Abstract

A technique based on multiresolution wavelet decomposition was developed for the merging and data fusion of a high-resolution panchromatic image and a low-resolution multispectral image. The standard data fusion methods may not be satisfactory, because they can distort the spectral characteristics of the multispectral data. The method presented here consists of adding the wavelet coefficients of the high-resolution image to the multispectral (low-resolution) data. More specifically, we add the high-order coefficients of the wavelet transform of the panchromatic image to the intensity component (L) of the multispectral image. The method is thus an improvement on standard intensity–hue–saturation (IHS or LHS) mergers. An alternative approach for correcting the red–green–blue coefficients is also discussed. We used the method to merge SPOT and Landsat Thematic Mapper images (SPOT means Système pour l’Observation de la Terre). The technique presented is clearly better than the IHS and LHS mergers for preserving both spectral and spatial information.

© 1999 Optical Society of America

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References

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  1. T. Taxt, A. H. Schistad-Solberg, “Data fusion in remote sensing,” in Proceedings of the Fifth International Workshop on Data Analysis in Astronomy, V. Di Gesu, L. Scarsi, eds. (World Scientific, Singapore, 1996), pp. 269–280.
  2. P. S. Chavez, S. C. Sides, J. A. Anderson, “Comparison of three different methods to merge multi-resolution and multispectral data: Landsat TM and SPOT panchromatic,” Photogramm. Eng. Remote Sens. 57, 295–303 (1991).
  3. J. C. Tilton, ed., Proceedings of Conference on Multisource Data Integration in Remote Sensing, NASA Conf. Publ. 3099 (NASA, Washington, D.C., 1991).
  4. J. W. Carper, T. M. Lillesand, R. W. Kiefer, “The use of intensity-hue-saturation transformations for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 56, 459–467 (1990).
  5. V. K. Shettigara, “A generalized component substitution technique for spatial enhancement of multispectral images using a higher resolution data set,” Photogramm. Eng. Remote Sens. 58, 561–567 (1992).
  6. M. Datcu, D. Luca, K. Seidel, “Multiresolution analysis of SAR images,” in Proceedings of the European Conference on Synthetic Aperture Radar (VDE-Verlag Gmbh, Berlin, 1996), pp. 375–378.
  7. D. A. Yocky, “Image merging and data fusion by means of the discrete two-dimensional wavelet transform,” J. Opt. Soc. Am. A 12, 1834–1841 (1995).
    [CrossRef]
  8. D. A. Yocky, “Multiresolution wavelet decomposition image merger of LANDSAT thematic mapper and SPOT panchromatic data,” Photogramm. Eng. Remote Sens. 62, 1067–1074 (1996).
  9. B. Garguet-Duport, J. Girel, J. M. Chassery, G. Pautou, “The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 62, 1057–1066 (1996).
  10. T. Ranchin, L. Wald, M. Mangolini, “The ARSIS method: a general solution for improving spatial resolution of images by the means of sensor fusion,” in Proceedings of the Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1996), pp. 53–58.
  11. J. Núñez, X. Otazu, O. Fors, A. Prades, “Simultaneous image fusion and reconstruction using wavelets. Applications to SPOT+LANDSAT images,” Vistas Astron. 41, 351–357 (1997).
    [CrossRef]
  12. A. R. Smith, “Color gamut transform pairs,” Comput. Graph. 12, 12–19 (1978).
    [CrossRef]
  13. Association for Computing Machinery, “Status report of the graphics Standard Planning Committee,” Comput. Graph. 13, (1979).
  14. Y. Meyer, Wavelets. Algorithms and Applications (SIAM Press, Philadelphia, Pa., 1993).
  15. R. K. Young, Wavelet Theory and its Applications (Kluwer Academic, Boston, 1993).
  16. I. Daubechies, Ten Lectures on Wavelets (SIAM Press, Philadelphia, Pa., 1992).
  17. C. K. Chui, An Introduction to Wavelets (Boston Academic, Boston, 1992).
  18. G. Kaiser, A Friendly Guide to Wavelets (Birkhauser, Boston, 1994).
  19. M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice Hall, Englewood Cliffs, N.J., 1995).
  20. J. L. Starck, E. Pantin, “Multiscale maximum entropy image restoration,” Vistas Astron. 40, 563–569 (1996).
    [CrossRef]
  21. F. Rué, A. Bijaoui, “A multiscale vision model applied to astronomical images,” Vistas Astron. 40, 495–502 (1996).
    [CrossRef]
  22. S. Mallat, “A theory for multiresolution signal: the wavelet representation,” IEEE Trans. Pattern. Anal. Mach. Intell. 11, 674–693 (1989).
    [CrossRef]
  23. J. L. Starck, F. Murtagh, “Image restoration with noise suppression using the wavelet transform,” Astron. Astrophys. 288, 342–350 (1994).
  24. M. Holschneider, P. Tchamitchian, “Regularité local de la fonction ‘non-differentiable’ de Riemann,” in Les ondelettes in 1989, P. G. Lemarié, ed., Lecture Notes in Mathematics No. 1438 (Springer-Verlag, Berlin, 1990), pp. 102–124.
  25. P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. COM-31, 532–540 (1983).
    [CrossRef]
  26. J. Núñez, X. Otazu, O. Fors, A. Prades, “Fusion and reconstruction of LANDSAT and SPOT images using wavelets,” in Proceedings of the Second Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1998), pp. 103–108.

