  We introduce a distortion measure for images, Wasserstein distortion, that
simultaneously generalizes pixel-level fidelity on the one hand and realism or
perceptual quality on the other. We show how Wasserstein distortion reduces to
a pure fidelity constraint or a pure realism constraint under different
parameter choices and discuss its metric properties. Pairs of images that are
close under Wasserstein distortion illustrate its utility. In particular, we
generate random textures that have high fidelity to a reference texture in one
location of the image and smoothly transition to an independent realization of
the texture as one moves away from this point. Wasserstein distortion attempts
to generalize and unify prior work on texture generation, image realism and
distortion, and models of the early human visual system, in the form of an
optimizable metric in the mathematical sense.
