New approach to multispectral image fusion based on a weighted merge

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  • 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN INTERNATIONAL JOURNAL OF ELECTRONICS AND 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMECOMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)ISSN 0976 – 6464(Print)ISSN 0976 – 6472(Online)Volume 4, Issue 1, January- February (2013), pp. 25-34 IJECET© IAEME: Impact Factor (2012): 3.5930 (Calculated by GISI) © NEW APPROACH TO MULTISPECTRAL IMAGE FUSION BASED ON A WEIGHTED MERGE Benayad NSIRI1, Salma NAGID1, Najlae IDRISSI2 1 (LIAD Faculty of Science Ain Chock, University Hassan II Ain Chock, Casablanca 20100, Morocco, 2 (TIT-Team Faculty of Sciences and Techniques, University Sultan Moulay Slimane, Beni-Mellal,B.P 523 Mguilla, Morocco, ABSTRACT Multispectral image fusion seeks to combine information from different images to obtain more relevant information than can derive from a single one. A wide variety of approaches addressing fusion at pixel level has been developed, but they suffer from several disadvantages, (1) the number of bands merging is limited, (2) color distortion, (3)Spectral content of small objects often lost in the fused images. The paper presents a new approach of image fusion based on a weighted merge of multispectral bands, each band is modeled by two or three Gaussian distributions, the mixture parameters (weights, mean vectors, and covariance matrices) are estimated by the Expectation Maximization algorithm (EM) which maximizes the log-likelihood criterion, the weighted coefficients of each band are extracted from the degree of similarity between this one and the other bands, it’s calculated by a cost function based on the distance between the parameters of the Gaussian distribution of each band. In our work we use an Extended Malhanobis distance. This cost function allows us to reduce data redundancy and given greater weight to the complementary data. We applied this approach to MRI and satellite images by using respectively a weighted average and weighted color composite method, the given results are promising. Keywords : Pixel-based Image Fusion, Expectation Maximization, Multispectral Merge, Mixture of Gaussian distributions, Image Similarity. 25
  • 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMEI. INTRODUCTION The goal of image fusion[1][2][3] is to combine information from two or more images of a scene into a single composite image that is more informative and is more suitable for visual perception or further image-processing tasks. However, the information provided by different images may be complementary and redundant. The fusion at pixel level is traditionally handled by the Multiscale Decomposition based methods, the principal component analysis (PCA) methods, the color composite transform method. Multiscale transforms combine the multiscale decomposition of the source images[18], this approach, constructs a composite representation of multiscale transform on the source images using some sort of fusion rule, and then construct the fused image by applying the inverse multiscale transform. Pyramid transforms and wavelet transforms [29][30] are the most commonly used multiscale decomposition fusion methods. A pyramid transforms fusion consists of a number of images at different scales which together represent the original image; the Laplacian Pyramid is an example of a pyramid transform. Each level of the Laplacian Pyramid is constructed from its lower level using blurs, size reduction, and interpolation and differencing in this order [18]. Alternative pyramid transforms are contrast pyramid which preserves local luminance contrast in the source images [19], and finally a gradient pyramid applies the gradient operator on each