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Feature-sensitive 3D Shape Matching

Feature-sensitive 3D Shape Matching Andrei Sharf Tel-Aviv University Ariel Shamir IDC Hertzliya Introduction Shape matching measures similarity distance between shapes Common distance metrics: Geometric Volumetric User defined No unique measure defines shape similarity Motivation

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Feature-sensitive 3D Shape Matching

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  1. Feature-sensitive 3D Shape Matching Andrei Sharf Tel-Aviv University Ariel Shamir IDC Hertzliya

  2. Introduction • Shape matching measures similarity distance between shapes • Common distance metrics: • Geometric • Volumetric • User defined • No unique measure defines shape similarity

  3. Motivation Goal: enhanced similarity measures Motivation: • Discrimination of complex shapes: • Complex topology models • CAD models • Molecules • Topology is hard (geometric matching can be assisted by user)

  4. Previous Work • General Shape Matching: [Prokop et. al 92] [Loncaric 98] [Paquet et. al 00] [Bardinet et. al 00] [Novotni et. al 01][Veltkamp 01] [Funkhouser et. al 03] • CAD: [Keim 99] [Cicirello et al. 01] • Molecular Biology: [Rackovsky et. al 88] [Vriend et. al 91] [Fischer 92] [Taylor 92] [Yee et. al 93] [Holm et. al 93] • Topological Matching: Topology matching for fully automatic similarity estimation of 3D shapes [Hilaga et. al 01]

  5. Overview • Topology and features are extracted from shape representation • Shape is represented with Union of Spheres and dual skeleton zero-alpha-complex • Feature sensitive multi-resolution hierarchy • Decimation operations preserve topology and features structure • Metric accounts features distance • Weighted distance

  6. Holes Rings Tunnels Shape Features • Topological features: • 0 - connected components • 1 - holes • 2 - voids • Sharp features • User defined

  7. Union of Spheres and Zero-Alpha-Complex Union of Spheres are topological equivalent to zero-alpha-complex Topological features are easy to compute on zero-alpha-complex Union of Spheres are extracted using distance transform

  8. Feature-sensitive Multi-resolution • Topology constrain: • clustering of shortest alpha-edge • Feature separation: • clustering inside a feature • propagate features properties to enclosing ball

  9. Feature-sensitive adaptive cut • Shape matching performs from coarse to fine • Match result is most influenced by coarse levels match • Feature approximation: shape approximation should correspond to distance metric

  10. Matching Algorithm • Initial best match • Descend hierarchy • Inherit match • Refine match among descendant spheres • Refine alignment based on new match

  11. Weighted distance metric • π(pi, qj): geometric distance • |Vi-Vj|: volume difference • Dt(si, sj): topology/feature distance

  12. Feature Enhanced Database

  13. topology weight geometry weight Topology Shape Queries

  14. sharpness weight geometry weight Feature Shape Queries

  15. Matching inside a molecular family features similarity geometric similarity

  16. Matching inside a molecular family features similarity geometric similarity

  17. Matching of dissimilar molecules features similarity geometric similarity

  18. The End

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