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To investigate the limits and merits of information extraction from a single high-resolution synthetic aperture radar (SAR) backscatter image, we introduce a model-based algorithm for the automatic reconstruction of building areas from single-observation meter-resolution SAR intensity data. The reconstruction is based on the maximum a posteriori estimation by Monte Carlo methods of an optimal scene that is modeled as a set of mutually interacting Poisson-distributed marked points describing parametric building objects. Each of the objects can be hierarchically decomposed into a collection of radiometrically and geometrically specified object facets that in turn get mapped into data features by ground-to-range projection and inverse Gaussian statistics. The detection of the facets is based on a likelihood ratio. Results are presented for airborne data with resolutions in the range of 0.5-2 m on urban scenes covering agglomerations of buildings. To achieve robust results for building reconstruction, the integration with data from other sources is needed.