In this report, we present a 3D building reconstruction method based on a structural approach. It consists in reconstructing buildings by assembling simple urban structures extracted from a grammar of 3D parametric models. This method is composed of two stages. The first one, which has already been tackled in previous works, consists in extracting the building footprints through configurations of connected quadrilaterals. The second stage, detailed in this report, corresponds to the 3D reconstruction from DEMs and obtained building footprints. An energy formulation is used within a Bayesian framework which is particularly well adapted to introduce prior knowledge related to urban structures and their assembling. In order to find the optimal solution of this energy, two different optimization techniques are used and compared.