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In this paper, a novel variational framework is introduced toward automatic 3-D building reconstruction from remote-sensing data. We consider a subset of building models that involve the footprint, their elevation, and the roof type. These models, under a certain hierarchical representation, describe the space of solutions and, under a fruitful synergy with an inferential procedure, recover the observed scene's geometry. Such an integrated approach is defined in a variational context, solves segmentation both in optical images and digital elevation maps, and allows multiple competing priors to determine their pose and 3-D geometry from the observed data. The very promising experimental results and the performed quantitative evaluation demonstrate the potentials of our approach.