, Volume 26, Issue 2, pp 361-408
Date: 28 Jun 2012

Generic uniqueness of minimizer for Blake & Zisserman functional

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Abstract

Blake-Zisserman functional \(F_{\alpha ,\beta}^{g} \) achieves a finite minimum for any pair of real numbers α, β such that 0<βα≤2β and any gL 2(0,1). Uniqueness of minimizer does not hold in general. Nevertheless, in the 1D case uniqueness of minimizer is a generic property for \(F_{\alpha ,\beta }^{g}\) 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(0,1) dependent on α and β.