A Systemic Approach for 3d Recognition of Simple Primitives in Discrete Models

Recognition of primitives from digital contents is an outstanding problem in volumetric modelling. In this work a bottom-up systems methodology is developed. Systems methodology involves not only to components but the role performed by them. Their role is specified following a hierarchical approach going from lowto high-level recognition which allows identify geometric, structural and semantic aspects involving simple geometric components playing a structural role in Architecture. In the discrete static domain, geometric aspects concern to spatial components emerging from clusters of points with similar spatial distribution. Structural aspects concern to 3D features and the relations between different components. Semantic aspects concern to the purpose or role identification of components inside a 3D object or scene as a whole. In this work, a methodology is developed for retrieval of some simple architectural elements from clouds of points. Architectural elements follow an increasing order of difficulty by starting with elementary geometric primitives (planar, spherical or cylindrical primitives), next by estimating elementary geometric properties (concavity or convexity), and finally by proposing a method for a coarse estimation of curvature from discrete data. Our strategy combines smart sampling techniques with propagation algorithms for identifying simple elements. This strategy is applied for semiautomatic identification of dominant planes and some typical quadrics which can be found in architectural surveying. The evaluation of differences between ideal geometric models and real range-based solids allows identify structural defects and provide an assistance to intervention policies, which has been applied in several Restoration interventions in Castilla y Leon (Spain).