1997 (1)

J. Núñez, X. Otazu, O. Fors, A. Prades, “Simultaneous image fusion and reconstruction using wavelets. Applications to SPOT+LANDSAT images,” Vistas Astron. 41, 351–357 (1997).
[CrossRef]

1996 (4)

D. A. Yocky, “Multiresolution wavelet decomposition image merger of LANDSAT thematic mapper and SPOT panchromatic data,” Photogramm. Eng. Remote Sens. 62, 1067–1074 (1996).

B. Garguet-Duport, J. Girel, J. M. Chassery, G. Pautou, “The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 62, 1057–1066 (1996).

J. L. Starck, E. Pantin, “Multiscale maximum entropy image restoration,” Vistas Astron. 40, 563–569 (1996).
[CrossRef]

F. Rué, A. Bijaoui, “A multiscale vision model applied to astronomical images,” Vistas Astron. 40, 495–502 (1996).
[CrossRef]

1995 (1)

1994 (1)

J. L. Starck, F. Murtagh, “Image restoration with noise suppression using the wavelet transform,” Astron. Astrophys. 288, 342–350 (1994).

1992 (1)

V. K. Shettigara, “A generalized component substitution technique for spatial enhancement of multispectral images using a higher resolution data set,” Photogramm. Eng. Remote Sens. 58, 561–567 (1992).

1991 (1)

P. S. Chavez, S. C. Sides, J. A. Anderson, “Comparison of three different methods to merge multi-resolution and multispectral data: Landsat TM and SPOT panchromatic,” Photogramm. Eng. Remote Sens. 57, 295–303 (1991).

1990 (1)

J. W. Carper, T. M. Lillesand, R. W. Kiefer, “The use of intensity-hue-saturation transformations for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 56, 459–467 (1990).

1989 (1)

S. Mallat, “A theory for multiresolution signal: the wavelet representation,” IEEE Trans. Pattern. Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

1983 (1)

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

1979 (1)

Association for Computing Machinery, “Status report of the graphics Standard Planning Committee,” Comput. Graph. 13, (1979).

1978 (1)

A. R. Smith, “Color gamut transform pairs,” Comput. Graph. 12, 12–19 (1978).
[CrossRef]

Adelson, E. H.

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

Anderson, J. A.

