A number of studies have investigated whether human visual performance can be related to the general form of the amplitude spectra (i.e., 1/f^α) of natural scenes. Here, it is argued that there are some discrepancies in the data between some of those studies and that one possible explanation for the discrepancies may be related to differences in methodology (e.g., stimuli presented to the fovea as opposed to the parafovea). We sought to resolve some of the discrepancies with two psychophysical paradigms involving α discrimination with visual noise and natural scene image patches presented to the fovea or parafovea. Fovea–parafovea threshold differences were apparent for stimuli possessing α values <1.0, with the parafovea typically showing highest thresholds for reference α values in the 0.74–0.85 range. Both fovea and parafovea thresholds were lowest in the 1.2–1.4 range. In addition, we conducted a local amplitude distribution analysis (i.e., assessed local α) with a large set of high-resolution natural scene imagery and found that the results of that analysis provided a better account of the α discrimination thresholds for stimuli presented to the fovea as opposed to the parafovea.