Sensitivity analysis for matching and pose computation using dihedral junctions

Abstract

Recognition-via-localization is a popular approach in 3-D object recognition. This approach relies on the propagation of constraints that arise from the matches of local geometric features and could therefore be treated as a constraint satisfaction problem. Hough clustering, which verifies the consistency of local geometric constraints by determining the pose of the object in parameter space, is a popular technique owing to its conceptual simplicity and potential ease of parallelization. Our previous work has shown the usefulness of dihedral junctions for the recognition and localization of polyhedral objects and dihedral feature junctions for the recognition and localization of curved objects made up of piecewise combinations of conical, cylindrical and spherical surfaces. Experimental results from our previous work showed that the computed pose parameters are sensitive to the difference in the included angle between the scene and model dihedral junctions or the scene and model dihedral feature junctions. A formal analysis of the sensitivity of the computed pose to the difference in the included angle between the scene and model dihedral junctions or the scene and model dihedral feature junctions is presented in this paper. The results of the formal sensitivity analysis were found to be in conformity with the experimental results from our previous work and so the work presented in this paper could be treated as a sequel to our previous work. Based on the results of the sensitivity analysis, the rotation parameters were found to be more sensitive than the translation parameters which, in comparison, were far more robust. It is also shown how the introduction of redundancy in parameter space results in greater robustness in the computed pose. Although the analysis in this paper is based on the matching of dihedral junctions or dihedral feature junctions, the approach taken in the sensitivity analysis is general and can be applied to the matching based on other feature types.