A Novel Metric for Performance Evaluation of Image Fusion Algorithms

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1 Vol:, o:7, 2007 A ovel Metric for Performance Evaluation of Image Fusion Algorithms edeljko Cvejic, Artur Łoza, David Bull, and ishan Canagarajah International Science Index, Computer and Information Engineering Vol:, o:7, 2007 waset.org/publication/8392 Abstract In this paper, we present a novel objective nonreference performance assessment algorithm for image fusion. It takes into account local measurements to estimate how well the important information in the source images is represented b the fused image. The metric is based on the Universal Image Qualit Index and uses the similarit between blocks of pixels in the input images and the fused image as the weighting factors for the metrics. Experimental results confirm that the values of the proposed metrics correlate well with the subjective qualit of the fused images, giving a significant improvement over standard measures based on mean squared error and mutual information. Kewords Fusion performance measures, image fusion, nonreference qualit measures, objective qualit measures. I. ITRODUCTIO MAGE and video fusion is emerging as a vital technolog I in man militar, surveillance and medical applications. It is a subarea of the more general topic of data fusion, dealing with image and video data [,2]. The abilit to combine complementar information from a range of distributed sensors with different modalities can be used to provide enhanced performance for visualization, detection or classification tasks. Multi-sensor data often present complementar information about the scene or object of interest, and thus image fusion provides an effective method for comparison and analsis of such data. There are several benefits of multi-sensor image fusion: wider spatial and temporal coverage, extended range of operation, decreased uncertaint, improved reliabilit and increased robustness of the sstem performance. In several application scenarios, image fusion is onl an introductor stage to another task, e.g. human monitoring. Therefore, the performance of the fusion algorithm must be measured in terms of improvement in the following tasks. For example, in classification sstems, the common evaluation measure is the number of the correct classifications. This sstem evaluation requires that the true correct classifications are known. However, in experimental setups the ground-truth data might not be available. Authors are with the Centre for Communications Research, Universit of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 UB, United Kingdom, (Corresponding author phone: ; fax: , n.cvejic@bristol.ac.uk). This work has been funded b the UK Ministr of Defence Data and Information Fusion Defence Technolog Centre. In man applications the human perception of the fused image is of fundamental importance and as a result the fusion results are mostl evaluated b subjective criteria [3,4]. Objective image fusion performance evaluation is a tedious task due to different application requirements and the lack of a clearl defined ground-truth. Various fusion algorithms presented in the literature [5] have been evaluated objectivel b constructing an ideal fused image and using it as a reference for comparison with the experimental results [6,7]. Mean squared error (MSE) based metrics were widel used for these comparisons. Several objective performance measures for image fusion have been proposed where the knowledge of ground-truth is not assumed. In [8], authors used the mutual information as a parameter for evaluation of the fusion performance. Xdeas and Petrovic [9] proposed a metric that evaluates the relative amount of edge information that is transferred from the input images to the fused image. In this paper, we present a novel objective non-reference qualit assessment algorithm for image fusion. It takes into account local measurements to estimate how well the important information in the source images is represented b the fused image, while minimizing the number of artefacts or the amount of distortion that could interfere with interpretation. Our qualit measures are based on an image qualit index proposed b Wang and Bovik [0]. II. DEFIITIO OF THE UIVERSAL IMAGE QUALITY IDEX The measure that was used as the basis for our objective performance evaluation of image fusion is the Universal Image Qualit Index (UIQI) [0]. The authors compared the proposed qualit index to the standard MSE objective qualit measure and the main conclusion was that their new index outperforms the MSE, due to the UIQI s abilit in measuring structural distortions [0]. Let X={x i i=,2,,} and Y={ i i=,2,,} be the original and the test image signals, respectivel. The proposed qualit index is defined as [0]: 4 x x Q = () ( x + )( [ x) + ( ) ] where x = xi, = i i= i= x = ( xi x), = ( i ) (2) i= i= x = ( xi x)( i ) i= International Scholarl and Scientific Research & Innovation (7) scholar.waset.org/ /8392

