Abstract
This dissertation considers the problem of modelling, feature extraction and recognizing 3D objects from a single perspective view. A solid modelling system based on generalized cylinder is presented. A new algorithm is proposed for grouping 2D line segments into intermediate token features to be used as geometric cues for indexing into the model database and for generating hypotheses for polyhedral objects. A polyhedral object recognition system using a hypothesis and verification paradigm has been proposed and developed. In the modelling system, generalized cylinders are used as geometric primitives for representing objects. The analysis of generalized cylinders is presented. A number of useful expressions and properties of the contour generators of straight homogeneous generalized cylinders are derived under perspective projection. Right and oblique straight homogeneous generalized cylinders with circular and abitrary cross-section are discussed. A novel algorithm for extracting geometric features such as triples of connected edges, triangle- pairings, image trihedral vertices and closed polygons is implemented. Both heuristic and physical rules are utilised to control the combinatorial explosion of the feature grouping process. Physical rules are used to reject closed polygons which are incompatible with a single planar surface hypothesis. Experiments are demonstrated on real data and many features which could reasonably be due to spatial physical properties of the objects are idenified. Only a few spurious features are accidently detected. These irrelevant features are then pruned away in the hypothesis generation and verification process modules of the proposed recognition system. A polyhedral object recognition system based on a single perspective image is developed. A hypothesis and verification paradigm based on the use of local geometric features of objects is presented. In the framework, two high-level geometric primitives, namely triangle-pair and quadrilateral are employed as key features for model invocation and hypothesis generation. Two geometric constraints, namely distance and angle constraints are proposed and integrated into the recognition system. Many model and scene correspondences are pruned away in the early stage of the matching process using the two geometric constraints. As a by-product of the hypothesis generation the relative pose of the 3D objects expressed in camera frame is recovered. A verification process for performing a detailed check on the model-to-scene correspondences is developed. Detailed experimental results are performed to confirm the feasibility and robustness of the recognition system. An 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 measured with respect to an object centered coordinate system is derived. The crux of this representation is that the angular attributes of pairs of spatial edges are object-independent. An effective hypothesis generation scheme is proposed which can take advantage of the commonality of this novel representation. It avoids replicating the same recognition module for every occurrence of the same triple feature in the same generic triple group. The groups are distinguished by the angles between the constituent model edges and do not involve any length metric property. Generally, a relatively small number of defined generic triple groups are employed to describe a wide range of polyhedral object models. Particular closed form solutions are derived for specific but common configurations of edges such as rectangular bar end and orthogonal triple. The practical significance and generality of our result are multifold. Extensive experiments are performed to verify the plausibility of employing connected triple edges and trihedral vertices as key features in the paradigm of hypothesis-generation and Hough-clustering approaches to object recognition. It is demonstrated that the accuracy of the estimated pose of objects is adequate. Finally, outstanding problems identified and possible solutions to these problems are discussed. Future research directions are proposed.