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Topology Matching For Fully Automatic Similarity Matching of 3D Shapes

Topology Matching For Fully Automatic Similarity Matching of 3D Shapes. Masaki Hilaga Yoshihisa Shinagawa Taku Kohmura Tosiyasu L. Kunii. Shape Matching Problem. Similarity between 3D objects Metric near-invariants Rigid transformations Surface simplification Noise Fast. Technique (1).

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Topology Matching For Fully Automatic Similarity Matching of 3D Shapes

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  1. Topology Matching For Fully Automatic Similarity Matching of 3D Shapes Masaki Hilaga Yoshihisa Shinagawa Taku Kohmura Tosiyasu L. Kunii

  2. Shape Matching Problem • Similarity between 3D objects • Metric near-invariants • Rigid transformations • Surface simplification • Noise • Fast

  3. Technique (1) • Construct Multiresolution Reeb Graph (MRG) • normalized geodesic distance Geodesic distance function Multiresolution Reeb Graph

  4. Technique (2) • MRG matching algorithm for similarity queries • Finds most similar regions Matching nodes of two MRGs Most similar regions on two frogs

  5. Reeb Graph • Same as in Chand’s presentation • Can use any function 

  6. Geodesic distance function • Integral of geodesic distances • (v) = p g(v,p) dS • Normalize • n(v) = ((v) – min()) / min()

  7. Geodesic Approximation • Approximate integral • Sample • Simplify distance • Use Dijkstra’s

  8. Multiresolution Reeb Graph • Binary discretization • Preserve parent-child relationships • Exploit them for matching

  9. Matching process • Calculate similarity • Match nodes • Find pairs with maximal similarity • Preserve multires hierarchy topology • Sum up similarity

  10. Matching Process R S Match if:

  11. Matching Process R S Match if: Same height range

  12. Matching Process R S Match if: Same height range Parents match

  13. Matching Process R S Match if: Same height range Parents match

  14. Matching Process R S Match if: Same height range Parents match Match on graph path

  15. Results • Invariants satisfied fairly well • Between pairs, similarity  0.94 • Across pairs, similarity  0.76

  16. Results • Database, 7 levels of MRG • Similarity calculated in tens of milliseconds • Database searched in average ~10 seconds

  17. Critique • Subjectively good matching • Meet invariance criteria • Approximation of geodesic distance • Reeb graph discretization • All models in DB must have same parameters • Similarity metric

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