2 Vol:, o:7, 2007 International Science Index, Computer and Information Engineering Vol:, o:7, 2007 waset.org/publication/8392 The dnamic range of Q is [-,]. The best value is achieved if and onl if i =x i for all i=,2,. The lowest value of - occurs when i =2 x -x i for all i=,2,. This qualit index models image distortions as a combination of three different factors: loss of correlation, luminance distortion and contrast distortion. In order to make this more understandable, the definition of Q can be rewritten as a product of three components: x 2x 2 x Q = (3) x ( x) + ( ) x + The first component is the correlation coefficient between X and Y and its dnamic range is [-,]. The best value is obtained when i =ax i +b for all i=,2,, where a and b are constants and a>0. Even if X and Y are linearl related, there still might be relative distortions between them and these are evaluated in the second and third component. The second component with a value range of [0,] measures how close the mean luminance is between X and Y. It equals if and onl if x =. x and can be viewed as an estimate of the contrast of X and so the third component measures how similar the contrasts of the images are. The range of values for the third component is also [0,], where the best value is achieved if and onl if x =. Since images are generall non-stationar signals, it is appropriate to measure Q 0 over local regions and then combine the different results into a single measure Q. In [0] the authors propose to use a sliding window: starting from the top-left corner of the two images X, a sliding window of a fixed size block b block over the entire image until the bottom-right corner is reached. For each window w the local qualit index Q 0 (X,Y w) is computed for the pixels within the sliding window w. Finall, the overall image qualit index Q is computed b averaging all local qualit indices: Q ( x, ) = Q ( a, b w) (4) 0 W w W where W is the famil of all windows and W is the cardinalit of W. Wang and Bovik [0] have compared (under several tpes of distortions) their qualit index with existing image measures such as MSE as well as with subjective evaluations. The tested images were distorted b: additive white Gaussian noise, blurring, contrast stretching, JPEG compression, salt and pepper noise, mean shift and multiplicative noise. The main conclusion was that UIQI outperforms the MSE, which due to the index s abilit of measuring structural distortions, in contrast to the MSE which is highl sensitive to the energ of errors. In order to appl the UIQI for image fusion evaluation, Piella and Heijmans [] introduce salient information to the metric. Q ( X, F ) = c( w) ( λ Q( X, + ( λ) Q( ) (5) p w W where X and Y are the input images, F is the fused image, c(w) is the overall salienc of a window and λ is defined as: s( X w) λ =. (6) s( X w) + s( Y w) λ should reflect the relative importance of image X compared to image Y within the window w. s(x w) denotes salienc of image X in window w. It should reflect the local relevance of image X within the window w, and it ma depend on e.g. contrast, sharpness, or entrop. As with the previous metrics, this metric does not require a ground-truth or reference image. Finall, to take into account some aspect of the human visual sstem (HVS) which is the relevance of edge information, the same measure is computed with the edge images (X, Y and F ) instead of the gre-scale images X, Y and F. α α QE ( X, Y, F ) = Q p ( X, Y, F ) Q p ( X ', Y ' F ') (7) where α is a parameter that expresses the contribution of the edge images compared to the original images. III. PROPOSED IMAGE FUSIO PERFORMACE METRICS In the computation of Piella s metric parameter λ in equation (4) is computed with s(x w) and s(y w) being the variance (or the average in the edge images) of images X and Y within window w, respectivel. Therefore, there is no clear measure of how similar each input image is to the final fused image. Each time the metric is calculated, an edge image has to be derived from the input images, which adds significantl to the computational complexit of the metric. In addition, the metrics calculated and presented in [] are onl for one window size (8x8). The window size has a significant influence on this fusion performance measure, as the main weighting factor is the ratio of the variances of the input images which tend to var significantl with the window size. We propose a novel fusion performance measure that takes into account the similarit between the input image block and the fused image block within the same spatial position. It is defined as: Qb X, F = sim( X, F wq ) X, F w + ( sim( X, F w)) Q( F w w W = sim( X, ( Q( X, Q( ) + Q( ( ) ( ) ) w W (8) where X and Y are the input images, F is the fused image, w is the analsis window and W is the famil of all windows. We define sim(x,f w) as: 0 if < 0 + f (9) sim ( X, Y, = if 0 + f + f if > + f where uv = ( ui u )( vi v ) (0) i= Each analsis window is weighted b the sim(x,f w) that is dependent on the similarit in spatial domain between the input image and the fused image. The image block from two of the input images that is more similar to the fused image block is assigned a larger weighting factor used for calculation of the fusion performance metric. The impact of the less similar block is accordingl decreased. In this sense, we are able to measure more accuratel the fusion performance, especiall in an experimental setup where the input images are distorted versions of the ground-truth data; obtained b e.g. blurring, JPEG compression, noise addition, mean shift, etc. International Scholarl and Scientific Research & Innovation (7) scholar.waset.org/ /8392

