ACTA ELECTRONICA SINICA. :, Contourlet. Color Image Fusio n Algorithm Using the Co nto urlet Transform
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1 007 ACTA ELECTRONICA SINICA Vol. 5 No. Jan. 007 Contourlet, (, 005) :, Contourlet. IHS( IntensityHueSaturation) RGB IHS, Contourlet I, I, I, IHS RGB. Contourlet,.,,Contourlet, IHS. : ; Contourlet ; ; IHS : TP9 : A : 07 (007) 000 Color Image Fusio n Algorithm Using the Co nto urlet Transform LI Guangxin,WANG Ke ( College of Communications Engineering, Jilin University, Changchun, Jilin 005, China) Abstract : With the particular research on thermal and visual images, a color image fusion algorithm using the contourlet transform is presented. Firstly,through the IHS (IntensityHueSaturation) transform,the color visual image is converted from RGB color space to IHS space. Next,with the contourlet transform and weighted average fusion rule,the intensity component and thermal image are merged into a grayscale image,which is then linearly stretched to have the same mean and variance as the intensity com ponent. Finally,the stretched grayscale fused image replaces the original intensity component,and the final RGB color fused image is achieved by the inverse IHS transform with the H,S and replacement component. On the one hand,with the proposed scheme,the contourlet transform as a new mathematical tool is introduced to image fusion area. On the other hand,the algorithm provided a new color image fusion strategy of thermal and visual images. The experimental results show that, with the proposed color fusion method,the fused image produced by the contourlet transform is of better quality than that obtained through the wavelet transform. Moreover,the color fusion approach obviously improves fusion performance over the traditional IHS transform fusion method. Key words : color image fusion ; contourlet transform ; wavelet transform ; IHS transform, [ ]. :,,,, ;,,,, [4 ]., Ridgelet [7 ],Curvelet [8 ]. Curvelet,Minh N Do Martin Vetterli :000 ; :0009 :Contourlet [5, ]. Contourlet, :Contourlet, ;, Curvelet. Contourlet,., Contourlet., IHS, ;, Contourlet, Contourlet.,,Contourlet,
2 : Contourlet, IHS. Contourlet Contourlet L (R ) ( ) : L (R ) = V J g [9 ], V J, < J : { < J, n ( t) = < J ( t - j n) } n Z gw j = V J j J g g () V J. W j j, Contourlet, W j l j W, Contourlet j : {, n l j - g W ( l ) j j J k = 0, ( ) Z () ( t) = ( t - j - S n) } k n Z () W,, S k = diag( l j -,),0 k < l j - ( ) (4) S k = diag(, l j - ), l j - k < l j ( ) (5), W j + l j - j j j + l j -, W., { l j } j J, : { < J, n, }, n j J,0 k l j -, n Z () L (R ), j k n. a L ( n) = f, < L, n f ( t) L ( R ) < L, n, a L Contourlet :, { a J, c } L < j J,0 k < l j - (7) a J ( n) = f, < J, n (8) c ( n) = f, (9), n Contourlet, LP(Laplacian Pyramid), DFB (Directional Filter Bank),Contourlet (Contour segment), Contoulet.LP DFB, Contoulet, Contoulet LP. Con tourlet. LP, a L J - L b j ( j = L +, L +,, J ) a J,, j LP, a j - a j b j, b j l j DFB l j c ( k = 0,,, l j - ),, Con toulet a L a J c. 4 Boat Contourlet, LP, DFB 4 8.,, [0 ].,,,,,., Contourlet, : () IHS RGB
3 4 007 IHS, [ ] IHS :. I V V = R G B (0) H = tan - [ V / V ] () S = V + V () () Contourlet I () I g, I : I g = ( g / ) ( I g - g ) + (), (, ) ( g, g ) I I g. I g I ( ),. (4) I g I, IHS RGB,IHS : R G B = I V V (4) (), : x A x B I, Con tourlet x A x B Contourlet { a A, J, c } { a A, B, J, c }, : B, a F, J ( n) = ( a A, J ( n) + a B, J ( n) ) (5), a F, J.,, ( ).,,, [ ]., : A B c A c B, A B, c A c B ; A B, c F. : c F, ( n) = w A, ( n) c A, ( n) + ( - w A, ( n) ) c B, ( n) (), w A, w A. q S, ( n) = ( l ) n R j ( n) c ( l ) j ( n + n) S, (7) S ( S = A, B), (7), R, ( n). [ ] : M AB, ( n) = q A, ( n) q B, ( n) (8) A B. T [0, ], M AB > / T A B, M AB < T B A, A B T < M AB < / T., M AB > / T, w A = ; M AB < T, w A = 0. (/ T,) ( T, 0), A B, : w A = M AB - T / T - T + M AB - / T T - / T 0 = T( M AB - T) - T (9), M AB = T, M AB = / T, w A : w A, ( n) =, M AB, ( n) / T 0, M ( n) < T AB, T( M ( n) - T) AB, - T, T M ( l j ) AB, ( n) < / T (0) c F, a F, J Contourlet { a F, J, c }, Contourlet F, x F, (), x F () I g. 4 [ ],.,,. UIQI [ ] (Universal Image Quality Index) (Loss of correlation) (Luminance distortion) (Contrast distortion),, [,4 ]. UIQI, Gemma Piella Henk Heijmans [5 ] : EFQI( EdgeDependent Fusion Quality Index) WFQI (Weighted Fusion Quality In dex), EFQI WFQI. EFQI : Q E ( y A, y B, y F ) = Q W ( y A, y B, y F ) - Q W ( y A, y B, y F ) ()