P. S. Chavez, S. C. Sides, J. A. Anderson, “Comparison of three different methods to merge multi-resolution and multispectral data: Landsat TM and SPOT panchromatic,” Photogramm. Eng. Remote Sens. 57, 295–303 (1991).

Bijaoui, A.

F. Rué, A. Bijaoui, “A multiscale vision model applied to astronomical images,” Vistas Astron. 40, 495–502 (1996).
[CrossRef]

Burt, P. J.

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

Carper, J. W.

J. W. Carper, T. M. Lillesand, R. W. Kiefer, “The use of intensity-hue-saturation transformations for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 56, 459–467 (1990).

Chassery, J. M.

B. Garguet-Duport, J. Girel, J. M. Chassery, G. Pautou, “The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 62, 1057–1066 (1996).

Chavez, P. S.

P. S. Chavez, S. C. Sides, J. A. Anderson, “Comparison of three different methods to merge multi-resolution and multispectral data: Landsat TM and SPOT panchromatic,” Photogramm. Eng. Remote Sens. 57, 295–303 (1991).

Chui, C. K.

C. K. Chui, An Introduction to Wavelets (Boston Academic, Boston, 1992).

Datcu, M.

M. Datcu, D. Luca, K. Seidel, “Multiresolution analysis of SAR images,” in Proceedings of the European Conference on Synthetic Aperture Radar (VDE-Verlag Gmbh, Berlin, 1996), pp. 375–378.

Daubechies, I.

I. Daubechies, Ten Lectures on Wavelets (SIAM Press, Philadelphia, Pa., 1992).

Fors, O.

J. Núñez, X. Otazu, O. Fors, A. Prades, “Simultaneous image fusion and reconstruction using wavelets. Applications to SPOT+LANDSAT images,” Vistas Astron. 41, 351–357 (1997).
[CrossRef]

J. Núñez, X. Otazu, O. Fors, A. Prades, “Fusion and reconstruction of LANDSAT and SPOT images using wavelets,” in Proceedings of the Second Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1998), pp. 103–108.

Garguet-Duport, B.

B. Garguet-Duport, J. Girel, J. M. Chassery, G. Pautou, “The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 62, 1057–1066 (1996).

Girel, J.

B. Garguet-Duport, J. Girel, J. M. Chassery, G. Pautou, “The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 62, 1057–1066 (1996).

Holschneider, M.

M. Holschneider, P. Tchamitchian, “Regularité local de la fonction ‘non-differentiable’ de Riemann,” in Les ondelettes in 1989, P. G. Lemarié, ed., Lecture Notes in Mathematics No. 1438 (Springer-Verlag, Berlin, 1990), pp. 102–124.

Kaiser, G.

G. Kaiser, A Friendly Guide to Wavelets (Birkhauser, Boston, 1994).

Kiefer, R. W.

J. W. Carper, T. M. Lillesand, R. W. Kiefer, “The use of intensity-hue-saturation transformations for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 56, 459–467 (1990).

Kovacevic, J.

M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice Hall, Englewood Cliffs, N.J., 1995).

Lillesand, T. M.

J. W. Carper, T. M. Lillesand, R. W. Kiefer, “The use of intensity-hue-saturation transformations for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 56, 459–467 (1990).

Luca, D.

M. Datcu, D. Luca, K. Seidel, “Multiresolution analysis of SAR images,” in Proceedings of the European Conference on Synthetic Aperture Radar (VDE-Verlag Gmbh, Berlin, 1996), pp. 375–378.

Mallat, S.

S. Mallat, “A theory for multiresolution signal: the wavelet representation,” IEEE Trans. Pattern. Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

Mangolini, M.

T. Ranchin, L. Wald, M. Mangolini, “The ARSIS method: a general solution for improving spatial resolution of images by the means of sensor fusion,” in Proceedings of the Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1996), pp. 53–58.

Meyer, Y.

