We propose to use evidential reasoning in order to relax Bayesian decisions given by a Markovian classification algorithm (ICM). The Dempster-Shafer rule of combination enables us to fuse decisions in a local spatial neighborhood which we further extend to be multisource. This approach enables us to more directly fuse information. Application to the classification of very noisy images produces interesting results. ).M. Germain and J.-M. Boucher are with the École Nationale Supérieure des Télécommunications de Bretagne, Brest, France.Publisher Item Identifier S 0018-9456(02)04315-2.

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Abstract-Radar images can show great variability from pixel to pixel, which is an obstacle to effective processing. This variability, due to speckle created by the radar wave coherence, necessitates the use of more adapted filters. Previous studies have shown that multiresolution wavelet analysis yields better results but produces artefacts due to multiscale decomposition. This paper proposes a method that reduces these effects by introducing the fractal dimension. The resultant filter combines wavelet decomposition and variance change model based on the level of variance estimated by studying the fractal dimension of the image.Index Terms-Adaptive filtering, fractal dimension, multiresolution analysis, synthetic aperture radar (SAR), speckle effect, wavelet transform.

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A new technique is presented for multiresolution analysis (MRA) of digital images. In 2D, it has four variants, two of which are applicable on square lattices; the Discrete Cosine Transform (DCT) is the simpler of the two. The remaining variants can be used in the same way on triangular lattices. The property of the Continuous Extension of the Discrete Group Transform (CEDGT) is used to analyse data for each level of decomposition. The MRA principle is obtained by increasing the data grid for each level of decomposition, and by using an adapted low filter to reduce some irregularities due to noise effect. Compared to some stationary wavelet transforms, the image analysis with a multiresolution CEDGT transform gives better results. In particular, a wavelet transform is capable of providing a local representation at multiple scales, but some local details disappear due to the use of the low pass filter and the reduction of the spatial resolution for a high level of decomposition. This problem is avoided with CEDGT. The smooth interpolation, used by the multiresolution CEDGT, gives interesting results for coarse-to-fine segmentation algorithm and others analysis processes.