This work presents a combined bottom-up and top-down approach to extraction and refinement of building footprints from airborne LIDAR data. Building footprints are interesting for many applications in urban planning. The cadastral maps, however, may be limited for certain areas or not be updated frequently. Airborne laser scanning data is therefore considered by many people in the last decade as an important alternative data for change detection and update of building footprints. Laser scanning data of city scenes, however, often shows noise and incompleteness because of, e.g., the clutter by vegetation and the reflection of windows/waterlogged depressions on the roof. Results of the bottom-up detection may thus be limited to incomplete or irregular polygons. We employ 3D Hough transform to detect the building points. An improved joint multiple-plane detection scheme is proposed to find and label the laser points on multiple roof facets synchronously. The bottom-up processing provides not only a rough point segmentation but also additional 3D information, e.g., roof heights and horizontal ridges. Using these as priors, a top-down reconstruction is conducted via generative models. We consider the building footprint as an assembly of regular primitives. A statistical search by means of Reversible Jump Markov Chain Monte Carlo and Maximum A Posteriori estimation is implemented to find the optimal configuration of the footprint. By these means a robust and plausible reconstruction is guaranteed. First results on point clouds with various resolutions show the potential of this approach.