Measuring Resemblance of Complex Patterns

  • Michiel Hagedoorn
  • Remco Veltkamp
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)


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 ℝn. The reflection metric is affine invariant and satisfies our axioms.


Topological Space Open Neighbourhood Pattern Match Computational Geometry Invariance Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Michiel Hagedoorn
    • 1
  • Remco Veltkamp
    • 1
  1. 1.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands

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