Blake-Zisserman functional F^g_{α,β} achieves a finite minimum for any pair of real numbers α, β such that 0 < β ≤ α ≤ 2 β and any g∈L^2 . Uniqueness of minimizer does not hold in general. Nevertheless, in the 1D case uniqueness of minimizer is a generic property in the sense that it holds true for almost all gray levels data g and parameters α, β: we prove that, whenever α/β∉ℚ, the minimizer is unique for any g belonging to a dense G_δ set of L^2 dependent on α and β.
Generic uniqueness of minimizer for Blake & Zisserman functional
TOMARELLI, FRANCO;
2013-01-01
Abstract
Blake-Zisserman functional F^g_{α,β} achieves a finite minimum for any pair of real numbers α, β such that 0 < β ≤ α ≤ 2 β and any g∈L^2 . Uniqueness of minimizer does not hold in general. Nevertheless, in the 1D case uniqueness of minimizer is a generic property in the sense that it holds true for almost all gray levels data g and parameters α, β: we prove that, whenever α/β∉ℚ, the minimizer is unique for any g belonging to a dense G_δ set of L^2 dependent on α and β.File in questo prodotto:
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