Image fusion by spatially adaptive filtering using downscaling cokriging

The aim of this paper was to extend the method of downscaling cokriging for image fusion by making the method spatially adaptive in that the filter parameters (cokriging weights) can change across the image. The method can adapt itself to the usual statistical non-homogeneity (spatially variable mean, variance and correlation length) of a satellite sensor image that covers an area with different spatial patterns of geographical objects or different terrain types. The solution adopted was to estimate the models of covariances and cross-covariances (or semivariograms and cross-semivariograms) by the same procedure as described in Pardo-Iguzquiza et al. (2006) but with the method applied locally instead of globally. The correct implementation of this local estimation is the key for computational feasibility and prediction efficiency. Two parameters to be taken into account are the grid of locations on which a moving window is centred (local modelling is performed inside this window) and the size of this moving window. With respect to the latter parameter, there is a trade-off between a size small enough to make the procedure locally adaptive and large enough to produce reliable statistical estimates. The computational burden will impose limits to the distance between grid points on which the local moving window is centred. A case study with Landsat ETM+ images was used to show the implementation of the method and the result was evaluated using several statistics widely used for assessing the quality of a fused image, apart from its visual appearance.