No abstract

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.

No abstract

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.

No abstract

Space-invariant and space-variant filtering of discrete images with unidimensional variation is performed in this paper through the Wigner distribution function (WDF). Low-pass, bandpass, and high-pass filtering is used in the Fourier domain and in the Wigner distribution, to compare their different behavior in both cases. A space-variant filter is generated to modify the WDF of an object to obtain, after inversion, a spatially variant filtered image. Finally, spatially variant defocused images generated through the Wigner distribution are restored by Wiener based filters applied in the Wigner domain. The method applied to recover the filtered images can easily be generalized to bidimensional images.

No abstract

Abstract. This paper proposes a method to determine, in an objective and accurate way, the weighting factor (α) to be applied to the detailed panchromatic image information that will be integrated with the background multispectral image information to obtain the "best" fused image with the same spatial and spectral quality. The fusion method is a weighting variant of the fusion algorithm based on the wavelet transform, calculated using the à trous (WAT) algorithm. The α factor is determined, for each band of the multispectral source images using the simulated annealing (SA) search algorithm, which optimizes an objective function (OF) associated with both spatial and spectral quality measures for the fused images. The results obtained have demonstrated that for each one of the spectral bands there is an α value that provides fused images with the optimal trade-off between the two qualities for any decomposition level value (n) of the wavelet transform.Résumé. Dans cet article, on propose une méthode pour déterminer, de façon objective et précise, le facteur de pondération (α) à appliquer à l'information détaillée d'une image panchromatique qui sera intégrée à l'information de l'image multispectrale de base afin d'obtenir la « meilleure » image fusionnée avec la même qualité spatiale et spectrale. La méthode de fusion est une variante de pondération de l'algorithme de fusion basé sur la transformée en ondelettes, calculée à l'aide de l'algorithme à trous. Le facteur α est déterminé, pour chaque bande des images multispectrales sources, en utilisant l'algorithme de recherche du recuit simulé (SA), qui optimise la fonction objectif (FO) associée avec les mesures de la qualité spatiale et spectrale des images fusionnées. Les résultats obtenus ont démontré que, pour chacune des bandes spectrales, il y a une valeur de α qui fournit aux images fusionnées un compromis optimal entre les deux qualités pour toute valeur de niveau de décomposition (n) de la transformée en ondelettes. [Traduit par la Rédaction]