A multifractal approach for terrain characterization and classification on SAR images

Texture classification and contour extraction classical techniques usually have lower performances when applied to radar images, because of the presence of speckle. The authors´ main purpose is to define both a contour extractor resistant to a noise of a known model and a complementary textural classifier; that could be applied on the various zones defined by the contouring processing, and that may take into account the offered information present in the speckle. The duality of the approach offered by the multifractal theory fits well to this purpose. In order to extract singularities from the images, the Holder exponent α is computed around each point, before evaluating the fractal dimension a(α) of the subset of points having the same Holder exponent α. This implies the definition of a multifractal measure or capacity from the radar data that should be resistant enough to speckle. On the other hand, in order to characterize the different textures, the generalized dimensions D_q of order q are computed. Both approaches are unified in the sole multifractal theory, and require the definition of a measure or capacity with multifractal properties on a support (in our case radar data) which may not have intrinsically fractal properties. For the classification of real radar images from their multifractal spectral description (α,f(α)) or (q,D_q), a Bayesian method is applied. The profound links found between multifractal and large deviation theories enables an estimate to be made of the a priori probabilities of the different classes. A preliminary study for the extraction of singularities has been made on synthetic images blurred by a known noise