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Several different methods for the fusion of multispectral and panchromatic images based on the wavelet transform have been proposed. The majority provide satisfactory results, but there is one, the à trous algorithm, that presents several advantages over the other fusion methods. Its computation is very simple; it only involves elementary algebraic operations, such as products, differences and convolutions. It yields a better spatial and spectral quality than the other methods. Standard fusion methods do not allow control of the spatial and spectral quality of the fused image; high spectral quality implies low spatial quality and vice versa. This paper proposes a new version of a fusion method based on the wavelet transform, computed through the à trous algorithm, that permits customization of the trade-off between the spectral and spatial quality of the fused image through the evaluation of two quality indices: a spectral index (the ERGAS index) and a spatial one. For the latter, a new spatial index based on ERGAS concepts and translated to the spatial domain has been defined. In addition, several different schemes for the computation of the fusion method investigated have been evaluated to optimize the degradation level of the source image required to perform the fusion process. The performance of the proposed fusion method has been compared with the fusion methods based on wavelet Mallat and filtering in the Fourier domain.

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Keywords: Fractal dimension Fusion image Wavelet transform TextureMost fusion satellite image methodologies at pixel-level introduce false spatial details, i.e. artifacts, in the resulting fused images. In many cases, these artifacts appears because image fusion methods do not consider the differences in roughness or textural characteristics between different land covers. They only consider the digital values associated with single pixels. This effect increases as the spatial resolution image increases. To minimize this problem, we propose a new paradigm based on local measurements of the fractal dimension (FD). Fractal dimension maps (FDMs) are generated for each of the source images (panchromatic and each band of the multi-spectral images) with the box-counting algorithm and by applying a windowing process. The average of source image FDMs, previously indexed between 0 and 1, has been used for discrimination of different land covers present in satellite images. This paradigm has been applied through the fusion methodology based on the discrete wavelet transform (DWT), using the a trous algorithm (WAT). Two different scenes registered by optical sensors on board FORMOSAT-2 and IKONOS satellites were used to study the behaviour of the proposed methodology. The implementation of this approach, using the WAT method, allows adapting the fusion process to the roughness and shape of the regions present in the image to be fused. This improves the quality of the fused images and their classification results when compared with the original WAT method.

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