A general method for partial point set matching
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Partial matching of planar polylines under similarity transformations
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Efficient Visual Recognition Using the Hausdorff Distance
Efficient Visual Recognition Using the Hausdorff Distance
Matching Convex Shapes with Respect to the Symmetric Difference
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
A New Visibility Partition for Affine Pattern Matching
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
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On a collection of subsets of a space, fundamentally different metrics may be defined. 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. Furthermore, a pattern metric should have sufficient discriminative power. We formalise these properties by presenting five axioms. Finding invariant metrics without requiring such axioms is a trivial problem. Using our axioms, we analyse various pattern metrics, including the Hausdorff distance and the symmetric difference. Finally, we present the reflection metric. This metric is defined on finite unions of n - 1-dimensional hyper-surfaces in IRn. The reflection metric is affine invariant and satisfies our axioms.