Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems Supplementary Material
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چکیده
1 h (1− β)κ(γ j − γ i ) + βκ(γ j − γ i ) concavity ≤ 1 h κ((1− β)(γ j − γ i ) + β(γ j − γ i )) = 1 h κ(γ j − γ α i ) (5) Noticing that (2) is precisely (1) for α, β ∈ {0, 1} (as κ(a) = 0⇔ a = 0) completes the proof. Proposition 2. For convex one-homogeneous η the discretization with piecewise constant φt and φx leads to the traditional discretization as proposed in [2], except with min-pooled instead of sampled unaries. Proof. The constraints in [2, Eq. 18] have the form φ̂t(i) ≥ η(φ̂x(i))− ρ(γi), (6) ∥∥ j ∑
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