Optimal Affine-Invariant Point Matching

The affine-transformation matching scheme proposed by Hummel and Wolfson (1988) is 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. This paper addresses the implementation of the affine-invariant point matching, applied to the problem of recognizing and determining the pose of sheet metal parts. It points out errors that can occur with this method due to quantization, stability, symmetry, and noise problems. By beginning with an explicit noise model which the Hummel and Wolfson technique lacks, we can derive an optimal approach which overcomes these problems. We show that results obtained with the new algorithm are clearly better than the results from the original method.