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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 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) • Construct Multiresolution Reeb Graph (MRG) • normalized geodesic distance Geodesic distance function Multiresolution Reeb Graph
Technique (2) • MRG matching algorithm for similarity queries • Finds most similar regions Matching nodes of two MRGs Most similar regions on two frogs
Reeb Graph • Same as in Chand’s presentation • Can use any function
Geodesic distance function • Integral of geodesic distances • (v) = p g(v,p) dS • Normalize • n(v) = ((v) – min()) / min()
Geodesic Approximation • Approximate integral • Sample • Simplify distance • Use Dijkstra’s
Multiresolution Reeb Graph • Binary discretization • Preserve parent-child relationships • Exploit them for matching
Matching process • Calculate similarity • Match nodes • Find pairs with maximal similarity • Preserve multires hierarchy topology • 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 • Invariants satisfied fairly well • Between pairs, similarity 0.94 • Across pairs, similarity 0.76
Results • Database, 7 levels of MRG • Similarity calculated in tens of milliseconds • Database searched in average ~10 seconds
Critique • Subjectively good matching • Meet invariance criteria • Approximation of geodesic distance • Reeb graph discretization • All models in DB must have same parameters • Similarity metric