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A Variational Model for P+XS Image Fusion

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Abstract

We propose an algorithm to increase the resolution of multispectral satellite images knowing the panchromatic image at high resolution and the spectral channels at lower resolution. Our algorithm is based on the assumption that, to a large extent, the geometry of the spectral channels is contained in the topographic map of its panchromatic image. This assumption, together with the relation of the panchromatic image to the spectral channels, and the expression of the low-resolution pixel in terms of the high-resolution pixels given by some convolution kernel followed by subsampling, constitute the elements for constructing an energy functional (with several variants) whose minima will give the reconstructed spectral images at higher resolution. We discuss the validity of the above approach and describe our numerical procedure. Finally, some experiments on a set of multispectral satellite images are displayed.

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References

  • Aiazzi, B., Alparone, L., Baronti, S., and Garzelli, A. 2002. Context-Driven Fusion of High Spatial and Spectral Resolution Images Based on Oversampled Multiresolution Analysis. IEEE Trans. on Geoscience and Remote Sensing, 40(10):2300–2312.

    Article  Google Scholar 

  • Ambrosio, L., Caselles, V., Masnou, S., and Morel, J. 2001. The Connected Components of Sets of Finite Perimeter. European Journal of Math, 3:39–92.

    Article  MathSciNet  Google Scholar 

  • Ambrosio, L., Fusco, N., and Pallara, D. 2000. Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs.

  • Ballester, C., Bertalmio, M., Caselles, V., Sapiro, G., and Verdera, J. 2001. Filling-In by Joint Interpolation of Vector Fields and Gray Levels. IEEE Transactions on Image Processing, 10(8):1200–1211.

    Article  MathSciNet  Google Scholar 

  • Ballester, C., Caselles, V., Rougé, B., and Verdera, J. 2003. Une méthode geométrique de fusion des images P+XS. Rapport CNES.

  • Caselles, V., Coll, B., and Morel, J. 1999. Topographic Maps and Local Contrast Changes in Natural Images. Int. J. Comp. Vision, 33(1):5–27.

    Article  MathSciNet  Google Scholar 

  • Caselles, V., Coll, B., and Morel, J. 2002. Geometry and Color in Natural Images. J. Math. Imaging and Vision, 16:89–107.

    Article  MathSciNet  Google Scholar 

  • Caselles, V., Sapiro, G., and Chung, D. 2000. Vector Median Filters, Vector Morphology, and Coupled PDE’s: Theoretical Connections. J. Math. Imaging and Vision, 12:109–120.

    Article  MathSciNet  Google Scholar 

  • Desolneux, A., Moisan, L., and Morel, J. 2002. Dequantizing Image Orientation. IEEE Transactions on Image Processing, 11:1129–1140.

    Article  MathSciNet  Google Scholar 

  • Evans, L. and Gariepy, R. 1992. Measure Theory and Fine Properties of Functions, Studies in Advanced Math., CRC Press.

  • Gousseau, Y. and Morel, J. 2001. Are natural images of bounded variation ? SIAM J. Math. Anal., 33(2001):634–648.

    Article  MathSciNet  Google Scholar 

  • Guichard, F. and Morel, J. 2003. Partial differential equations and image iterative filtering, Forthcoming book.

  • Hunt, R. 1998. Measuring Color, England: Fountain Press.

    Google Scholar 

  • Lisani, J. and Morel, J. 2000. Comparaison morphologique d’images. Rapport CNES.

  • Monasse, P. 1999. Contrast invariant image registration. Proc. of the International Conf. on Acoustics, Speech and Signal Processing, Phoenix, Arizona, 6:3221–3224.

    Google Scholar 

  • Rudin, L., Osher, S., and Fatemi, E. 1992. Nonlinear Total Variation Based Noise Removal Algorithms. Physica D, 60(1992):259–269.

    Article  Google Scholar 

  • Serra, J. 1982. Image analysis and mathematical morphology. Academic Press.

  • Wald, L., Ranchin, T., and Mangolini, M. 1997. Fusion of Satellite Images of Different Spatial Resolutions: Assessing the Quality of Resulting Images. Photogramm. Eng. Remote. Sensing, 63(6):691–699.

    Google Scholar 

  • Wertheimer, M. 1923. Untersuchungen zur Lehre der Gestalt, II. Psychologische Forschung, 4:301–350.

    Article  Google Scholar 

  • Ziemer, W. 1989. Weakly Differentiable Functions, GTM 120, Springer Verlag.

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Authors and Affiliations

  1. Departament de Tecnologia, University Pompeu Fabra, Pg. Circumvalació 8, 08003, Barcelona, Spain

    Coloma Ballester, Vicent Caselles, Laura Igual & Joan Verdera

  2. CNES, Av. Ed Belin, 31401, Toulouse, France

    Bernard Rougé

Authors
  1. Coloma Ballester
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  2. Vicent Caselles
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  3. Laura Igual
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  4. Joan Verdera
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  5. Bernard Rougé
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Correspondence to Coloma Ballester.

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Ballester, C., Caselles, V., Igual, L. et al. A Variational Model for P+XS Image Fusion. Int J Comput Vision 69, 43–58 (2006). https://doi.org/10.1007/s11263-006-6852-x

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  • DOI: https://doi.org/10.1007/s11263-006-6852-x

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