Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure

Abstract : This paper aims at determining under which conditions the semi-discrete optimal transport is twice dierentiable with respect to the parameters of the discrete measure and exhibits numerical applications. The discussion focuses on minimal conditions on the background measure to ensure dierentiability. We provide numerical illustrations in stippling and blue noise problems.
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Frédéric de Gournay, Jonas Kahn, Léo Lebrat. Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure. Numerische Mathematik, Springer Verlag, 2019, 141 (2), pp.429-453. ⟨hal-01721681v2⟩

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