Affine invariant pattern metrics are useful for shape recognition. It is important that such a metric is robust for various defects. We formalize these types of robustness using four axioms. Then, we present the250L affine invariant metric defined for the large family of "boundry patterns". A boundary pattern is a finite union of n-1 dimensional algebraic surface patches in R~n. Such a pattern may have multiple connected components. We prove that the reflection metric satisfies the four robustness axioms.
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