level of the Gaussian pyramid representation [20]. Discrete Wavelet transforms are a type of multi-resolution function approximation that allow for the hierarchical decomposition of a an image [21][22][18]. The wavelet transforms W are first calculated for two input images ‫ܫ‬ଵ ሺ݅, ݆ሻ and ‫ܫ‬ଶ ሺ݅, ݆ሻ, then the results are combined using the ߔ fusion rules. Finally, the inverse wavelet transform ܹ ିଵ is computed and the image fusion ‫ܫ‬ሺ݅, ݆ሻ is re-constructed. The wavelet transform has several advantages over other pyramid-based transforms: It provides a more compact presentation, separate spatial orientation in different bands, and decorrelates interesting attributes in the original image. PCA (Principal Component Analysis)[26] is a general statistical technique which transforms multivariate data with correlated variables into multivariate data with uncorrelated ones. These new variables are obtained as a linear combination of the original variables. The PCA have been used to fuse the images by two ways researchers. The first approach assigns the first principal component (PC) band to one of the RGB bands and the second component to another RGB band in a color composite technique while the second method separates the first and the second PCs to intensity and hue band in an IHS image [23][24]. The color composite method [25], assigns in order the first, the second and the third band to the R, B and G channel. It will work well if we merge three images but problems occur beyond this number. To overcome these problems we developed during earlier work a new method termed a color composite Composed CCC (4) [9] that is an extension of the color composite method for merging four bands. The principle is to give each band a certain coefficient αi during the merge. Suppose that we have four images ሺ‫ܫ‬ଵ , ‫ܫ‬ଶ , ‫ܫ‬ଷ , ‫ܫ‬ସ ሻ to merge, the merger will be done as follows: ܴ ߙଵ . ‫ܫ‬ଵ ൅ ߙଶ . ‫ܫ‬ଶ ൥‫ ܩ‬൩ ൌ ൥ߙଷ . ‫ܫ‬ଶ ൅ ߙସ . ‫ܫ‬ଷ ൩ …..……………………... (1) ‫ܤ‬ ߙହ . ‫ܫ‬ଷ ൅ ߙ଺ . ‫ܫ‬ସ 26
  • 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME We can see from (1) that we use a weighted fusion by a set of constant coefficients αi , where : {αi /i = {1..6}} = {0.75, 0.25, 0.50, 0.50, 0.25, and 0.75} ……………….... (2) This method has given promising results in view of the amount of information retrieved, but it remains limited by the number of bands to fuse (increasing number of bands will cause a color distortion) and the management of complementary and of redundant data. Despite the advantages of the pixel level methods they still suffer from several disadvantages, (1) the number of bands merging is limited, (2) color distortion, (3) Spectral content of small objects often lost in the fused images. In this paper we develop a new approach that addresses both the problem of band numbers and the weight assigned to each band according to the information it contains and its reliability with other bands. The idea is to give a weight to the images during the merger process to handle the redundancy and complementarily of data. Two ways are addressed to compare our approach with the PCA: visual evaluation and quantitative evaluations-based on RMSE and UIQI indexes quality. The results are promising. The remainder of this paper is organized as follows. In Section 2, we explain our fusion method in detail, including how to select the similarity characteristics of source images, obtain the weight of each image, and fuse images. Section 3, provides the simulation scenarios and evaluates the results. Finally, conclusions are drawn in Section 4.II. THE WEIGHTED MERGING OF BANDS 1. The image modeling by mixture of Gaussian distributions A Gaussian mixture model is a weighted sum of k component Gaussian densities given by the equation ݂൫‫⁄ݔ‬Θ୮ ൯ ൌ ∑௣ ߙ௞ ݂௞ ሺ‫⁄ݔ‬Θ୩ ሻ ൌ ∑௣ ߙ௞ ݂௞ ൫‫⁄ ݔ‬µ୩ , Σ௞ ൯ …………….. (3) ௞ୀଵ ௞ୀଵ Where p is the numbers of components in the mixture, (α k ≥ 0) are the mixing proportions of components satisfyingΣ௣ ߙ௞ ൌ 1, and each component density ݂௞ ൫‫⁄ݔ‬µ୩ , Σ௞ ൯ is a Gaussian ௞ୀଵ probability density function given by ଵ ݂௞ ൫‫⁄ ݔ‬µ୩ , Σ௞ ൯ ൌ ሺଶగሻ೙/మ |Σ exp ሺെ1⁄2ሻሺx െ µ୩ ሻ் Σିଵ ൫‫ ݔ‬െ µ୩ ൯ሻ ………….. (4) ௞ ೖ| భ/మ Where ݊ is the dimensionality of the vector x, µ୩ is the mean vector and Σ௞ is the covariance matrix assumed to be positive definite. We suppose Θ୮ the collection of all the parameters in the mixture Θ୮ ൌ ሺߠଵ , … , ߠ௣ , ߙଵ , … ߙ௣ ሻ the log-likelihood function for the Gaussian mixture mo Del of a set of ܰ i.i.d. samples, ܺ ൌ ሼ‫ݔ‬௜ ሽே is ௜ୀଵ log ሺ݂ሺܺ⁄Θ୮ ሻሻ ൌ ݈‫݃݋‬ሺΠ୒ ሺ‫ݔ‬௜ ⁄Θ୮ ሻሻ ൌ ∑ே ݈‫݃݋‬ሺ∑ே ߙ௞ ݂ሺ‫ݔ‬௜ ⁄ߠ௞ ሻሻ ……………. ୧ୀଵ ௜ୀଵ ௜ୀଵ (5) 27
  • 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMEThen we maximize (5) to get a Maximum Likelihood (ML) and estimate of Θ୩ via the EMalgorithm as follow: ߙ௞ ൌ 1⁄݊ ∑ே ݂ ሺ݇ ⁄‫ݔ‬௜ ሻ ௜ୀଵ ………………………………….. (6) ∑ಿ ௫ೖ ௙ሺ௞⁄௫೔ ሻ ߤ௞ ൌ ೔సభ ∑ಿ ௙ሺ௞⁄௫೔ ሻ ……………………………………… (7) ೔సభ ሺ∑ಿ ௙ሺ௞⁄௫೔ ሻሺ௫೔ିఓ೔ ሻሺ௫೔ ିఓ೔ ሻ೅ ሻ Σ௞ ൌ ೔సభ ∑ಿ ௙ሺ௞⁄௫೔ ሻ .....…………………….. (8) ೔సభWhere ݂௞ ሺ݇ ⁄x୧ ሻ ൌ ߙ௞ fሺx୧ ⁄θ୩ ሻ/ ∑୧ୀଵ ߙ௞ ݂ሺx୧ ⁄θ୩ ሻ are the posterior probabilities ୮ 2. Distance measures between Gaussian Mixtures ModelsThe Extended Mahalanobis distance metric is an extension of a distance measure betweentwo distributions (in our case a Gaussian distribution).The Extended Mahalanobis distance is based on the statistical distribution of data and not ondata directly. We consider two Gaussian distributions ܰଵ ሺߤଵ , Σଵ ሻ and ܰଶ ሺߤଶ , Σଶ ሻ, the measurebetween the two distributions is defined as follows: ‫ܦ‬ሺܰଵ , ܰଶ ሻ ൌ ඥሺߤଵ െ ߤଵ ሻ் ሺΣଵ ൅ Σଶ ሻିଵ ሺߤଵ െ ߤଶ ሻ ………………….. (9)However, this measure creates a singularity for singular covariance matrices. In practicalproblems it often appears in learning such models mixture. The acquired covariance matrix isnot always conditioned and their inversion creates a problem. In our implementation, wereplace the inverse of singular covariance matrix by its pseudo inverse. Singular valuedecomposition is used for the calculation of the pseudo inverse. Round of errors can lead to asingular value not being exactly zero even if it should b e. Tolerance parameter places athreshold when comparing singular values with zero and improves the numerical stability ofthe method with singular or near-singular matrices. 3. Approach and Conception of the Proposed Method The computation of co efficients fusion is based on the degrees of similarity betweenimages to b e merged and the quantity of additional information provided with each one. a. Extraction of parameters and the cost function Each image is modelled by a mixture of two Gaussian distributions. This modelingconsists in estimating the parameters of the mixture (weight, mean vectors, and covariancematrix).We calculate the distance of Malhanobis Dij between each two models. 28
  • 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME ் ‫ܦ‬൫ܰ௜ , ܰ௝ ൯ ൌ ට൫ߤ௜ െ ߤ௝ ൯ ሺΣ௜ ൅ Σ௝ ሻିଵ ൫ߤ௜ െ ߤ௝ ൯ ……………………….. (10)ܰ௜ ሺߤ௜ , Σ௜ ሻ : The Gaussian distribution of image݅.We calculate the weighted coefficients ݀௜ of each image by the cost function as follows: ݀௜ ൌ ൛max൫‫ܦ‬௜௝ ൯ /ሺ݅ ് ݆ሻൟ ………………………….. (11)Where ݀௜ is the weighted coefficient of the fusion attributed to the image ݅ each coefficientthen attributes to its image, and used in the fused rule.We normalize the d i distances, we got: ௗ೔ ߙ௜ ൌ ∑೙ ೔సభ ௗ೔ …………………………………….. (12)ߙ௜ : The normalized weighted coefficient of the ݅ image.In the following we call ߙ௜ the weighted coefficients and we use it on the fusion rules. b. Application to some fusion rulesWe consider ሼ‫ܫ‬ଵ , … , ‫ܫ‬௡ ሽ the set of images to fuse, and ሺߙଵ , … ߙ௡ ሻ the set of weightedcoefficients of the images to fuse. • Weighted averaging ‫ ܫ‬ൌ ∑௡ ߙ௜ ‫ܫ‬௜ ………………………………….. (13) ௜ୀଵ • Weighted color composite ܴ ൌ ∑௞ ߙ௜ ‫ܫ‬௜ ൅ ߦଵ ‫ܫ‬௞ାଵ ………………………………….. (14) ௜ୀଵWhere ∑௞ ߙ௜ ௜ୀଵ ൅ ߦଵ ൌ 1 ‫ ܩ‬ൌ ሺߙ௞ାଵ െ ߦଵ ሻ‫ܫ‬௞ାଵ ൅ ∑௞ା௠ ߙ௜ ‫ܫ‬௜ ൅ ߦଶ ‫ܫ‬௞ା௠ାଵ ……………. (15) ௜ୀ௞ାଶWhere ∑௞ା௠ ߙ௜ ൅ ߦଶ ൅ ሺߙ௞ାଵ െ ߦଵ ሻ ൌ 1 ௜ୀ௞ାଶ ‫ ܤ‬ൌ ∑௡ ௜ୀ௞ା௠ାଶ ߙ௜ ‫ܫ‬௜ ൅ ሺߙ௞ା௠ାଵ െ ߦଶ ሻ‫ܫ‬௞ା௠ାଵ …………… (16)The sum of coefficients ߙ௜ attributed to each band must b e equal to 1, when∑௞ ߙ௜ ൏ 1, we ௜ୀଵcan add a constant ߦ௧ to have∑௞ ߙ௜ ൅ ߦ௧ଵ ൌ 1. ௜ୀଵ We use a ߦଵ quantity of the information from the image ݇ ൅ 1 in the band ܴ and ሺߙ௞ାଵ െ ߦଵ ሻof its information in the band‫.ܩ‬ 29
