Topology Matching For Fully Automatic Similarity Matching of 3d shapes Masaki Hilaga
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02.10.2018
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Metric near-invariants Rigid transformations Surface simplification Noise Fast
Technique (2) MRG matching algorithm for similarity queries
Integral of geodesic distances
Use Dijkstra’s Multiresolution Reeb Graph
Matching process Calculate similarity
Matching Process Matching Process
Results Database, 7 levels of MRG
Meet invariance criteria
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
Technique (2)
MRG matching algorithm for similarity queries
Finds
most similar regions
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
Matching Process
Matching Process
Matching Process
Matching Process
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
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