Y. Meyer, Wavelets. Algorithms and Applications (SIAM Press, Philadelphia, Pa., 1993).

Murtagh, F.

J. L. Starck, F. Murtagh, “Image restoration with noise suppression using the wavelet transform,” Astron. Astrophys. 288, 342–350 (1994).

Núñez, J.

J. Núñez, X. Otazu, O. Fors, A. Prades, “Simultaneous image fusion and reconstruction using wavelets. Applications to SPOT+LANDSAT images,” Vistas Astron. 41, 351–357 (1997).
[CrossRef]

J. Núñez, X. Otazu, O. Fors, A. Prades, “Fusion and reconstruction of LANDSAT and SPOT images using wavelets,” in Proceedings of the Second Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1998), pp. 103–108.

Otazu, X.

J. Núñez, X. Otazu, O. Fors, A. Prades, “Simultaneous image fusion and reconstruction using wavelets. Applications to SPOT+LANDSAT images,” Vistas Astron. 41, 351–357 (1997).
[CrossRef]

J. Núñez, X. Otazu, O. Fors, A. Prades, “Fusion and reconstruction of LANDSAT and SPOT images using wavelets,” in Proceedings of the Second Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1998), pp. 103–108.

Pantin, E.

J. L. Starck, E. Pantin, “Multiscale maximum entropy image restoration,” Vistas Astron. 40, 563–569 (1996).
[CrossRef]

Pautou, G.

B. Garguet-Duport, J. Girel, J. M. Chassery, G. Pautou, “The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 62, 1057–1066 (1996).

Prades, A.

J. Núñez, X. Otazu, O. Fors, A. Prades, “Simultaneous image fusion and reconstruction using wavelets. Applications to SPOT+LANDSAT images,” Vistas Astron. 41, 351–357 (1997).
[CrossRef]

J. Núñez, X. Otazu, O. Fors, A. Prades, “Fusion and reconstruction of LANDSAT and SPOT images using wavelets,” in Proceedings of the Second Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1998), pp. 103–108.

Ranchin, T.

T. Ranchin, L. Wald, M. Mangolini, “The ARSIS method: a general solution for improving spatial resolution of images by the means of sensor fusion,” in Proceedings of the Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1996), pp. 53–58.

Rué, F.

F. Rué, A. Bijaoui, “A multiscale vision model applied to astronomical images,” Vistas Astron. 40, 495–502 (1996).
[CrossRef]

Schistad-Solberg, A. H.

T. Taxt, A. H. Schistad-Solberg, “Data fusion in remote sensing,” in Proceedings of the Fifth International Workshop on Data Analysis in Astronomy, V. Di Gesu, L. Scarsi, eds. (World Scientific, Singapore, 1996), pp. 269–280.

Seidel, K.

M. Datcu, D. Luca, K. Seidel, “Multiresolution analysis of SAR images,” in Proceedings of the European Conference on Synthetic Aperture Radar (VDE-Verlag Gmbh, Berlin, 1996), pp. 375–378.

Shettigara, V. K.

V. K. Shettigara, “A generalized component substitution technique for spatial enhancement of multispectral images using a higher resolution data set,” Photogramm. Eng. Remote Sens. 58, 561–567 (1992).

Sides, S. C.

P. S. Chavez, S. C. Sides, J. A. Anderson, “Comparison of three different methods to merge multi-resolution and multispectral data: Landsat TM and SPOT panchromatic,” Photogramm. Eng. Remote Sens. 57, 295–303 (1991).

Smith, A. R.

A. R. Smith, “Color gamut transform pairs,” Comput. Graph. 12, 12–19 (1978).
[CrossRef]

Starck, J. L.

J. L. Starck, E. Pantin, “Multiscale maximum entropy image restoration,” Vistas Astron. 40, 563–569 (1996).
[CrossRef]

J. L. Starck, F. Murtagh, “Image restoration with noise suppression using the wavelet transform,” Astron. Astrophys. 288, 342–350 (1994).