  • 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMEIII. EXPERIMENTAL RESULTS Evaluation results can be achieved in two ways visual and quantitative. 1. Visual evaluation a. Brain MRI images Figure 1 show four types of Brain MRI images (T1, PD, T 2, MRGad) used in the fusion process. The corresponding visual result of image fusion based on the weighted average method compared to PCA is shown in figure 2. Compared to PCA, our approach reconstructs clearly different brain structures than the original down to the smallest details. the black spot in the right of the MRGad image is found in the merged one whereas the PCA, some structures are less clear and/or confused. b. Satellite images Figure 3 shows five satellites images used in the fusion process. The corresponding visual result of image fusion based on the weighted color composite method compared to PCA is shown in figure 4. Compared to PCA, the color composite effect of our approach is evident in the fused image while in the PCA method, there is no color effect. Figure 1: The MRI images of Meningioma tumour: T1; PD; T2; MRGad Figure2: Result of fused image from Brain MRI images. (Left) our approach, (right) PCA 30
  • 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Figure3: Examples of satellite imagesFigure 4: Results of fused images from satellite examples. (Left) our approach, (right) PCA 2. Quantitative evaluation To evaluate the proposed approach, we retain two quantitative measures widely usedin the literature to assess the quality of reconstructed images by fusion method [28]: UIQI (Universal Image Quality Index)[27] : it measures how much of the salientinformation contained in original image. The range of this measure varies from -1 to +1where high value of UIQI significates better fusion. If A and B are respectively the originaland fused image and ߤ௔, ߤ௕ ,ߪ௔ , ߪ௕ are the mean and standard deviation of A and B, thecorresponding UIQI is defined as: ఙ ଶఓೌ ఓ ଶఙೌ ఙ ‫ݍ‬௜ ൌ ఙ ೌ್ ఓమ ାఓ್ ఙమ ାఙ್ ……………………………… (17) ఙ మ మ ೌ ್ ೌ ್ ೌ ್Where ߪ is covariance and ߤ is mean. 31
  • 8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME RMSE (Root Mean Squared Error): it calculates the difference of standard deviation and the mean between the original and the fused image. Smaller value corresponds to better fusion method. ∑ಾ ∑ಿ ሾிሺ௜,௝ሻି஺ሺ௜,௝ሻሿమ ߜൌට ೔సభ ೕసభ ேൈெ …………………………... (18) Where ‫ܣ‬ሺ݅, ݆ሻ is original image and ‫ ܨ‬ሺ݅, ݆ሻ is fusion image. Table 1 reports the results of RMSE and UIQI applied on the Brain MRI fused image. For both RMSE and UIQI our approach works much better than PCA. It reduces the RMS error around 30% relative to PCA while the UIQI value retains more than 75% of the salient information for 1st, 2nd and 3rd band. Quality index Method Band 1 Band 2 Band 3 Band 4 Average RMSE PCA 32.6284 33.0610 33.2983 35.6705 33.6645 Our 22.0949 22.5831 23.1733 26.4562 23.5769 UIQI approch PCA 0.3201 0.3041 0.3047 0.4899 0.3547 Our 0.6185 0.5345 0.5853 0.6486 0.5967 approch Table 1: The comparison between the indexes quality values of our approach and PCA Method relative to Brain MRI image Bands Band R Band G Band B Average PCA Band 1 0.7630 0.8711 0.7349 0.7897 0.7696 Band 2 0.8711 0.7308 0.8040 0.8020 0.7675 Band 3 0.7349 0.7736 0.7198 0.7428 