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Abstract : |
On a collection of subsets of a space, fundamentally dierent metrics may be dened. In pattern matching, it is often required that a metric is invariant for a given transformation group. In addition, a pattern metric should be robust for defects in patterns caused by discretisation and unreliable feature detection. We formalise these properties by presenting axioms. Finding invariant metrics without requiring such axioms is a trivial problem. Using our axioms, we analyse various pattern metrics, including the Hausdor distance and the symmetric dierence. Finally, we present the re ection metric. This metric is dened on nite unions of (n 1)-dimensional hyper-surfaces in R n. The re ection metric is ane invariant and satises our axioms. 1, |
