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.
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