FEG structures for representation and recognition of 3-D polyhedral objects

The paper proposes a fast O(n^2.5) recognition algorithm for partially occluded 3D polyhedral objects, where n is the number of the polyhedron vertices. Our approach is based on the generate and test mechanism using the alignment approach as its basic recognition tool. The first stage is to align one face of the unknown polyhedron with one face of one library model (generate). The second stage is a recursive test procedure that checks the matching of the remaining faces. A new structure called FEG - Face Edge Graph is introduced. This structure stores information about the 2D coordinates of each face and the identity of its adjacent faces. A very low complexity is achieved by using a divide and conquer strategy. Instead of trying to recognize the whole object at once, we divide it and conquer (recognize) it face by face. This is done by reducing the recognition problem to generalized subgraph matching problem in which two subgraphs are equal not only when they are isomorphic, but also when they represent the same part of the same object. A special mechanism handles false splitting and false merging of adjacent faces as a result of wrong segmentation. The process lends itself to hierarchical parallel processing in that the matching with each library model may be carried out independently, and also for each model - processing at the pixel level may also be done in parallel. We evaluated our approach with several real range data images as well as some synthetic objects. Four of these cases are reported here.