Topology Matching For Fully Automatic Similarity Matching of

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

Shape Matching Problem Similarity between 3 D objects n Metric nearinvariants n Rigid transformations n Surface simplification n Noise n n Fast

Technique (1) n Construct Multiresolution Reeb Graph (MRG) n normalized geodesic distance Geodesic distance function Multiresolution Reeb Graph

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

Reeb Graph Same as in Chand’s presentation n Can use any function n

Geodesic distance function n Integral of geodesic distances n n (v) = p g(v, p) d. S Normalize n n(v) = ( (v) – min( )) / min( )

Geodesic Approximation n Approximate integral n Sample Simplify distance n Use Dijkstra’s n

Multiresolution Reeb Graph Binary discretization n Preserve parent-child relationships n Exploit them for matching n

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

Matching Process R S Match if:

Matching Process R S Match if: Same height range

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

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

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

Results n Invariants satisfied fairly well Between pairs, similarity 0. 94 n Across pairs, similarity 0. 76 n

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

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