Consistency grammar for 3D indoor model checking

Abstract

Indoor 3D models are digital representations of building interiors reconstructed from scanned data acquired by laser scanners, digital depth (RGBD) cameras, and CAD drawings. Consequently, there is noise in the source data and a notable variety in the methods used to treat the noise and to process these data into reconstructed models. Alas, the correctness of these reconstructions and thus their suitability for a given application are uncertain. There is a lack of a robust base logic that would allow for controlling the consistency of these (automatically) generated models. Fortunately, correctness criteria are well-defined through existing international standards. Hence, we propose a conceptual framework based on formal grammars to check the semantic, geometric, and topological consistency of a reconstructed 3D model. The proposed method proceeds in three steps to validate the model: (1) correctness checking of individual components; (2) consistency verification of instances’ interactions; and (3) model consistency check for targeted applications. Our method identifies the components in the model that violate the given rules derived from the current standards and expert knowledge. Ultimately, we propose a quantified formulation of our method that may be straightforwardly integrated into industrial-level model checkers. The approach is independent of level of details and reconstruction method.