Image Synthesis by Rank-1 Lattices

Considering uniform points for sampling, rank-1 lattices provide the simplest generation algorithm. Compared to classical tensor product lattices or random samples, their geometry allows for a higher sampling efficiency. These considerations result in a proof that for periodic Lipschitz continuous functions, rank-1 lattices with maximized minimum distance perform best. This result is then investigated in the context of image synthesis, where we study anti-aliasing by rank-1 lattices and using the geometry of rank-1 lattices for sensor and display layouts.

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