06 07 very simple and basic image fusion technique in DCT domain. X(,)X(,)X(,)X(,)X(,)X(,)X(,)X(,)10 11 12 13 14 15 16 17 X(k,kf 1 2 )05 . X(k,k1 1 2 ) X(k,k 2 1 2 ) (5) X(,)X(,)X(,)X(,)X(,)X(,)X(,)X(,)20 21 22 23 24 25 26 27 Where k,k12 0 ,, 1 2 ,...,N 1 X(,)X(,)X(,)X(,)X(,)X(,)X(,)X(,)30 31 32 33 34 35 36 37 X DCTma: The DC components from both image blocks are X(,)40 X(,)X(,)X(,)X(,)X(,)X(,)X(,)41 42 43 44 45 46 47 averaged. The largest magnitude AC coefficients are chosen, since the detailed coeficients correspond to sharper brightness X(,)X(,)X(,)X(,)X(,)X(,)X(,)X(,)50 51 52 53 54 55 56 57 changes in the images such as edges and object boundaries etc. These coeficients are fluctuating around zero. X(,)X(,)X(,)X(,)X(,)X(,)X(,)X(,)60 61 62 63 64 65 66 67 X(,).X(,)X(,)0 0 0 5 0 0 0 0 X(,)X(,)X(,)X(,)X(,)X(,)X(,)X(,)70 71 72 73 74 75 76 77 f 12 (6a) X(k,k) X(k,k) X(k,k) Fig-1 DCT output of an image or a bock size of 8x8 1 1 2 1 1 2 2 1 2 X ( k ,k ) f 12 X(k,k) X(k,k) X(k,k) IV. IMAGE FUSION 2 1 2 1 1 2 2 1 2 (6b) Six different types of image fusion techniques using DCT are Where k,k1 , 2 , 3 ,...,N 1 12 presented in this section. Image to be fused are divided into non-overlapping blocks of size NxN as shown in Fig-2. DCT DCTah: The lowest AC components including DC coefficients coefficients are computed for each block and fusion rules are are averaged and the remaining AC coefficients are chosen applied to get fused DCT coefficients. IDCT is then applied on based on largest magnitude. the fused coefficients to produce the fused image/block. The procedure is repeated for each block. X(k,kf 1 2 )05 . X(k,k1 1 2 ) X(k,k 2 1 2 ) (7a) Where k,k12 0 ,,,...,.N 1 2 0 5 1 CT (7b) Where k,k0 .N,. 5 0 5 1 ,.N 0 5 2 ,...,N 1 12 T DCTcm: The DC coefficients are averaged and the AC coefficients are chosen based on largest contrast measure. CT (8a) X(k,k1 1 2 ) C(k,k 1 1 2 ) C(k,k 2 1 2 ) Xf ( k12 ,k ) X(k,k2 1 2 ) C(k,k 1 1 2 ) C(k,k 2 1 2 ) (8b) Fig-2 Framework of DCT based image fusion algorithm Where k,k12 1 , 2 , 3 ,...,N 1 The following fusion rules are used in image fusion process. DCTch: It is very much similar to DCT ah. The lowest AC components including DC coefficients are averaged and the Let the X1 be the DCT coefficients of image block from image remaining AC coefficients are chosen based on largest contrast I1 and similarly let the X 2 be the DCT coefficients of image measure. block from image I . Assume the image block is of size 2 (9a) NxN and X f be the fused DCT coefficients. Where 36 Discrete Cosine Transform based Image Fusion Techniques X(k,k1 1 2 ) C(k,k 1 1 2 ) C(k,k 2 1 2 ) 2 : Variance of Xf ( k12 ,k ) It X(k,k ) C(k,k ) C(k,k ) 2 1 2 1 1 2 2 1 2 (9b) 2 : Variance of If Where If : Covariance of and DCTe: It is similar to DCTcm. DC components are averaged IItf together. AC coefficients correspond to the frequency band 2 2 having largest energy is chosen. c1 (0 . 01 L ) and c3 (0 . 03 L ) are the constants to stabilize the division with weak denominator (10a) X1 ( k 1 , k 2 ) Ejj 1 E 2 When the ground truth image is not available, the following metrics can be used to evaluate the proposed six fusion Xf ( k12 , k ) algorithms. X2 ( k 1 , k 2 ) Ejj 1 E 2 (10b) X(,).X(,)X(,)f 10. 0Spatial 0 5 Frequency12 0 0 [6,21] 0 0 Where and j k12 k The frequency in spatial domain indicates the overall activity level in the fused image and it is computed as V. FUSION EVALUATION METRICS Row frequency: MN11 1 2 (13a) The following fusion evaluation metrics are used to evaluate RF I(i,j)I(i,jff1 ) MN the performance of the developed six image fusion algorithms. ij01 When the ground truth image is available: Column frequency: NM11 1. Peak Signal to Noise Ratio (PSNR) [3,6,18] 1 2 (13b) CF I(i,j)I(iff1 ,j) PSNR value will be high when the fused and the ground MN ji01 truth images are comparable. Higher value implies better fusion. The peak signal to noise ratio is computed as: Spatial frequency: SF RF 2 CF 2 (14) The fused image with high SF would be considered. 2 L PSNR 20 log (11) 10 M N 2. Fusion quality index [22] 1 2 The range of this metric is 0 to 1. One indicates the fused image I r (i, j) I f (i, j) MN i 1 j 1 containsk,k 12all the information0 .N,.
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