Bil 717! Image Processing! Review -markov Random Fields! Review -solving Mrfs ! with Graph Cuts" Review -solving Mrfs ! with Graph Cuts"

0:-logP(y i = 0 ; data)! 1:-logP(y i = 1 ; data) ! ∑ ∑ ∈ + = edges j i j i i i data y y data y data Energy , 2 1 θ ψ θ ψ θ y D.#Hoiem# Main idea: ! • Construct a graph such that every st-cut corresponds to a joint assignment to the variables y " ! • The cost of the cut should be equal to the energy of the assignment, E(y; data). " ! • The minimum-cut then corresponds to the minimum energy assignment, y = argmin y E(y; data). ! S.#Gould# Requires non-negative energies! Source (Label 0)! Sink (Label 1)! Cost to assign to 1! Cost to assign to 0! Cost to split nodes! ∑ ∑ ∈ + = edges j i j i i i data y y data y data Energy , 2 1 θ ψ θ ψ θ y D.#Hoiem# Cost to split nodes! ∑ ∑ ∈ + = edges j i j i i i data y y data y data Energy , 2 1 θ ψ θ ψ θ y D.#Hoiem#