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. Shape Features Topological features: –  0 - connected components –  1 - holes –  2 - voids Sharp features User defined TunnelsRings Holes

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

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 a)Initial best match b)Descend hierarchy c)Inherit match d)Refine match among descendant spheres e)Refine alignment based on new match

11. Weighted distance metric π(p i, q j ): geometric distance |V i -V j |: volume difference D t (s i, s j ): topology/feature distance

12. Feature Enhanced Database

13. Topology Shape Queries topology weight geometry weight

14. Feature Shape Queries sharpness weight geometry weight

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