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Topology Matching For Fully Automatic Similarity Matching of 3D Shapes Masaki Hilaga Yoshihisa...
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Transcript of Topology Matching For Fully Automatic Similarity Matching of 3D Shapes Masaki Hilaga Yoshihisa...
Topology Matching For Fully Automatic Similarity
Matching of 3D Shapes
Masaki HilagaYoshihisa ShinagawaTaku KohmuraTosiyasu 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
distanceGeodesic distance function
Multiresolution Reeb Graph
Technique (2) MRG matching algorithm
for similarity queries Finds most similar regions
Most similar regions on two frogsMatching nodes of two MRGs
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