3 Vol:, o:7, 2007 International Science Index, Computer and Information Engineering Vol:, o:7, 2007 waset.org/publication/8392 The sim(x,f w) function is designed to have the upper limit at one, so that impact of the less significant block is completel eliminated when the other input block similarit measure equals one. Calculation of the sim(x,f w) function is computationall significantl less demanding, compared to the metrics proposed in [8] and []. IV. EXPERIMETAL RESULTS In this section we test the proposed fusion qualit measure in Eq. (8) to evaluate several multiresolution (MR) image fusion algorithms and compare it to standard objective image metrics. The MR-based image fusion approach consists of performing an MR transform on each input image and, following specific rules, combining them into a composite MR representation. The composite image is obtained b appling the inverse transform on this composite MR representation [2]. During the tests we use the simple averaging method, the ratio pramid, Principal Component Analsis (PCA) method and the discrete wavelet transform (DWT), and in all MR cases we perform 5-level decomposition. We perform the fusion of the coefficients of the MR decomposition of each input image b selecting at each position the coefficient with a maximum absolute value, except for the coefficients from the lowest resolution where the fused coefficient equals to the mean value of the coefficients in that subband. The first pair of test images used is the complementar pair shown in the top row of Fig.. The test images have been created artificiall b blurring the original Goldhill image of size 52x52, using Gaussian blurring with a radius of 0 pixels. The images are complementar in the sense that the blurring takes place at the complimentar horizontal strips in the first and the second image, respectivel. The fused images obtained b the average method, the ratio pramid, the PCA method and DWT domain fusion are depicted in the first and the second row, from left to right. Table compares the qualit of these composite images using our proposed qualit measures. The first three rows correspond to the proposed fusion qualit measure, as defined in Eq. (4). The rows 4 to 6 show the proposed fusion performance measure defined in Eq. (8). The proposed metrics are calculated for three window sizes: 4x4, 8x8 and 6x6 pixels, in order to examine the dependence of the metric s output values versus the analsis window size. For comparison, we also compute the PSR between the original Goldhill image and each of the generated fused images. In real life image fusion scenarios we do not have access to the original image, so the PSR value is provided just as a reference. In addition, we have provided as references the fusion performance metric developed b Petrovic and Xdeas [8] (given in the fourth row of the Table -3) and the metric based on mutual information [9] (the fifth row of the Table -3). Petrovic and Xdeas metric measures the amount of edge information transferred from the source image to the fused image in order to give an estimation of the performance of the fusion algorithm. It uses a Sobel edge operator to calculate the strength and orientation information of each pixel in the input and output images. In this method the visual information is primaril associated with the edge information, while the region information is ignored. More precisel, the results in the fifth row of Table have been obtained b adding the mutual information between the composite image and each of the inputs and dividing it b the sum of the entropies of the inputs: I( X, F) + I( F) MI( X, F) = () H ( X ) + H ( Y ) where I(X,F) is the mutual information between X and F,and H(X) the entrop of X. In this wa, the measure is normalized to the range [0,]. The following two pairs of input images are contaminated b or Gaussian additive noise (Fig.2) and Salt and Pepper (SP) noise (Fig.3). Although the additive noise can be tackled b performing hard thresholding of the parameters in the transform domain and SP noise b median filtering we did not perform denoising in order to get more balanced data for the proposed metric. The results for the nois input images are given in the Table 2 and Table 3 for the image distorted b Gaussian additive noise and SP noise, respectivel. TABLE I COMPARISO OF DIFFERET OBJECTIVE QUALITY MEASURES FOR THE COMPOSITE IMAGES I FIG. metrics average ratio PCA DWT Q b (4x4) Q b (8x8) Q b (6x6) Petrovic MI PSR (db) TABLE II COMPARISO OF DIFFERET OBJECTIVE QUALITY MEASURES FOR THE COMPOSITE IMAGES I FIG. 2 metrics average ratio PCA DWT Q b (4x4) Q b (8x8) Q b (6x6) Petrovic MI PSR (db) TABLE III COMPARISO OF DIFFERET OBJECTIVE QUALITY MEASURES FOR THE COMPOSITE IMAGES I FIG. 3 metrics average ratio PCA DWT Q b (4x4) Q b (8x8) Q b (6x6) Petrovic MI PSR (db) Test results show that the DWT domain fusion visuall outperform the other three schemes. It is most noticeable as, International Scholarl and Scientific Research & Innovation (7) scholar.waset.org/ /8392

