A quasi-concavity formulation turns global convexity into local differentiable inequalities on a segmentation mask and its derivatives, yielding a convolutional loss that unifies prior convex shape models.
Proof of Theorem 1 Zero-order quasi-concavity condition:u∈C 0 is quasi- concave⇐ ⇒For anyx,y∈Ω, λ∈[0,1],u(λx+ (1− λ)y)≥min{u(x), u(y)}
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D-Convexity: A Unified Differentiable Convex Shape Prior via Quasi-Concavity for Data-driven Image Segmentation
A quasi-concavity formulation turns global convexity into local differentiable inequalities on a segmentation mask and its derivatives, yielding a convolutional loss that unifies prior convex shape models.