现代优化方法现代优化方法 (3).pdf
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1、9.4 Quadratic Penalty Method forHypergraph MatchingQingna Li(BIT)9.4 Quadratic Penalty Method for Hypergraph Matching1/15IntroductionRelaxation ProblemQuadratic Penalty MethodNumerical ResultsQingna Li(BIT)9.4 Quadratic Penalty Method for Hypergraph Matching2/15Graph MatchingQingna Li(BIT)9.4 Quadra
2、tic Penalty Method for Hypergraph Matching3/15Applications of Graph Matching:computer visionQingna Li(BIT)9.4 Quadratic Penalty Method for Hypergraph Matching4/15Graph MatchingFigure:Illustration of graph matchingAim of graph matching:Establish correspondence between two feature sets.Qingna Li(BIT)9
3、.4 Quadratic Penalty Method for Hypergraph Matching5/15Hypergraph MatchingQingna Li(BIT)9.4 Quadratic Penalty Method for Hypergraph Matching6/15Mathematical FormulationGiven hypergraphs G1=V1,E1,G2=V2,E2V1and V2:sets of points,|V1|=n1,|V2|=n2.For example,V1=1,2,3,4,V2=a,b,c,d,eE1,E2:sets of hyperedg
4、es.For example,(1,2,3)E1,(a,b,c)E2Aim:find assignment matrix X IRn1n2:Xl1l2=1,if l1 V1is assigned to l2 V2;0,otherwise.Qingna Li(BIT)9.4 Quadratic Penalty Method for Hypergraph Matching7/15Hypergraph MatchingMatching of Hyperedges(l1,j1,k1)E1and(l2,j2,k2)E2:if Xl1l2Xj1j2Xk1k2=1,i.e.,l1 l2,j1 j2and k
5、1 k2Matching Score B:Bl1l2j1j2k1k2:matching score between(l1,j1,k1)and(l2,j2,k2).Bl1l2j1j2k1k2 0,if(l1,j1,k1)E1and(l2,j2,k2)E2;otherwise,0.B Rn1n2n1n2n1n2:a sixth order tensor.Qingna Li(BIT)9.4 Quadratic Penalty Method for Hypergraph Matching8/15Formulation of Hypergraph MatchingProblems StatementGi
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