Taxt, T.

T. Taxt, A. H. Schistad-Solberg, “Data fusion in remote sensing,” in Proceedings of the Fifth International Workshop on Data Analysis in Astronomy, V. Di Gesu, L. Scarsi, eds. (World Scientific, Singapore, 1996), pp. 269–280.

Tchamitchian, P.

M. Holschneider, P. Tchamitchian, “Regularité local de la fonction ‘non-differentiable’ de Riemann,” in Les ondelettes in 1989, P. G. Lemarié, ed., Lecture Notes in Mathematics No. 1438 (Springer-Verlag, Berlin, 1990), pp. 102–124.

Vetterli, M.

M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice Hall, Englewood Cliffs, N.J., 1995).

Wald, L.

T. Ranchin, L. Wald, M. Mangolini, “The ARSIS method: a general solution for improving spatial resolution of images by the means of sensor fusion,” in Proceedings of the Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1996), pp. 53–58.

Yocky, D. A.

D. A. Yocky, “Multiresolution wavelet decomposition image merger of LANDSAT thematic mapper and SPOT panchromatic data,” Photogramm. Eng. Remote Sens. 62, 1067–1074 (1996).

D. A. Yocky, “Image merging and data fusion by means of the discrete two-dimensional wavelet transform,” J. Opt. Soc. Am. A 12, 1834–1841 (1995).
[CrossRef]

Young, R. K.

R. K. Young, Wavelet Theory and its Applications (Kluwer Academic, Boston, 1993).

Astron. Astrophys. (1)

J. L. Starck, F. Murtagh, “Image restoration with noise suppression using the wavelet transform,” Astron. Astrophys. 288, 342–350 (1994).

Comput. Graph. (2)

A. R. Smith, “Color gamut transform pairs,” Comput. Graph. 12, 12–19 (1978).
[CrossRef]

Association for Computing Machinery, “Status report of the graphics Standard Planning Committee,” Comput. Graph. 13, (1979).

IEEE Trans. Commun. (1)

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

IEEE Trans. Pattern. Anal. Mach. Intell. (1)

S. Mallat, “A theory for multiresolution signal: the wavelet representation,” IEEE Trans. Pattern. Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

J. Opt. Soc. Am. A (1)

Photogramm. Eng. Remote Sens. (5)

J. W. Carper, T. M. Lillesand, R. W. Kiefer, “The use of intensity-hue-saturation transformations for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 56, 459–467 (1990).

V. K. Shettigara, “A generalized component substitution technique for spatial enhancement of multispectral images using a higher resolution data set,” Photogramm. Eng. Remote Sens. 58, 561–567 (1992).

P. S. Chavez, S. C. Sides, J. A. Anderson, “Comparison of three different methods to merge multi-resolution and multispectral data: Landsat TM and SPOT panchromatic,” Photogramm. Eng. Remote Sens. 57, 295–303 (1991).

D. A. Yocky, “Multiresolution wavelet decomposition image merger of LANDSAT thematic mapper and SPOT panchromatic data,” Photogramm. Eng. Remote Sens. 62, 1067–1074 (1996).

B. Garguet-Duport, J. Girel, J. M. Chassery, G. Pautou, “The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data,” Photogramm. Eng. Remote Sens. 62, 1057–1066 (1996).

Vistas Astron. (3)

J. L. Starck, E. Pantin, “Multiscale maximum entropy image restoration,” Vistas Astron. 40, 563–569 (1996).
[CrossRef]

F. Rué, A. Bijaoui, “A multiscale vision model applied to astronomical images,” Vistas Astron. 40, 495–502 (1996).
[CrossRef]

J. Núñez, X. Otazu, O. Fors, A. Prades, “Simultaneous image fusion and reconstruction using wavelets. Applications to SPOT+LANDSAT images,” Vistas Astron. 41, 351–357 (1997).
[CrossRef]

Other (12)

M. Holschneider, P. Tchamitchian, “Regularité local de la fonction ‘non-differentiable’ de Riemann,” in Les ondelettes in 1989, P. G. Lemarié, ed., Lecture Notes in Mathematics No. 1438 (Springer-Verlag, Berlin, 1990), pp. 102–124.