4 : Contourlet 5 Q E EFQI, Q W WFQI, y A y B y F y A y B y F. WFQI : Q W ( y A, y B, y F ) = c ( ) ( A ( ) Q 0 ( y A, y F, ) + ( - A ( ) ) Q 0 ( y B, y F, ) ) () c ( ) = C( ) C( ) () C( ) = max( ( y A ), ( y B ) ) (4) A ( ) = ( y A ) / ( ( y A ) + ( y B ) ) (5) ( y A ) y A,,, Q 0 (Overall image quality index), [5 ]. WFQI EFQI,WFQI, WFQI,EFQI, [ -, ],. IHS. Octec, ( a) ( b) IHS Octec EFQI WFQI Octec, IHS, IHS ( R G B) , ( R G B) ,Octec Contourlet ( R G B) Octec Octec, Octec,, EFQI WFQI IHS IHS, ( R G B) Octec IHS ( R G B) I, Contourlet ( R G B) ,. Contourlet, ( ( c) ( f) ). IHS, (),,. Contourlet ;, IHS [ ],, IHS. Octec Octec ( 5) ; 5, 4 ;Contourlet LP 5, 4,DFB 45 Quincunx [7 ], ; Contourlet, T 07,, { {/,/ 8,/ },{ / 8,/ 4,/ 8},{ /,/ 8,/ } }.,., ( Contourlet ) EFQI WFQI IHS,
5 007. Contourlet, () I, ( H S).,. Contourlet,, R G B,Contourlet EFQI WFQI, Contourlet. Con tourlet,,,contourlet,, Contourlet,,. ( c) ( d) ( e) ( f) Contourlet Octec Octec,,Con tourlet,., Contourlet, Contourlet. N N, Contourlet LP DFB K( LP DFB,, ), Contourlet ( K + ) N + 4 K max{ l j} N ; K, 8 KN. max{ l j } = ( ),Contourlet ( K + ) N. 5 Contourlet,, IHS,, Contourtlet.,Contourlet, Contourlet. [8,9 ],,,., ( () ),.,Contourlet,,,. Octec,. : [ ] G Pajares,J M Cruz. A waveletbased image fusion tutorial[j ]. Pattern Recognition,004,7 (9) : [ ] Z Zhang, R S Blum. A categorization and study of multiscale decompositionbased image fusion schemes with a performance study for a digital camera application [ J ]. Proceedings of the IEEE,999,87 (8) :5 -. [ ] G Piella. A general framework for multiresolution image fusion : from pixels to regions [J ]. Information Fusion,00,4 (4) : [4 ],. : [J ].,00, (A) : Jiao Licheng, Tan Shan. Development and prospect of image multiscale geometric analysis [ J ]. Acta Electronica Sinica, 00, (A) : (in Chinese) [5 ] M N Do, M Vetterli. Contourlets [ A ]. G V Welland. Beyond Wavelets [ C ]. New York :Academic Press,00. [ ] M N Do, M Vetterli. The contourlet transform : an efficient di rectional multiresolution image representation [J ]. IEEE Trans actions on Image Processing,005,4 () :09-0. [7 ] E J Cand s. Ridgelets : Theory and Applications [ D ]. USA :De partment of Statistics,Stanford University,998. [8 ] E J Cand s, D L Donoho. CurveletsA surprisingly effective nonadaptive representation for objects with edges [ A ]. L L Schumaker,et al. Curves and Surfaces [ C ]. Nashville : Vander bilt University Press,999. [9 ] S G Mallat. A Wavelet Tour of Signal Processing [ M ]. San Diego, California :Academic Press,998. [0 ] D A Scribner,J M Schuler, P R Warren, et al. Infrared color vision :separating objects from backgrounds [J ]. Proceedings of SPIE,998,79 : - 9. [ ] Z Wang,D Ziou, C Armenakis, et al. A comparative analysis of image fusion methods [J ]. IEEE Transactions on Geoscience and Remote Sensing,005,4 () :9-40. [ ],,. [J ].,005,0 () :59-5. Li Guangxin, Wang Ke, Zhang Libao. Computationally effi cient algorithm of multiresolution image fusion with weighted average fusion rule[j ]. J ournal of Image and Graphics,005, 0 () :59-5. (in Chinese) [ ] Z Wang, A C Bovik. A universal image quality index [J ]. IEEE Signal Processing Letters,00,9 () :8-84. [ 4 ] A Toet,M A Hogervorst. Performance comparison of different graylevel image fusion schemes through a universal image quality index[j ]. Proceedings of SPIE,00,509 :55-5.
6 : Contourlet 7 [5 ] G Piella, H Heijmans. A new quality metric for image fusion [ A ]. Proceedings of IEEE International Conference on Image Processing[ C ]. Barcelona,Spain,00. III7-7. [ ] E M Schetselaar. Fusion by the IHS transform :Should we use cylindrical or spherical coordinates? [J ]. International J ournal of Remote Sensing,998,9 (4) : [7 ] S M Phoong, C W Kim, P P Vaidyanathan,et al. A new class of twochannel biorthogonal filter banks and wavelet bases [J ]. IEEE Transactions on Signal Processing, 995, 4 () : [ 8 ] A Toet,J Walraven. New false color mapping for image fusion [J ]. Optical Engineering,99,5 () : [9 ] A M Waxman,D A Fay,A N Gove,et al. Color night vision : fusion of intensified visible and thermal IR imagery [J ]. Pro ceedings of SPIE,995,4 :58-8. :,978, ,.. guangxin. com,955,,.. edu. cn
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