Integrating Algebraic Functions of Views with Indexing and Learning for 3D Object Recognition

This paper focuses on the problem of 3D object recognition from different viewing angles and positions. In particular, we propose a new approach that integrates Algebraic Functions of Views (AFoVs) with indexing and learning. During training, we consider groups of point features and we represent a sparse number of views that they can produce in a k-d tree. Moreover, we learn the manifold formed by a dense number of views using mixture models and Expectation-Maximization (EM). Learning takes place in a "universal", lower-dimensional, space computed through Random Projection (RP). The images that a group of model points can produce are computed off-line using AFoVs by combining a small number of reference views that contain the group. Rigidity constraints are imposed during this step to remove unrealistic views. During recognition, groups of point features are extracted from the scene and used to retrieve from the k-d tree the most feasible model groups that might have produced them. To reduce the number of hypotheses for verification, we rank them by computing the probability that the hypothesized model group is present in the scene. Only hypotheses ranked high enough are considered for further verification. The proposed method has been evaluated using both artifical and real data, illustrating good performance.