A Robust Affine Invariant Metric on Boundary Patterns

Affine invariant pattern metrics are useful for shape recognition. It is important that such a metric is robust for various defects. We formalise these types of robustness using four axioms. Then, we present the reflection metric. This is an affine invariant metric defined for the large family of "boundary 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