Hierarchical Mesh Decomposition using Fuzzy Clustering and Cuts

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Binary case (1/4)• Assign ProbabilityChoose two faces REP A <strong>and</strong> REP B with largest distanceas initial representative of the two clusterAssign probabilities to every faces according to thedistances to the initial patches:P ( fBiDist(fi,REPA)) PA( fi)1PB( fi)Dist(f , REP ) Dist(f , REP )iADist(f i ,f j ) is the shortest path from f i to f j in mesh’s dualgraph withiGeod ( fi,fj) Ang _ Dist(ij)Weight ( dual(fi), dual(fj)) (1 ) avg(Geod ) avg(Ang _ Dist)Ang _ Dist( ) (1cos )ijijB
Binary case (2/4)• Generating fuzzy decompositionGoal: cluster faces by minimize the functionAlgorithmF probability ( f patch ( p)) Dist(f , p)1. Compute the probabilities of faces to belong to each patch2. Re-compute the set of representatives to minimize F byREPA minf (1 PB( fi)) Dist(f , fi)REPB minf PB( fi) Dist(f , fi)fi3. If the representative set is changed, go back to 14. If no change, partition faces aspffiA { fB { fiiC { fi| PB( fi| P ( fBi) 0.5 }) 0.5 }| 0.5 PB( fi) 0.5 }
Page 1 and 2: Hierarchical MeshDecomposition usin
Page 3: Introduction• Fuzzy decomposition
Page 7 and 8: Binary case (4/4)• Hierarchy deco
Page 9 and 10: K way case(2/3)• The number of re
Page 11 and 12: Result
Page 13: Thank you

Hierarchical Mesh Decomposition using Fuzzy Clustering and Cuts

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