When one looks up a hill from below, its peak appears lower than it is; when one looks at a hill across a valley from another peak, the peak of that hill appears higher than it is. These illusions have sometimes been explained by assuming that the subjective horizontal is assimilated to the nearby slope: when looking up a slope, the subjective horizontal is raised, diminishing the height of the peak above the subjective horizontal, and making the peak appear lower than it is. When looking down a slope towards another hill, the subjective horizontal is lowered, increasing the height of that hill above the subjective horizontal, and making its peak appear higher than it is. To determine subjective horizontals we measured visually perceived eye levels (VPELs) in 21 real-world scenes on a range of slopes. We found that VPEL indeed assimilates by about 40% to slopes between 7 degrees downhill and 7 degrees uphill. For larger uphill slopes up to 23 degrees, VPEL asymptotes at about 4.5 degrees. For larger downhill slopes, the assimilation of VPEL diminishes, and at 23 degrees is raised by about 1 degrees. These results are consistent with the assimilation explanation of the illusions if we assume that steep downhill slopes lose their effectiveness by being out of view. We also found that VPEL was raised when viewing from a height, in comparison with ground-level views, perhaps because the perceived slope increases with viewing height
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