Frequently, terrestrial LiDAR and image data are used to extract high resolution building geometry like windows, doors and protrusions for 3D facade reconstruction. However, such a purely data driven bottom-up modelling of facade structures is only feasible if the available observations meet considerable requirements on data quality. Errors in measurement, varying point densities, reduced accuracies, as well as incomplete coverage affect the achievable correctness and reliability of the reconstruction result. While dependence from data quality is a general disadvantage with data driven bottom-up approaches, model based top-down reconstructions are much more robust. Algorithms introduce knowledge about the appearance and arrangement of objects. Thus, they cope with data uncertainty and allow for a procedural modelling of building structures in a predefined architectural style, which is inherent in grammar or model descriptions.

We aim at a quality sensitive facade reconstruction which is on the one hand robust against erroneous and incomplete data, but on the other hand not subject to prespecified rules or models. For this purpose, we combine bottom-up and top-down strategies by integrating automatically inferred rules into a data driven reconstruction process. Facade models reconstructed during a bottom-up method serve as knowledge base for further processing. Dominant or repetitive features and regularities as well as their hierarchical relationship are detected from the modelled facade elements and automatically translated into rules. These rules together with the 3D representations of the modelled facade elements constitute a formal grammar. It holds all the information which is necessary to reconstruct facades in the style of the given building.

The paper demonstrates that the proposed algorithm is very flexible towards different data quality and incomplete sensor data. The inferred grammar is used for the verification of the facade model produced during the data driven reconstruction process and the generation of synthetic facades for which only partially or no sensor data is available. Moreover, knowledge propagation is not restricted to facades of one single building. Based on a small set of formal grammars derived from just a few observed buildings, facade reconstruction is also possible for whole districts featuring uniform architectural styles.