0.7372 Band 4 0.6031 0.6441 0.6166 0.6213 0.6141 Band 5 0.7901 0.7583 0.7445 0.7643 0.7586 Table 2: The comparison of the UIQI index quality value of our approach and PCA method. For the satellite images, the results are reported in table2. For most satellite bands the weighted color composite approach is competitive to PCA.IV. CONCLUSION In this work, we propose a new method for multispectral image fusion based on the weighted merge to overcome the problem of limited number of merged bands for the other multispectral image fusion. The quality of fused image by our proposed method is much better than obtained with PCA approach for both Brain MRI and satellite images.V. ACKNOWLEDGEMENTS This article is dedicated to Miss Salma NAGID who had realized first version before she passed away. 32
  • 9. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMEREFERENCES[1] A.A.Goshtasby, S.Nikolov, ”Image fusion:advances in the state of the art”, InformationFusion 8(2)114−118, 2008. [2] H.B.Mitchell, ”Image Fusion: Theories, Techniques and Applications”, 1st editionSpringer Verlag, Berlin Hidelberg, 2010. [3] C.Pohl, J.L.VanGenderen, ”Multisensor image fusion in remote sensing:concepts,methods and applications”, International Journal of Remote Sensing 19(5)823−854,1998.[4] Y.Yang ,C.Z.Han, X.Kang, D.Q.Han, ”An overview on pixel-level image fusion inremote sensing”, in:Proceedings of the IEEE International Conference on Automation andLogistics, Jinan, China, pp.18−21, 2007. [5] O. Rockinger, T. Fechner, ”Pixel-level image fusion: the case of image sequences”,SPIE Proceedings 3374 378−388, 1998.[6] T.Tu, S.Su, H.Shyu, P.Huang, ”A new look at IHS-like image fusion methods”Information Fusion 2, 177−186, 2001.[7] T.Tu, P.S.Huang, C.Hung, C.Chang, ”A fast intensity-hue-saturation fusion techniquewith spectral adjustment for IKONOS imagery”, IEEE Transactions on Geoscience andRemote Sensing Letter 1 (4), 309−312,2004.[8] M.Choi, ”A new intensity-hue-saturation fusion approach to image fu- sion with a tradeoparameter”, IEEE Transaction on Geosciences Re- mote Sensing 44 (6), 1672−1682, 2006. [9] S.Nagid, B.Nsiri, N.Idrissi, ”New method of multispectral image fusion: application tothe brain tumor MRI images”, in Proceedings of the IEEE International Conference OnMultimedia Computing And Systems, 2012.[10] V.Karathanassi, P.Kolokusis, S.Ioannidou, ”A comparison study on fu- sion methodsusing evaluation indicators”, International Journal of Re- mote Sensing 28 (10), 2309−2341,2007.[11] Z. Wang, A.C. Bovik, ”A universal image quality index”, IEEE Signal ProcessingLetters 9 (3) 81−84, 2002.[12] G.Qu, D.Zhang, P.Yan, ”Information measure for performance of image fusion”,Electronics Letter, Vol. 38(7), pp. 313−315, 2002.[13] A.P.Dempster, N.M.Laird, D.B.Rubin, Maximum likelihood from incomplete datavia the EM algorithm, J.R.Stat.Soc.Ser.B (Methodological) 39(1) (1977) 138.[14] R.J.A.Little,D.B.Rubin, Statistical Analysis with Missing Data,seconded.,Wiley,NewYork,2002.[15] G.J.McLachlan,T.Krishnam,The EM Algorithm and Extensions, 2nd ed.,Wiley,NewYork, 2008.[16] C.Biernacki, G.Celeux, G.Govaert, Choosing starting values for the EM algorithm forgetting the highest likelihood in multivariate Gaussian mixture models, Comput. Stat.DataAnal.41(2003)561575.[17] K. Younis, M. Karim, R. Hardie, J. Loomis, S. Rogers, and M. DeSimio, Clustermerging based on weighted Mahalanobis distance with appli- cation in digitalmammography, in Proceedings of the IEEE National Aerospace and Electronics Conference(NAECON 98), pp. 525530, July 1998.[18] Zhang Z, Blum R.S. (1999). A categorization of multiscale – decomposition - basedimage fusion schemes with a performance study for a digital camera application,Proceedings of the IEEE 87(8), 1315- 1326 33
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