Peripheral perception is limited in terms of visual acuity, contrast sensitivity, and positional uncertainty. In the present study we used an image-manipulation algorithm (the Eidolon Factory) based on a formal description of the visual field as a tool to investigate how peripheral stimuli appear in the presence of such limitations. Observers were ... asked to match central and peripheral stimuli, both configurations of superimposed geometric shapes and patches of natural images, in terms of the parameters controlling the amplitude of the perturbation (reach) and the cross-scale similarity of the perturbation (coherence). We found that observers systematically tended to report the peripheral stimuli as having shorter reach and higher coherence. This means that their matches both were less distorted and had sharper edges relative to the actual stimulus. Overall, the results indicate that the way we see objects in our peripheral visual field is complemented by our assumptions about the way the same objects would appear if they were viewed foveally.