Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure
arXiv:1803.0082725 citationsh-index: 17
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Provides theoretical foundations for differentiability in semi-discrete optimal transport, enabling gradient-based optimization for practitioners in graphics and geometry processing.
This paper establishes conditions for twice differentiability of semi-discrete optimal transport with respect to discrete measure parameters, with applications in stippling and blue noise.
This paper aims at determining under which conditions the semi-discrete optimal transport is twice differentiable 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 differentiability. We provide numerical illustrations in stippling and blue noise problems.