Correctness and Robustness of 3D Rigid Matching with Bounded Sensor Error

We present in this paper a precise study of Alignment and Geometric Hashing for the recognition of 3D rigid objects in the presence of uncertainty. Given a bounded error on point features, we propagate it through the computations to determine the translation and rotation error. This allows the computation of the compatibility zone, either in the image or in the hash table, to insure the correctness of the algorithm, i.e. the absence of false negatives. This work is presented for the least squares and a basis de nition methods. We show the equivalence of these two methods and point out the accuracy of the compatibility zones. We also study the robustness of the alignment algorithm in computing the mean number of hypotheses and false positives with uniform random models and scene. Experiments con rm our analysis. This theoretical study has important practical applications: in Volume Medical Images Analysis, we show that for typical situations, an alignment scheme can achieve 3D registration for an occlusion ratio as large as 80% with a negligible risk of false match (lower than 10 ). Key-words: Volume Image Processing, 3D Rigid Recognition, 3D Registration, Alignment, Geometric Hashing, Correctness, Compatibility Zones, Robustness.