Optimal affine-invariant matching: performance characterization

The geometric hashing scheme proposed by Lamdan and Wolfson can be very efficient in a model-based matching system, not only in terms of the computational complexity involved, but also in terms of the simplicity of the method. In a recent paper, we discussed errors that can occur with this method due to quantization, stability, symmetry, and noise problems. These errors make the original geometric hashing technique unsuitable for use on the factory floor. Beginning with an explicit noise model, which the original Lamdan and Wolfson technique lacks, we derived an optimal approach that overcomes these problems. We showed that the results obtained with the new algorithm are clearly better than the results from the original method. This paper addresses the performance characterization of the geometric hashing technique, more specifically the affine-invariant point matching, applied to the problem of recognizing and determining the pose of sheet metal parts. The experiments indicate that with a model having 10 to 14 points, with 2 points of the model undetected and 10 extraneous points detected, and with the model points perturbed by Gaussian noise of standard deviation 3 (0.58 of range), the average amount of computation required to obtain an answer is equivalent to trying 11 of the possible three-point bases. The misdetection rate, measured by the percentage of correct bases matches that fail to verify, is 0.9. The percentage of incorrect bases that successfully produced a match that did verify (false alarm rate) is 13. And, finally, 2 of the experiments failed to find a correct match and verify it. Results for experiments with real images are also presented.