T. Ranchin, L. Wald, M. Mangolini, “The ARSIS method: a general solution for improving spatial resolution of images by the means of sensor fusion,” in Proceedings of the Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1996), pp. 53–58.

Y. Meyer, Wavelets. Algorithms and Applications (SIAM Press, Philadelphia, Pa., 1993).

R. K. Young, Wavelet Theory and its Applications (Kluwer Academic, Boston, 1993).

I. Daubechies, Ten Lectures on Wavelets (SIAM Press, Philadelphia, Pa., 1992).

C. K. Chui, An Introduction to Wavelets (Boston Academic, Boston, 1992).

G. Kaiser, A Friendly Guide to Wavelets (Birkhauser, Boston, 1994).

M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice Hall, Englewood Cliffs, N.J., 1995).

J. C. Tilton, ed., Proceedings of Conference on Multisource Data Integration in Remote Sensing, NASA Conf. Publ. 3099 (NASA, Washington, D.C., 1991).

J. Núñez, X. Otazu, O. Fors, A. Prades, “Fusion and reconstruction of LANDSAT and SPOT images using wavelets,” in Proceedings of the Second Conference on Fusion of Earth Data, T. Ranchin, L. Wald, eds. (SEE/URISCA, Nice, France, 1998), pp. 103–108.

T. Taxt, A. H. Schistad-Solberg, “Data fusion in remote sensing,” in Proceedings of the Fifth International Workshop on Data Analysis in Astronomy, V. Di Gesu, L. Scarsi, eds. (World Scientific, Singapore, 1996), pp. 269–280.

M. Datcu, D. Luca, K. Seidel, “Multiresolution analysis of SAR images,” in Proceedings of the European Conference on Synthetic Aperture Radar (VDE-Verlag Gmbh, Berlin, 1996), pp. 375–378.

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Figures (2)

Fig. 1
Fig. 1

Detail of the SPOT image.

Fig. 2
Fig. 2

(a) Detail of the Landsat (TM) image, (b) Result of fusion by the standard IHS method, (c) Result of fusion by the standard LHS method, (d) Result of fusion by the AWL method.

Tables (1)

Tables Icon

Table 1 Correlation between IHS, LHS, and AWL Merging Methods and SPOT and Landsat (TM) Images

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

I=I(R, G, B)=max(R, G, B), L=L(R, G, B)=(R+G+B)/3, L=L(R, G, B)=[max(R, G, B)+min(R, G, B)]/2.
wm[f(t)]=Fm+1[f(t)]-Fm[f(t)].
wm[f(t)]=nWm,n(f)ψm,n(t),
Wm,n(f)=-+f(t)ψm,n(t)dt.
ψm,n(t)=2m/2ψ(2mt-n).
f(t)=mnWm,n(f)ψm,n(t).
F1(p)=p1,F2(p1)=p2,F3(p2)=p3,.
12561464141624164624362464162416414641.
p=l=1nwl+pr.
R=l=1nwRl+Rr,G=l=1nwGl+Gr, B=l=1nwBl+Br.
PAN=l=1nwPl+PANr.
Rnew=l=1nwPl+Rr,Gnew=l=1nwPl+Gr, Bnew=l=1nwPl+Br.
PAN=l=1nwPl+PANr.
Rnew=l=1nwPl+R,Gnew=l=1nwPl+G, Bnew=l=1nwPl+B.
PAN=l=1nwPl+PANr.
Lnew=l=1nwPl+L.
Corr(A/B)=1-j=1npix(Aj-Bj)2j=1npixBj2.

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