A Distance Judgment Function Based on Space Perception Mechanisms: Revisiting Gilinsky's (1951) Equation

In her seminal article in Psychological Review , A. S. Gilinsky (1951) successfully described the relationship between physical distance ( D ) and perceived distance ( d ) with the equation d = DA /( A + D ), where A = constant. To understand its theoretical underpinning, the authors of the current article capitalized on space perception mechanisms based on the ground surface to derive the distance equation d = H cosα/sin(α + η), where H is the observer's eye height, α is the angular declination below the horizon, and η is the slant error in representing the ground surface. Their equation predicts that (a) perceived distance is affected by the slant error in representing the ground surface; (b) when the slant error is small, the ground-based equation takes the same form as Gilinsky's equation; and (c) the parameter A in Gilinsky's equation represents the ratio of the observer's eye height to the sine of the slant error. These predictions were empirically confirmed, thus bestowing a theoretical foundation on Gilinsky's equation.