Estimator reliability and distance scaling in stereoscopic slant perception

When a horizontal or vertical magnifier is placed before one eye, a frontoparallel surface appears slanted. It appears slanted away from the eye with horizontal magnification (geometric effect) and toward the eye with vertical magnification (induced effect). According to current theory, the apparent slant in the geometric and induced effects should increase with viewing distance. The geometric effect does scale with distance, but there are conflicting reports as to whether the induced effect does. Ogle (1938 Archives of Ophthalmology 20 604-623) reported that settings in slant-nulling tasks increase systematically with viewing distance, but Gillam et al (1988 Perception & Psychophysics 44 473-483) and Rogers et al (1995 Perception 24 Supplement, 33) reported that settings in slant-estimation tasks do not. We re-examined this apparent contradiction. First, we conducted two experiments whose results are consistent with the literature and thus replicate the apparent contradiction. Next, we analyzed the signals available for stereoscopic slant perception and developed a general model of perceived slant. The model is based on the assumption that the visual system knows the reliability of various slant-estimation methods for the viewing situation under consideration. The model's behavior explains the contradiction in the literature. The model also predicts that, by manipulating eye position, apparent slant can be made to increase with distance for vertical, but not for horizontal, magnification. This prediction was confirmed experimentally.