Sublabel - Accurate Convex Relaxation of Vectorial Multilabel Energies – Supplementary Material –
نویسندگان
چکیده
منابع مشابه
Sublabel-Accurate Convex Relaxation of Vectorial Multilabel Energies
Convex relaxations of multilabel problems have been demonstrated to produce provably optimal or near-optimal solutions to a variety of computer vision problems. Yet, they are of limited practical use as they require a fine discretization of the label space, entailing a huge demand in memory and runtime. In this work, we propose the first sublabel accurate convex relaxation for vectorial multila...
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We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel–accurate solution to multilabel problems. We show that previously proposed functional lifting methods optimize an energy which is linear between two labels and hence require (often infinitely) many labels for a faithful approximation. In contrast, the...
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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 i...
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تاریخ انتشار 2016