4 Vol:, o:7, 2007 International Science Index, Computer and Information Engineering Vol:, o:7, 2007 waset.org/publication/8392 for instance, the blurring (e.g., edges in the background and small details) and the loss of texture in the fused image obtained b the ratio pramid and averaging. Furthermore, in the ratio-pramid method fused image, some details of the images and background have been completel lost, and in the average composite image, the loss of contrast is ver evident. These subjective visual comparisons agree with b the results obtained b the proposed metric, presented in Table -3. ote that the proposed metric has ver similar qualit measures as the Petrovic s metric and that these two metrics considerabl outperform the MI measure and PSR. It is clear from the experiments that MI metric and PSR often assign the highest value of the fusion performance measure to the algorithm that does not perform well in the subjective terms. The values obtained from the proposed metrics correlate well to the subjective qualit of the fused images, which was not achievable b the standard MI fusion performance measure and PSR. In addition, the proposed metrics is not significantl dependent on the size of the analsis window as the difference in fusion performance does not change extensivel with the variation of window size. V. COCLUSIO We present a novel objective non-reference performance assessment algorithm for image fusion. It takes into account local measurements to estimate how well the important information in the source images is represented b the fused image. Experimental results confirm that the values of the proposed metrics correlate well with the subjective qualit of the fused images, giving a significant improvement over standard measures based on mean squared error and mutual information. Compared to alread presented fusion performance measures [8,], it obtains comparable results with considerabl decreased computational complexit. Further research will focus on how to select the salient points in order to optimize the fusion performance. Another extension of the work will be performance measure based on regions of the image, obtained b segmentation of the input images, rather than calculating the measure in square windows. REFERECES [] H. Maitre and I. Bloch, Image fusion, Vistas in Astronom, Vol. 4, o. 3, pp , 997. [2] S. ikolov, P. Hill, D. Bull, and. Canagarajah, Wavelets for image fusion, Wavelets in Signal and Image Analsis, Kluwer, Dordrecht, The etherlands, pp , 200. [3] D. Ran and R. Tinkler, ight pilotage assessment of image fusion, Proc. SPIE, Vol. 2465, Orlando, FL, pp , 995. [4] A. Toet and E. M. Franken "Perceptual evaluation of different image fusion schemes", Displas, Vol. 24, o., pp , [5] G. Piella, "A general framework for multiresolution image fusion: from pixels to regions", Information Fusion, Vol. 9, pp , [6] H. Li, B. S. Manjunath, and S. K. Mitra, "Multisensor image fusion using the wavelet transform", Graphical Models and Image Processing, Vol. 57, o. 3, pp , 995. [7] O. Rockinger, Image sequence fusion using a shift invariant wavelet transform. Proc. IEEE International Conference on Image Processing, Washington, DC, pp , 997. [8] C. Xdeas and V. Petrovic "Objective pixel-level image fusion performance measure", In Proc. SPIE, Vol. 405, Orlando, FL, pp , 2000 [9] G. H. Qu, D. L. Zhang, and P. F. Yan Information measure for performance of image fusion, Electronics Letters, Vol. 38, o. 7, pp , [0] Z. Wang and A. C. Bovik. A universal image qualit index IEEE Signal Processing Letters, Vol. 9, o. 3, pp. 8 84, [] G. Piella and H. Heijmans, "A new qualit metric for image fusion" In Proc. Int. Conf. Image Processing, Barcelona, Spain, pp. 73-6, International Scholarl and Scientific Research & Innovation (7) scholar.waset.org/ /8392

5 International Science Index, Computer and Information Engineering Vol:, o:7, 2007 waset.org/publication/8392 World Academ of Science, Engineering and Technolog Vol:, o:7, 2007 Fig. Fusion results, the original image blurred in stripes. Top: input image X (one half of stripes in the original image blurred, left), input image Y (other half of stripes in the original image blurred, middle), fused image F using averaging (right). Bottom: fused image F using ratio pramid decomposition (left), fused image F using the PCA decomposition (middle), fused image F using DWT domain fusion (right) Fig. 2 Fusion results, the original image corrupted b additive Gaussian noise and partial blurring. Top: input image X (the original image with added noise and a blurred segment, left), input image Y (the original image with added noise and another blurred segment, middle), fused image F using averaging (right). Bottom: fused image F using ratio pramid decomposition (left), fused image F using the PCA decomposition (middle), fused image F using DWT domain fusion (right) International Scholarl and Scientific Research & Innovation (7) scholar.waset.org/ /8392

6 International Science Index, Computer and Information Engineering Vol:, o:7, 2007 waset.org/publication/8392 World Academ of Science, Engineering and Technolog Vol:, o:7, 2007 Fig. 3 Fusion results, the original image corrupted b the salt and pepper noise and partial blurring. Top: input image X (the original image with added noise and a blurred segment, left), input image Y (the original image with added noise and another blurred segment, middle), fused image F using averaging (right). Bottom: fused image F using ratio pramid decomposition (left), fused image F using the PCA decomposition (middle), fused image F using DWT domain fusion (right) International Scholarl and Scientific Research & Innovation (7) scholar.waset.org/ /8392