Recognition of polyhedral objects using triplets of projected spatial edges based on a single perspective image

Abstract A novel and intuitive mathematical formulation is proposed for the interpretation of the geometric relationships of a triple of spatial edges and their perspective projection forming image lines. No restriction is imposed on the configuration of the triple of spatial edges. An eighth-degree polynomial equation explicitly defined by the space angles between the corresponding three spatial edges in an object frame is derived. The crux of this representation is that the angular attributes of pairs of spatial edges are expressed in an object-independent coordinate system. An effective hypothesis generation scheme is proposed which can take advantage of the representation. In the proposed recognition framework, triples of connected spatial edges and trihedral vertices are employed as key features for model invocation, hypothesis generation and pose estimation. Extensive experiments are performed to verify the plausibility and robustness of the proposed recognition methods. In general, the success rate for identifying and localising polyhedral objects using the proposed recognition method is relatively high.